Notebook 4 — On Philosophical and Theological Arguments

With God’s help

On "Philosophical" and "Theological" Arguments

Michael Abraham

Contents

Part One: Methodology: The Distinction between the "Theological" and the "Philosophical"

Chapter 1: Between "Philosophical" Inference and "Theological" Inference: Deduction

Chapter 2: Between "Philosophical" Inference and "Theological" Inference: Abduction

Chapter 3: The Philosophical Basis of Abduction: Ockham’s Razor – A Logical and Mathematical Analysis

Part Two: The Physico-Theological Argument from a "Philosophical" Perspective and from a "Theological" Perspective: The Argument from Epistemology

Chapter 4: The Physico-Theological Argument from the Reverse Perspective

Chapter 5: The Argument from Epistemology

Chapter 6: The Book of the Universe Is Written in the Language of Mathematics

Chapter 7: Challenges to the Argument from Epistemology

Chapter 8: The Relation between Rationality and Faith

Part Three: The Argument from Morality

Chapter 9: What Is Morality?

Chapter 10: The Meaning of Commandment in Jewish Religiosity

Chapter 11: The Proof from Morality

Chapter 12: The Proof from Morality According to Kant

Chapter 13: An Analytic Perspective

Chapter 14: Is There a Moral Atheist?

Chapter 15: The Argument from Meaning

Chapter 16: A Look at the Theological Meaning of "Theological" Arguments

Part One

Methodology: Between the "Theological" and the "Philosophical"

1. Between "Philosophical" Inference and "Theological" Inference: Deduction

Introduction

There is a well-known joke about the difference between theology and philosophy: the philosopher posits assumptions and derives conclusions from them, whereas the theologian posits conclusions and derives assumptions from them. Theologians generally do not wonder whether or not there is a God. They believe in Him, and look for a way to construct an argument that will prove His existence. In the notebook on the ontological argument, chapter 4, we saw that this is exactly what Anselm did in the Proslogion, when, as he set out to prove the existence of God, he opened the discussion with a stormy and emotional prayer to God to help him do so.

To be sure, as we explained there, there is no essential problem with this. Anselm’s goal was not to clarify an issue on which he had no position, but to move from faith to understanding ("to give understanding to faith," as he puts it there). We brought an example of the mathematician Andrew Wiles, who proved Fermat’s conjecture after centuries in which people believed it but could not prove it. It is highly plausible that Wiles too, before approaching the discussion, believed that the conjecture was true (for otherwise he would not have invested such enormous effort, time, and energy in seeking a proof), and yet no one raises against him the claim that his proof is problematic. The conclusion is twofold: a. There is nothing problematic in a person wanting to prove a proposition he already believes to be true. b. Proofs and arguments should be examined solely on their own merits, not on the merits of the person presenting them. The important question is whether the argument or proof holds water, not what the agenda of the person presenting it is, or even how intellectually honest he is.

In this notebook we will go one step further. We shall see here that not only is the situation of proving something one already believes not problematic, but that most philosophical arguments are built in such a way that they prove to us what we already believe beforehand. To a considerable extent, the distinction between philosophy and theology as presented above is illusory. Many philosophers, if not all, construct arguments in a "theological" rather than a "philosophical" way—that is, from conclusions to assumptions.

Therefore, instead of dividing between disciplines, we shall divide here between two types of argument: a "philosophical argument"—which proceeds from assumptions to a conclusion, and a "theological argument"—which assumes a conclusion and works backward to the assumptions. From here on, the terms "theological" and "philosophical" when they appear in quotation marks indicate directions of logical inference: movement from the conclusion to the assumptions will be called a "theological argument," and the opposite logical direction will be called "philosophical." This, of course, is to be distinguished from occurrences of either of these two terms without quotation marks, which indicate the relevant fields of inquiry themselves, philosophy or theology. In this chapter I shall try to define more sharply the difference between these two directions of argument.

The Emptiness of the Analytic

In chapters 4 and 11 of the notebook on the ontological argument I described the emptiness of logic. We saw there that a valid logical argument always assumes what is to be proved; that is, in some sense its conclusion is already contained in its premises. To refresh this, let us consider the following hackneyed logical argument: all human beings are mortal; Socrates is a human being; therefore Socrates is mortal. Here we derive the conclusion from two premises, and it is clear that it is contained within them (if all human beings are mortal, then each one of them, and Socrates in particular, is mortal). So which comes before which, on the logical plane? Does the knowledge that Socrates is mortal come after the knowledge that all human beings are mortal, or before it? Seemingly after it, since it is a conclusion derived from the premise about all human beings. But this is an illusion, for one cannot determine that all human beings are mortal without having first determined that Socrates is such.

Think of two people who disagree over whether Socrates is mortal. So-and-so tries to convince his friend of this, and uses the above argument. The argument is of course worthless, for his friend will certainly not accept its premises (if he does not agree that Socrates is mortal, then of course he also does not accept the premise that all human beings are mortal). And what value is there in an argument whose premises your interlocutor does not accept? Can you convince him that way? And what shall we say when a person is deliberating with himself over whether Socrates is mortal, and raises this argument in his mind? What exactly is the process he undergoes? It seems that this is a possible process, when the person relies on the facts known to him—that all the human beings known to him are mortal—generalizes from them, that is, determines that all human beings are mortal, and infers from this that Socrates in particular is also mortal. In this process the person does not come with a settled position regarding Socrates, and therefore this argument has meaning for him.

But there may even be a situation in which a person already, before coming to the discussion, believes that Socrates is mortal, and yet this argument has meaning for him. Perhaps he even constructs this argument for himself precisely so that this will be its conclusion. This is a "theological" move, since he starts from the conclusion and seeks premises on which an argument leading to it can be built. In Anselm’s terminology one could say that here he is giving understanding to his faith.

Above I claimed that in a certain sense almost every philosopher does this. When some philosopher proves proposition X, he of course constructs an argument leading to it. But what made him seek arguments in favor of X? Usually the fact that he believed X was true. Conclusions usually do not land on philosophers by surprise. Moreover, where does the philosopher get the premises of the argument he constructs? Why does he choose precisely those? One should remember that these are premises that contain the conclusion X in some sense within them, which at first glance gives off a smell of intellectual dishonesty. On the other hand, the selection of premises is not made on the basis of a logical argument that compels them. So why does our philosopher choose precisely those premises? In most cases the philosopher constructs the argument so that it will lead to the conclusion whose truth he already desires. So long as the premises are plausible, and so long as the conclusion really follows from them, this move is legitimate and perhaps even necessary.

Immanuel Kant was already aware of this, when he discussed the problems raised by David Hume. In the notebook devoted to the ontological argument, chapter 14, I briefly presented the problem of the synthetic a priori (and we shall return to it at greater length later in this notebook). Kant showed that there is no avoiding the assumption that synthetic a priori judgments are indeed possible, for otherwise we inevitably arrive at skepticism. One would expect an intellectually honest philosopher to place the skeptical possibility on the table, and not simply dismiss it a priori. But Kant consciously and explicitly replaced the question “Are synthetic a priori judgments possible?” with the question “How are synthetic a priori judgments possible?” That is, he assumes that they exist, and looks for an explanation, or an argument, that will show or justify this. This is exactly what we above called a "theological" argument, since it assumes a conclusion (that such judgments exist, that is, that skepticism is not correct), and looks for premises on which an argument can be built that will prove or explain this. As noted, Kant was only the one who pointed to this feature of philosophical discussion, but in fact most if not all of his predecessors proceeded in similar ways, even if perhaps some were not aware of it. The exceptions to this are perhaps only the skeptics themselves, who really were willing to adopt the conclusion that arose from their arguments without simply assuming things (and even this I doubt: does a skeptic really assume no premises?). But every philosophy that is not skeptical certainly assumes something without justification and then derives conclusions from it. There is no escaping the understanding that in such cases the structure is in fact built in the reverse order, from the conclusion to the assumptions.

On Clouds and Rain: Between Logical Implication and Physical Causation

From the point of view of everyday discourse, a sentence like if there is rain, there are clouds sounds very strange, for it is the clouds that produce the rain, not the rain that produces the clouds. And indeed, on the physical plane it is clear that the causal direction is from clouds to rain. But it is equally clear that there are situations in which there are clouds and yet no rain falls. Therefore, on the logical plane one cannot infer from the fact that there are clouds the conclusion that there is rain. Hence, on the logical plane the direction of implication is reversed: if there is rain one may necessarily infer that there are clouds (for without clouds it would never have rained), but the converse is not true.

And in our terminology, the "philosopher" (= the physicist) will say that rain comes from clouds, but the "theologian" will argue that if there is rain then there must have been clouds. He already knows the conclusion (that is, the claim that is later on the physical axis—rain, which comes after clouds), and he looks for or exposes the premises that lead to it. In fact he is seeking what this conclusion contains within it. That is, the "theological" move exposes premises that are implicit in a claim we adopt out of faith or for any other reason. Thus, if we adopt the claim that there is rain, then we have implicitly said that there are clouds that caused it. Likewise, if someone thinks Socrates is mortal, and especially if he has no specific information about Socrates himself, he probably assumes that all human beings are mortal. More precisely (as we shall explain later), if someone thinks Socrates is not mortal, then it is clear that he rejects the proposition that all human beings are mortal.

So while I cannot prove to someone in this way that Socrates is mortal, I can address someone whom I know thinks Socrates is mortal and argue before him that he probably implicitly assumes that all human beings are mortal. In this way I take the conclusion of the argument (that Socrates is mortal) and expose the logical move implicit in his thinking (of which that conclusion is only the tip of the iceberg). This is what we shall call in this notebook a "theological argument." It is an argument that assumes some conclusion, and tries to burrow into it and expose what is contained within it, that is, the premises on which it is built.

It is important to understand that this type of argument has both a disadvantage and an advantage. Its disadvantage is that it can address only a person who accepts the conclusion, and it has no significance for a person who does not accept it. Its advantage is that someone who accepts the conclusion cannot escape the fact that these are indeed premises he implicitly assumes. Perhaps they are not true in themselves, but it is clear that he himself assumes them. An objection to a "philosophical" argument is usually a challenge to its premises. But in a "theological" argument my interlocutor cannot raise arguments against those premises, for the conclusion testifies that he himself accepts them. Thus, the "theological" move is in fact a logical procedure addressed only to the already convinced, since by its very nature it exposes to a person premises that are already implicit within him.

On Pragmatism and Initial Intuitions

As noted, there is a whiff of intellectual dishonesty here. We desire the truth of certain conclusions, and in order to prove them we choose premises on which arguments can be built that will lead to them. What is the justification for this kind of move? At first glance there is a pragmatist fallacy here.

Pragmatism ties the true to the useful; that is, it maintains that a given proposition is true because it is useful. On its face this is completely absurd. Why should the useful be the true? What guarantees that what is useful to us is also true? It would be very useful for me to be a millionaire—does that make the proposition that I am a millionaire true? It would have been very useful had a certain candidate been elected prime minister. Does that mean he was indeed elected? But this is not only about facts. As we shall see in the third part of the notebook, even values are not judged in terms of utility (such a judgment is a fallacy, called the naturalistic fallacy).

Some have wanted to ground the pragmatist position on a metaphysical belief, perhaps of religious origin, according to which what is useful must be true. Thus, for example, if Zionism succeeded, that is a sign that it is right and true (that God wants it and assists it). The belief that justice always ultimately prevails is likewise a reflection of such a meta-philosophical position (the Allies won the Second World War because they were the just and moral side). But a religious source for this view empties the move of its content. If indeed we have a source of information (divine) that revealed to us that utility is an indication of truth, then there is not really an identification of the true with the useful here. This is not an identity but an ordinary logical inference. Premise a: X is useful. Premise b (revealed to us directly by God): what is useful is true (in other words: God arranged His world so that the useful is the true, and vice versa). Conclusion: X is true. But pragmatism is an identification of the useful with the true on the conceptual plane, not the result of a theological or any other argument. The pragmatist claims that true means useful. In a certain sense, for him this is really a definition, not a proposition.

In my view, in most cases what underlies essential pragmatism is skepticism: since we have no way of knowing what is true and what is not, let us decide to adopt as true what is useful. In the absence of a criterion of truth, it is convenient for us to adopt utility as such a criterion. So it is not really a matter of identifying truth with utility, but of despair of truth. Pragmatism is essentially an expression of skepticism and despair of truth in its classical sense.

The movement described above from the conclusion to the premises is also, ostensibly, a kind of pragmatism. The fact that I want to believe that Socrates is mortal, or that God exists, does not constitute any indication that the premises I laid at the base of the argument I constructed to reach that conclusion are true. At most they are useful (that is, they lead me where I want to go). But is this a necessary indication that they are true?

Here we must introduce another important element, which we also dealt with in chapter 4 of the notebook on the ontological argument, namely belief, or initial intuition.^[1] Anselm had a belief that God exists. Others have an initial intuition that Socrates is mortal. If so, the adoption of premises that lead to that conclusion is not necessarily a failed or skeptical pragmatism, but following our intuitions. Our intuitions yield conclusions; these lead us to premises that in turn reaffirm those same conclusions. "Theological" arguments address a person who already has some intuition, and try to expose to him which premises are implicit in those intuitions and generate them. Again, this is a process that gives understanding to faith. In many cases that person is not aware of those premises, even though he implicitly believes them, and therefore there is a kind of self-discovery here. The conclusion is an indication that these are his premises. The person becomes exposed to his own premises, of which until now he was not aware.

"Theology" as Self-Discovery

My book The Science of Freedom deals with the question of freedom of the will: do we have free will or not? This question touches the question of materialism, that is, whether there is something in us beyond matter. In the sixteenth chapter of the book I proposed a series of thought experiments that would help a person form a position on these issues. For example, I argued there that, on the materialist picture, a person standing at equal distance from two tables laden with every good thing might die of hunger, for in the absence of a criterion by which he can choose to eat from one of them rather than the other he will be unable to do so. The basis of this is that every physical system behaves in a manner that accords with the symmetry of the state in which it finds itself. Therefore, if the person is a purely physical system, he must act in a way that fits the symmetry of the situation around him. Thus, when there are two tables in symmetrical positions on either side of him, he must die of hunger (this is a variation on what is known as Buridan’s ass).

I received a response from one of the readers who was very surprised by my argument. He claimed that according to the materialist picture the person really ought to die of hunger in such a situation. He wondered why, in my view, such a consideration proves anything against materialism. If you are an intellectually honest materialist, then you must honestly conclude that this is indeed what will happen. On the contrary, to retreat from materialism and become a libertarian because of such an argument is, at first glance, intellectual dishonesty. You are a kind of pragmatist, for here you adopt the useful as the true. Perhaps it is convenient and pleasant for us to think that we will not die in such a situation, and perhaps habit indeed leads us to hold such a view, but it has no real basis. If we have indeed become convinced that the correct picture is a materialist one, we must be honest and draw the conclusion that we really would die in such a situation, and give up our comfort zone.

I explained to him (what is already explained in the book itself) that such an argument cannot convince a genuine materialist, but it can expose to someone the fact that deep down he is not really a materialist. The purpose of the thought experiment is to help you test yourself and see whether, according to your intuition, such a person would indeed die of hunger or not. If so—then you have confirmed for yourself the fact that you really are a materialist. But if you share my intuition, according to which such a person can always deviate from physical symmetry and choose one of those tables at random and eat from it, then you may discover that despite appearances you are not a genuine materialist. You discover that buried within you is actually a libertarian outlook of which you were unaware. The whole difference is that I do not regard this intuition as a comfort zone, or as nothing more than a useful idea. For me it is a conception of reality, and I take it seriously. I do not abandon my initial intuitions unless I am shown good reasons to do so. Therefore there will be cases in which holding a certain conclusion will lead me to revise my worldview so that the conclusion will be coherent with my worldview, and in fact so that an argument can be built from my premises whose conclusion will be that very proposition.

The example I gave here is in fact a "theological" argument in favor of libertarianism, for it begins with the conclusion, that such a person will not die of hunger, and infers from it the assumptions (that there is in man a free, non-material dimension). The "philosophical" direction of the argument is to derive from a materialist picture of reality the conclusion that a person in such a state would die of hunger. The "theological" argument, by contrast, takes us in the opposite direction: from the conclusion that such a person will not die of hunger, it derives the libertarian premises. It is important to understand that the conclusion of such an argument is not death from hunger but the libertarian conception itself. It is presented as an assumption underlying the conclusion, but in a "theological" argument the assumption we have exposed is the conclusion we sought to prove.

The same applies to every thought experiment (a number of which are offered in that chapter of my book). Every such experiment is essentially a "theological" argument. For example, I ask the reader there whether he would agree to a proposal that we kill him and then reconstruct him molecule by molecule, cell by cell (assuming that we have the full scientific and technological ability to do this exactly and with certainty), thereby bring him back to life, and at the end of the process he will receive a million dollars. If he is a materialist—the logic says that he ought to agree to such an experiment, since in the end he is alive and well. True, he underwent an unpleasant experience temporarily and briefly, but he gained a vast fortune. If he does not agree to such a proposal—he is not a genuine materialist. Again, of course, the claim can be raised: what does such an experiment prove? Indeed, the honest materialist ought to agree to the experiment, and even if he does not agree it is simply because he does not feel like it (a psychological defect and nothing more). Why does this prove anything in favor of dualism (that is, that there is something in us beyond matter)? And again the answer is that it is not a proof but self-discovery. If you do not agree to this experiment, then it seems that despite what you thought you have discovered that deep in your heart you are not really a genuine materialist. This is, of course, on the assumption that this lack of agreement exposes one of your intuitions and is not merely a psychological defect.

Thus, a theological argument is essentially a journey of self-discovery and not a proof. The "philosophical" argument takes us from dualism to refusal of the experiment, or from materialism to agreement to it. The "theological" argument, by contrast, takes us from refusal back to dualism. In my book there I defined these thought experiments as a collection of diagnostic tools whose role is to help us examine what our positions are. The same is true of every "theological" argument. Such an argument is a thought experiment that functions as a diagnostic tool, that is, a tool that exposes to me positions already implicit in my conceptions, and not a tool of conversion, that is, of changing positions. Conversion is accomplished, if at all, only by "philosophical" arguments.

The Relations between the Two Types of Argument

Another conclusion that can be drawn from this is that alongside every "philosophical" argument one can present a "theological" argument that goes in the opposite direction. The philosophical argument can show us what conclusion we ought to adopt from our premises, whereas the "theological" argument exposes, from within our conclusions, what our real premises are. It is important to understand that the "theological" argument is no more speculative than its "philosophical" counterpart. If the "philosophical" argument is a valid argument, then the "theological" argument too is valid, since, as we shall now see, logic always allows us to reverse the direction (so long as we do so correctly. See below).

Take as an example the following conditional proposition: "If your origin is in Africa, then you are black-skinned." It is easy to see that one cannot infer from it the converse proposition: "If you are black-skinned, your origin is in Africa" (perhaps you are from India, or from South America. There too there are black-skinned people). In the first proposition African origin is a sufficient condition for your being black-skinned, but not a necessary condition. It is enough for me to know that your origin is in Africa in order to infer that you are black-skinned. But it is clear that even if you are not from Africa (for example, India or Brazil), you may still have black skin. The logical rule is that if A is a sufficient condition for B, then B is a necessary (though not necessarily sufficient) condition for A. That is, your being black-skinned does not mean that you are from Africa, but it is a necessary condition for your being African (without it, clearly you are not African). Now we can see that from the first proposition it follows that black skin is a necessary but not sufficient condition for African origin. By contrast, in the second proposition your being black-skinned is a sufficient but not necessary condition for African origin, and therefore it is clear that these two propositions are not equivalent.

And more generally, if we are given the implication "if A then B", which we denote as follows: A → B (where A is the antecedent of the implication and B is the consequent), one cannot infer from it the reverse implication: B → A. What, then, can be derived from it? According to the law of denying the consequent in logic (Modus Tollens), one can derive from this the reverse negated implication, namely: ¬B → ¬A (where the sign ¬ expresses negation, that is, ¬A means "not A"). This means that from the proposition "if your origin is in Africa then you are black-skinned" one can derive the proposition "if you are not black-skinned then your origin is not in Africa." It is easy to prove this by contradiction: if your origin were in Africa, then according to the first proposition you would also necessarily have to be black-skinned, which contradicts the assumption in the antecedent (that you are not black-skinned). This is also what we saw above regarding rain and clouds. If there is rain there are clouds, but it does not necessarily follow that if there are clouds there is rain. What is necessary is that if there are no clouds, then clearly there is no rain.

And in general, if we have an argument based on several premises A₁,A₂,A₃ from which the conclusion C is derived, this can be presented as a logical implication as follows: (A₁ ∧ A₂ ∧ A₃) → C. According to the law of denying the consequent, this is also equivalent to the following implication: ¬C → ¬(A₁ ∧ A₂ ∧ A₃).^[2]

The rule of denying the consequent states that these two arguments are logically equivalent, but philosophically there is a very significant difference between them. The first formulation is "philosophical," since it derives a conclusion (C) from premises (A₁,A₂,A₃). The second formulation is "theological," since it derives assumptions from a conclusion. For example, in the Buridan experiment mentioned above, one can derive from the materialist picture the conclusion that the person will die of hunger, and therefore, according to the law of denying the consequent, one can also derive the dualist picture (= the non-materialist one) from the assumption (= the conclusion) that the person will not die of hunger. One immediately sees that despite the fact that both moves are valid and logically equivalent, there is an important philosophical difference between them: one is a converting move, that is, one whose role is to change a worldview, or to persuade me of a conclusion with which I did not initially agree (= that a person in such a situation would die of hunger), whereas the other is a revealing move, that is, one that discloses to me the worldview that was already implicit within me, perhaps even unconsciously (= dualism).

We have thus seen that the "philosophical" argument is an argument whose purpose is to change a person’s beliefs, that is, it is a converting argument, whereas a "theological" argument has a revealing character. But from the logical discussion we have conducted here it becomes clear that whenever we have a "philosophical" argument we can construct in this way (by denying the consequent) a parallel "theological" argument, so long as we build it correctly (that is, by denying the consequent and not merely reversing the direction of implication). What matters is to discover, in every situation and discussion, which of the two formulations will serve us better. Later in the notebook we shall bring several examples of these reversals of direction and their significance.

Summary

We see that a "theological" argument does not reveal to us something new, but rather exposes before us something that was already latent within us and of which we were sometimes unaware. In this notebook I shall present several "theological" arguments in favor of the existence of God. These arguments are all derivatives of converting "philosophical" arguments, and yet it seems that sometimes they are more effective and it is more correct to use them. Here we shall consider the defects and advantages of these arguments.

In the first part we shall see the "theological" presentation of the physico-theological argument. Its "philosophical" (converting) formulation was discussed at length in the previous notebook, and here we shall present its revealing, or "theological," formulation, and see the meaning of this reversal. In the second part of the notebook we shall see the argument from morality, which also has a "theological" character. As we shall see, both of these are essentially thought experiments whose purpose is to help us discover (expose) whether we already possess implicit beliefs, and not to persuade an atheist and turn him into a believer (that is, to convert his beliefs). While reading, the reader may feel some discomfort, a sense of dishonesty or tendentiousness, in relation to these arguments, and I have therefore put this chapter first in order to clarify why this is not so. After the examples we shall encounter of such arguments, I assume that the general distinctions I have made here will take on more concrete form and become sharper and clearer. From this we shall also be able to see where and when it is correct to use each of these two types of argument.

1. Between "Philosophical" Inference and "Theological" Inference: Abduction

Introduction

In the previous chapter we saw the difference between a "philosophical" argument and a "theological" argument, when both were valid logical arguments. One can perform a similar exercise and create a "theological" argument from any "philosophical" inference whatever, whether as rigid as deduction, or softer, like analogy and induction. In this chapter we shall see how this is done, and point out that this is in fact the essence of scientific generalization. In logical terminology this is called abduction (Abduction).

Abduction: An Initial Definition^[3]

The American philosopher and logician Charles Peirce (Pierce), who worked in the second half of the nineteenth century and the beginning of the twentieth, was the first to introduce the term abduction, in contrast to analogy and induction. Analogy makes a comparison between some object a and another similar object b. From the existence of some property in a one can infer by analogy the existence of that property in b. The condition for this is that there be some known and given similarity between them. Induction, by contrast, is a generalization in which one infers from the existence of some property in a (and perhaps in a few other particulars) to a general law stating that this property exists in an entire group (which includes those particulars). Abduction too is an inference that proceeds from several states we have observed, except that here we derive from those states a general theory from which those states can be derived as particular cases. Thus, abduction differs from the other two non-deductive modes of inference (analogy and induction). Abduction is the transition from cases to theory, whereas analogy and induction are inferences moving from one case or cases to other case or cases.

Thus, for example, analogy can teach us that if a certain book that we left suspended in the air fell to the earth, the same will happen if we do this with another book. There is similarity between the two objects because they are both books, and so there may be justification for comparing them also with respect to falling to the earth. Induction will infer from a similar consideration, on the basis of the same similarity, that all books will fall to the ground. Abduction, however, goes in the opposite direction: it examines the various objects that fall to the earth and infers from this a general law that there is a force that causes books to fall to the earth. Alternatively, the law of gravity states that every object with mass falls to the earth, and books are a particular case of it. Now, after we have formulated the general law, we can deduce from it that if some object has mass, it too will fall to the earth. Deduction is the reverse of abduction, since it takes us from theory to cases. These two differ from analogy and induction, since those two modes of inference move us from cases to other cases (and not from cases to theory or vice versa).

A few decades later, the philosopher of science Carl Hempel explained the transition from observational facts to theory in a schema he called deductive-nomological. He defined a theory as a general law (= nomos) from which the particular cases (the situations we observe) can be deduced. This is a parallel description to that of Peirce, except that he defines the theory in the Peircean sense as a scientific explanation.

Peirce related to abduction, that is, to scientific generalization, as a kind of guess. Why? Because it is very difficult to justify the leap from particular cases to theory. This is in fact another aspect of David Hume’s problem of induction (which we shall elaborate on later in the notebook). True, there is an element of guesswork in ordinary analogy and induction as well, since there too we have no certainty (unlike deduction). But it seems that abduction is much more speculative than those two modes of inference, and this for two reasons: 1. It moves from particular cases to a general law. In this sense it is highly speculative, much like ordinary induction. 2. It moves from concrete observable states to theory. Theory includes theoretical entities and various concepts that cannot be confirmed through direct observation. In the example above, the force of gravity or the law of gravity are not states or entities that can be observed directly. We observe events (such as falling to the earth), but not theoretical concepts and principles (such as attractive force). Therefore, in scientific methodology we try to confirm or refute the theory through its practical consequences, since only they are accessible to empirical testing.

The Connection to the Distinction between "Philosophical" and "Theological"

Think of someone who makes an analogy between a book falling to the ground and another book falling to the ground, or who makes a generalization to all books. The similarity between the datum and the result of the inference is self-evident (they are all books), and therefore it does not require theoretical assumptions. The application, of course, does assume the assumption that being a book is the datum that causes the fall. But the similarity is not based on any hidden theory.

Now think of an analogy from a book to a pencil, that is, an argument that infers from the falling of the book that the pencil too will fall to the earth. In the background of this comparison stands some theory. In effect, this argument implicitly assumes a similarity between the book and the pencil, and in this case it probably implicitly assumes that both have mass. It examines the characteristics of the book and the pencil and makes a theoretical assumption that their having mass is the parameter that determines falling to the earth. Sometimes this assumption is not even conscious. If you ask him why there is similarity between the two things, he will not always be able to answer, but he assumes it implicitly.

The meaning is that behind the comparison between the book and the pencil stands, even if only implicitly, a theory that every thing with mass that is released in the air falls to the earth. This is the general law to which abduction leads us. It takes the analogy and exposes the theory that lies at its foundation. The facts that objects fall to the earth serve scientists in reaching the theory that objects with mass fall to the earth. Creating a scientific law is abduction on the basis of cases we have observed. Abduction is a theoretical generalization broader than the simple analogies, according to which any two objects with mass attract one another (the earth is only a particular example of an object with large mass, which attracts to itself every other massive object).

Can we derive from the observations we described any proof that there is a force of gravity, and that it acts on every object with mass? Certainly not. It is possible that the book and pencil we saw falling to the earth were merely exceptional cases. They fell for some other reason, and not because they have mass. Beyond that, it is possible that there is another theory that relies on similarity in some other parameter between the book and the pencil, and explains accordingly why these two fell to the earth. For example, perhaps all wooden products that are released in the air fall to the earth, and the book and the pencil are both wooden products. So how do we know that the law of gravity, which states that every object with mass falls to the earth, is indeed correct? What is the logical justification for abduction? At most this is a hypothesis, and in Peirce’s language—a guess.

Let us return for a moment to the analogy between the book and the pencil. A person could reject this analogy and say that the book happened to fall to the earth, or that it fell because it was rectangular. If these hypotheses are correct, then there is no possibility of inferring that the pencil too will fall to the earth, since this analogy assumes that the falling depends on the fact that the object has mass or is made of wood. As we saw, the move from cases to theory is apparently just a guess. But one thing is clear: if someone nevertheless makes this analogy, then implicitly he assumes some theory within whose framework there is a relevant similarity between them. This is a "theological" argument. When someone makes the analogy, it may be that what he is doing is unjustified, and it may be that he has no way of justifying it, but the very fact that he himself makes the analogy proves that he at least implicitly assumes the theory at the base of that analogy. Even if the law of gravity is unjustified, he himself cannot deny that he believes in it (that he has an intuition about it). This is a claim about him and not about the world, and that is what we called in the previous chapter a "theological" argument.

Thus, we begin with a "philosophical" argument: if there is a force of gravity, then objects with mass fall to the earth. This is the physical-causal direction. For the time being, we have no way at all to justify the law of gravity itself. Abduction makes the reverse, "theological," move, and states that if objects fall to the earth then there is probably a force of gravity. This is a logical indication of the existence of that force, or of someone’s belief in such a force. The relation between the force and the cases is causal-physical, whereas the relation between the cases and the force (abduction) is logical (though not deductive). This is similar to the example we saw in the previous chapter: physically, clouds produce rain, but logically it is rain that teaches us of the existence of clouds.

So what is the difference between what we see here and what we saw in the previous chapter? Here the two directions are not logically equivalent. If there is a force of gravity then necessarily objects with mass fall to the earth. This is a necessary deduction. But the opposite direction is not necessary. If objects fall to the earth, this does not necessarily mean that there is a force of gravity. There may be other explanations for this. Abduction is not a necessary inference, that is, a valid logical inference. It is a softer inference, and therefore empirical observations can disprove it (which, of course, cannot happen with a valid logical inference). This inference is in some respects similar to analogy or induction, since abduction too is a soft (non-necessary) inference, but, as stated, it works in a different direction from them (they operate between cases and cases, whereas it operates between cases and theory). It is important to understand that science is built precisely on abductive inferences, and not on deductions, and for that reason it is falsifiable.

What Kind of "Theological" Reversal Is Involved Here?

At first glance, this is a reversal similar to the one we saw in the previous chapter. The scientific theory is a general law from which the cases we observed (the explained cases) can be validly deduced, and abduction is an argument that operates in the opposite direction, from the conclusions (= the facts) to the premises (= the theory). Therefore this is a kind of "theological" reversal. What kind of reversal is there here? Why is it that, here, when we reverse the deductive argument, we do not obtain a valid logical argument as we saw in the previous chapter? As we shall see immediately, the root of the matter is that in this case we are not dealing with denial of the consequent.

To see this, we must formalize (= give form to, render formal) the following claims: A – the law of gravity is true. B – objects such as a book or a pencil (which have mass) fall to the earth. Our first assumption is that if the law of gravity is true then a book or pencil should fall to the earth, namely: A → B. Our second assumption is that a book and a pencil do in fact fall to the earth, namely: B. Can one derive from this the law of gravity, that is, A? Certainly not. If one makes such a derivation, one is in fact assuming a direct reversal of the implication in the first premise, namely: B → A. But as we saw in the previous chapter, such a reversal is not necessarily correct, for the reverse implication is not equivalent to the first. If the first gives a sufficient condition, the second turns it into a necessary one, and vice versa.

Thus, the abductive reversal too begins with the implication A → B. The "theological" reversal that we saw in the previous chapter, which relies on denying the consequent, produces from this the following implication: ¬B → ¬A. As stated, this is a valid logical inference, since according to the rule of denying the consequent those two implications are equivalent. But scientific abduction takes the first implication and turns it into the reverse implication (switching antecedent and consequent): B → A. As we have already seen, this does not yield a valid logical inference.

It is important to understand that invalidity does not mean that this inference is untrue or worthless. Ordinary induction and analogy are also not valid, and nevertheless they serve us in all areas of thinking, including science. We are dealing with a softer kind of inference, one that has value but is not necessary.

The Relation to Popper’s Criterion for a Scientific Theory: Corroboration and Refutation

The reason that this is not a necessary inference is that there may be additional theories that generate the same set of facts. In the example of gravity, the falling of these objects can also be explained by theory C, according to which all objects that are wooden products fall to the earth. From this theory too we get that a book and a pencil, because they are wooden products, fall to the earth. Thus the observational fact B can be a result of theory C and not of the law of gravity A; therefore, given the cases (the observational facts) B, one still cannot infer A. Thus for every set of facts there may be several different theoretical explanations (C or A). That is the reason one cannot derive the law of gravity A from the observations B.

The twentieth-century philosopher of science Karl Popper argued that a scientific theory can only be refuted, not proved. In our example, if we discover observationally that the book or pencil does not fall to the earth, then theory A (and of course C) has necessarily been refuted. But an empirical proof of a scientific theory such as the law of gravity (that is, a valid logical derivation of the theory from observational facts) is impossible, since there may always be additional theories that explain those facts.

Popper indeed leaves the matter there, that is, a scientific theory is never strengthened in light of observations, but at most not refuted. Even if we have seen thousands of objects with mass fall to the earth, we cannot say that we have proved the theory of gravity, or even that we have strengthened it in any way. But our ordinary intuitions, as a number of philosophers of science have already remarked, tell us that passing a test does strengthen (in their language: corroborate) the theory. True, it does not prove it, as we have seen, but there is some soft inference here. The observations lead in a non-certain and non-necessary way to the theory. That is why physics proceeds from a collection of objects that fall to the earth and infers from this the theory of gravity. The falls are regarded as something that strengthens or corroborates that theory, and this is precisely abductive inference.

The conclusion is that the reversal of implication performed above is indeed invalid, but we nevertheless use it in our scientific way of thinking. We have seen that this is a kind of "theological" argument, that is, an argument that exposes the assumptions from within the facts or conclusions, but is not a deduction. We ask which assumptions could explain the facts we have observed. The facts are in fact a conclusion of the ordinary scientific implication from the theory: theory → facts. But abduction takes us along the reverse route: facts ⇢ theory. Here the doubled implication sign denotes a non-necessary abductive inference, which is not logically valid. It is corroboration, not proof.

Another philosopher of science, Hans Reichenbach, distinguished between the context of discovery and the context of justification. A scientist discovers some theory in various ways, and only afterward derives predictions from it and subjects them to empirical tests of refutation. Reichenbach argued that discovery is a process that has no logical explanation and no justification, and in fact belongs to psychology and not to science or philosophy. This is exactly the same claim as Peirce’s, who thought that this was a matter of guessing. Reichenbach’s claim is that the discovery stage has no scientific significance at all. Only the context of justification, that is, subjecting the theory to a test of refutation, is part of the scientific procedure. Here the logic is clear, since if the theory predicts that B will occur and in the experiment we conduct it does not occur (the book does not fall to the earth), then the theory has been refuted. This is essentially denial of the consequent: if A → B, and not-B occurs, then not-A follows.

For now, the question of the philosophical justification of abduction remains open for us. It is not clear what justifies our choosing theory A to explain the cases B. Why do we not choose C or any of infinitely many other possible theories?

Two Types of Explanation

In the notebook on the physico-theological argument, chapter 5, we pointed out that in the scientific context there are two types of explanation: a. Explanation by appeal to the known, which explains an event or state in terms of some known scientific theory. b. Explanation by appeal to the unknown, which explains an event or state in terms of a new (unknown) theory. When Newton discovered the law of gravity, he explained familiar phenomena (tides, the falling of objects to the earth, the courses of the stars) by a law that was not known in his time. Every new scientific law is created in this way. By contrast, after the scientific community became convinced of Newton’s law of gravity, we can now use that law to explain new events or states that we encounter. This is explanation by appeal to the known.

We can now see that the latter explanatory process is based on deduction (we derive the cases, the facts, from the general law, the theory), whereas the former explanation is based on abduction ("deriving" the general law from the cases, where the term "deriving" here means a non-necessary inference, marked above by ⇢).

In that chapter we showed that the physico-theological proof in fact operates like a scientific generalization, for it takes certain facts about the universe or about some existing entity (that it is complex/designed/coordinated), and derives from them a theory (that there is a God who assembled/designed/coordinated it) that tries to offer them an explanation. We can now say that this is a process of abduction. Let us recall what we noted there, that this inference resembles scientific generalization in its logic, but its conclusion (that there is a God) is probably not a scientific claim, since it does not stand up to empirical falsification. There is no practical prediction of the theory that there is a God that could be subjected to observational testing.^[4]

1. The Philosophical Basis of Abduction: Ockham’s Razor – A Logical and Mathematical Analysis

Introduction

This chapter presents a complex subject in a concise and somewhat difficult way. Since the chapter is not essential to the course of the argument, but only illuminates it from another angle, a reader who wishes may read it quickly without entering into the details, or even skip it and go directly to the next chapter.

The Basis of Abduction: Ockham’s Razor

So what, then, is abduction based on? If there really are infinitely many theories that can explain any collection of situations or events, how do we choose among them? Peirce already pointed out that the selection is based on the principle of Ockham’s razor, that is, the principle of simplicity. We choose the simplest theory that succeeds in explaining the totality of situations and events. The question why the simple is also the true is a good question, and we cannot enter into it here. I will suffice with the claim that scientific thinking makes use of the criterion of simplicity, and it works there quite well. In fact, the principle of simplicity is one of the cornerstones of rational thought.^[5]

In this chapter we shall try to trace it in greater detail and see how exactly this works. How do we build a theory on the basis of facts? How is the principle of simplicity used in the process of abduction? I shall now briefly propose the fundamental principles of the process, and my aim here is mainly to clarify in principle how it works. For those interested, the matters are set out in greater detail in the sixth part of my book True but Unstable, and even more so in the first volume of our series, Studies in Talmudic Logic, The Logical Hermeneutic Rules: Non-Deductive Inferences in the Talmud.^[6] I shall demonstrate this here through the terminology of Talmudic hermeneutical methods, although the cases with which we shall deal are not taken from the Talmud. As can be seen in the above sources, Talmudic exegesis includes the basic building blocks for the theory of non-deductive inference in all fields of thought.

Analogy: "Binyan Av"

I shall begin the discussion with the simplest and most common case of non-deductive inference, analogy. In Talmudic jargon this is called "binyan av from one text." As we have seen, an analogy between two things is based on some similarity between them. For example, a book falls to the earth and I infer from this that the pencil too will fall to the earth. This analogy assumed that there is some similarity between them, although neither the assumption nor the definition of the similarity appears explicitly in the inference. It is embedded and implicit within it.

One can construe this similarity in two main ways: 1. Notice that both have some common property, such as that they have mass or are wooden products. 2. See that they behave similarly in another situation (perhaps both burn in fire), and infer that the similarity between them will also be preserved in the situation of falling from the air to the earth. What is the difference between these two processes? In case 1, the parameter of similarity is explicit and known. It is a result of direct observation. In effect, we have direct access to the theoretical plane, and the parameter of similarity deals directly with it. They are similar in that they have mass or are wooden products, and the theoretical claim is that having mass or being a wooden product is what causes falling to the earth. So the similarity is formulated here in terms that belong to the theory (mass, wooden products). By contrast, in case 2 we see similarity on the plane of the cases, or the states, and not on the theoretical plane. We do not know exactly what the similarity between a book and a pencil is, but we have a practical indication that there is some similarity here. If both behave the same way in some situation (they burn in fire), one may infer from this that there is something similar in them, and from that infer that this similarity will also cause both to fall to the earth. Here the similarity lies on the plane of the situations and not on the theoretical plane. The theoretical similarity is implicit. The practical similarity hints at the existence of a theoretical similarity. Even at the end of the process we have no explicit theory of what causes falling to the earth. We only assume that there exists some factor.

To proceed toward a formal treatment of analogy, let us take an example. We have two students, Reuven and Shimon. We know that Reuven and Shimon succeeded on the literature exam, and that Shimon also succeeded on the composition exam. The analogy infers from this that Reuven too will succeed on the composition exam. We shall present the situation in a data table, in which the known factual cases and the unknown case are recorded, the latter with a question mark:

Student/Exam	Literature	Composition
Shimon	1	1
Reuven	1	?

Table 1. Analogy

Here 1 is success on the exam and 0 is failure. The question mark expresses the research question. The analogy teaches us that Reuven will succeed in composition, that is, it fills in the place of the question mark with the result 1.

One should note that the analogy we have described here is of type 2 above. The assumption that Reuven is similar to Shimon stems from the fact that they both succeeded on the literature exam, that is, from a factual case. We have no explicit theoretical parameter of similarity. In light of this similarity we infer that if Shimon succeeded in composition, Reuven too will succeed in it.

An analogy of type 1 could be the following: Reuven and Shimon were tested at a psychometric institute, and it became clear that they had similar linguistic abilities. Shimon succeeded on the composition exam, and from this it follows that Reuven will probably succeed as well.

What is the difference between these two logical procedures? For the sake of discussion, the theory is that whoever has good linguistic abilities will succeed on the composition exam. In the analogy described in the table above, the similarity is based on cases and not on theoretical parameters, that is, on success on the literature exam. This is the result of a practical state and not a theoretical determination. We have an implicit assumption (an analogy) that success in literature is based on abilities similar to those needed for success in composition. But we have not formulated what those abilities are, nor have we needed to do so in the process of inference.

By contrast, the second analogy we proposed is based on similarity on the theoretical plane. The similarity is given to us explicitly in terms of the abilities that cause success on the composition exam, which is the parameter that appears in the theory as the cause of success in composition. So here the analogy is made on the basis of theoretical similarity.

How is an analogy of type 2 made? Why do we decide to fill the unknown slot in the table above with the result 1? The process can be presented in two ways, an inference of columns and an inference of rows:

Inference of columns: from the literature column we learn that the abilities of the two students are similar, and from this we infer that the same will also hold for their abilities in composition. Therefore the required conclusion is that Reuven will succeed in composition.

Inference of rows: from Shimon’s row we learn that the difficulty of the two subjects is similar, and infer from this that if Reuven succeeded in literature he will also succeed in composition.

Be that as it may, an analogy of this type takes place entirely on the plane of cases, or situations. We manipulate results of an experiment (successes on an exam), and apparently infer from a number of given facts to another fact. But it is clear that behind this inference stands a theory (the abilities that cause successes and failures). Even so, the theory is not explicit in the process of inference we have described here. We only move from cases to cases, as we saw that analogy does. The theory is implicit behind the inference, and in this case the theory is that the abilities required for success in literature and composition are similar linguistic abilities. Below we shall return to this important point, because arriving at the theory requires a process of abduction.

Later we shall see that from the analogy that passes from cases to cases one can extract the theory that stands at its basis, and that extraction is precisely the process of abduction.

Another Kind of Analogy: Biblical and Talmudic A Fortiori

Another building block in the toolbox of Jewish legal exegesis is the inference called "a fortiori" (or "all the more so"). This is essentially a kind of analogy, somewhat stronger than ordinary analogy. Logicians sometimes call it an a fortiori argument.

Such a simple inference appears several times in the Bible, for example (Exod. 6:12):

And Moses spoke before the Lord, saying: Behold, the Israelites have not listened to me; how then shall Pharaoh listen to me, seeing that I am of uncircumcised lips?

Moses our teacher, who was sent by the Holy One, blessed be He, to redeem Israel, argues before Him that if the Israelites did not heed his voice, how can one expect Pharaoh to do so?! There is of course a hidden assumption here that the probability that Pharaoh will heed him is lower than the probability that the Israelites will heed him. This is an a fortiori inference because it goes from the lighter to the heavier, or from the easier to the harder.

In this inference there is one premise and a conclusion inferred from it. In the background there is another hidden premise (after all… how…), namely the premise of hierarchy, which concerns the relation between the probabilities of the two events (that Pharaoh will listen to him and that Israel will listen to him). This is a typical biblical a fortiori. By contrast, in most of its Talmudic appearances, a fortiori reasoning is carried out in a more complex way. In the Talmud, most a fortiori inferences assume three premises (and not just one as in the biblical case) and from them derive the conclusion. For example: if money, which cannot effect marriage, nevertheless succeeds in effecting betrothal—then a marriage canopy, which does succeed in effecting marriage, certainly should succeed in effecting betrothal. And in an everyday context: if Shimon, who failed the literature exam, passed the composition exam—then Reuven, who passed the literature exam, will certainly also pass the composition exam. Notice that in these inferences there are three data points (money does not effect marriage, the canopy effects marriage, money effects betrothal; Shimon failed literature, Shimon passed composition, Reuven passed literature) and not just one as in the biblical a fortiori, and from them the conclusion is derived (a canopy can effect betrothal; Reuven will pass composition).

This case is very similar to the analogy described in the previous section, and one could carry over to a fortiori all the description given there. The data table in this case is the following:

Student / Exam	Literature	Composition
Shimon	0	1
Reuven	1	?

Table 2. A Fortiori

The difference between this table and the previous one is only in Shimon’s literature cell. Here there is a hierarchical relation between Reuven and Shimon, and between literature and composition, whereas there the relation was one of similarity.

Beyond that, here too one can say that this a fortiori is of type 2, since it operates on the plane of cases and not on the theoretical plane. On the other hand, it is clear that behind this inference there is implicitly a theory according to which there is some factor that governs success in literature and in composition, and Reuven’s relative strength in literature will serve him in composition as well. Alternatively, the difficulty of literature as against composition, which is revealed in Shimon’s results, will be preserved with respect to Reuven as well. And thus here too we arrive at two different formulations of the inference, by comparing the columns or by comparing the rows.

What is the relation between the biblical a fortiori and the Talmudic one? They look quite similar, since all of them go from the lighter to the heavier. But in the exam inference we have no prior information about the relation between Reuven’s and Shimon’s talents, that is, which of them is more talented, and therefore we use two factual premises (for example, their results on the literature exam) to rank their talent levels relative to one another. The conclusion from these two facts is that Reuven is a better student than Shimon. This conclusion then itself becomes a premise paralleling the hidden hierarchy premise in the biblical inference, and if we add to it the premise that Shimon passed the composition exam, we immediately infer that Reuven—whom we have seen to be more talented—will all the more so pass it. Thus, the difference between the Talmudic inference and the biblical one is that in the Talmudic one two additional premises are required in order to extract the hierarchy relation, whereas there it was self-evident. From here on the structure of both types of inference is very similar: (premise + hierarchy relation) → conclusion.

We have seen that in the Talmudic inference the hierarchy relation does not appear explicitly. This is only our analysis of what stands behind the inference. Exactly as we saw with ordinary analogy, here too the way to extract the hierarchy relation is in fact the way to find the theory from the cases, that is, abduction.

A Refutation of a Talmudic A Fortiori Inference

Suppose that now someone comes and brings us the results of another exam, this time in English, and there Shimon passed and Reuven failed. In the presentation of the data table, this means that our database has now grown:

Student/Exam	Literature	Composition	English
Shimon	0	1	1
Reuven	1	?	0

Table 3. A Fortiori with a Column Refutation

Now we ask again, in light of the new data, what can be predicted regarding Reuven’s result in composition (the unknown)? Note that if in the a fortiori procedure we assumed that Reuven is a better student than Shimon (in light of the achievements in literature), the new column teaches us that this is not necessarily so. In English Shimon’s achievements are better. This calls into question the possibility of making an a fortiori inference and learning that if Shimon succeeded in composition then Reuven will certainly succeed there. It seems that this depends on whether the abilities required in composition are similar to those required in literature or to those required in English. Since the table does not let us infer which of the two is more similar to composition, we are left in a state in which we have no way to decide whether Reuven will succeed in composition or not. In light of the new data, the two possibilities are equivalent for us. Therefore the new datum about the English exam is treated as a refutation of the a fortiori inference. It can no longer be made. It is important to understand that a refutation does not mean proof that Reuven will fail, but only the collapse of the inference that he will succeed. After the refutation the question remains open.

We could of course repeat this process also with respect to Table 1, and see that a similar refutation topples the analogical inference as well. What does this say about the inferences made in Table 1 or 2 before we knew the results of the English exam? It should be clear to us from the outset that there is a possibility that these will be the results of some third exam. Therefore the inferences of analogy or a fortiori are not absolute even before the refuting data become known (as in Table 3). A fortiori and analogy are inferences that derive a conclusion from data (cases), but the conclusion is not certain; future data can refute it. To sharpen the point, a valid logical inference will never fall because of a refutation. No future datum can undermine it, since it is absolute and certain. Whoever accepts the premises must accept the conclusion as well. A fortiori, analogy, or induction—all are non-deductive modes of inference, that is, plausible but not certain inferences.

A Remarkable Talmudic Phenomenon

Let us now return to the analysis of a fortiori inference, and for that purpose let us once again look at Table 3 above. The additional column does indeed refute the hierarchy assumption of the column argument (that Reuven is a better student than Shimon), but does it have anything to say about the hierarchy assumption of the row argument (that literature is an easier subject than composition)? At first glance, no. What connection is there between the data in the third column and the relative difficulty of two completely different subjects? The fact that there is a subject in which Reuven succeeded and Shimon did not says nothing about the previous subjects.

Thus, even if following the refutation we reject the column inference, it seems we can still use the second form of inference (the row inference) and arrive at our conclusion despite the data of the third column. The same applies to a refutation of the row inference. For the same reason, it will leave the column inference intact. At first glance, this means that these two explanations are not equivalent, that is, that we are not dealing here with two different formulations of the same logical move but with two different logical moves. Therefore, when one falls, the other need not fall.

And behold, this is the wonder: throughout the entire Talmud, in dozens and hundreds of examples discussed across all its expanses, when a row refutation or a column refutation is brought, the a fortiori and the analogy are immediately thrown into the trash. The Talmud never tries to rehabilitate them on the basis of the other inference (the columns or the rows). That is, the Talmud holds that every such refutation (rows or columns) completely topples the a fortiori or the analogy; in other words, it treats these two forms of inference (the columns and the rows) as equivalent. The Talmud sees these two types of argument as two faces of the same argument.

But from the description we saw above it seems, at first glance, that these are two different arguments. The row argument assumes a hierarchy between the difficulty of the two subjects, whereas the column argument assumes a hierarchy between the skills of the two students. So why does the Talmud assume that these are two different formulations of the same argument? To see this, let us look again at Tables 1 and 2, and analyze more deeply how exactly we infer the conclusion there.

Talmudic A Fortiori: Analysis

What is the assumption that the talent required for composition is the same talent as for literature based on? Perhaps Reuven is better than Shimon in literature but weaker than him in composition? There is an intuition here that composition and literature are similar subjects in some sense. That traits concerning talent in literature are relevant also to the discussion of talent in composition. As we saw above, that is what we assume if these are all the facts before us, but we know that this may turn out to be mistaken. The refutation in fact attacks the assumption of relevance, which is the Achilles’ heel of the inference. The refutation shows that there is no necessity that the results in literature be similar to the results in composition and therefore no necessity that they be relevant to the discussion of them.

What would we say if the right-hand column contained results in physics? Would that too give us indications regarding the results of a composition exam? Highly doubtful. Perhaps there would still be more reason to rely on this than on no data at all, but here the inference already seems weaker. That is, an a fortiori inference implicitly assumes an affinity between the abilities required in the two subjects. Without this, there is no possibility of carrying out the inference. In other words, the fact that we placed all these data in one table indicates a hidden assumption that there is an affinity among them, that one can learn from one to the other, since they belong to the same field of discussion. Note that we assumed this already at the stage when we wrote the table, before we performed the inference itself. That is, it is not an assumption of the inferential move but something prior to the inference.

Let us refine the description of the a fortiori process a bit further. The structure of Table 2 teaches us that in the background there is an unarticulated assumption: there is some type of talent responsible for success on the literature and composition exams, and it is the same talent (or a similar talent; for the sake of simplicity we shall assume complete identity between them here). Let us denote this talent by t, and let the level of talent be measured in units of t. For example, each student has talent at level 1, 2, 3, and so on (if you like, these are units of IQ, or perhaps the score obtained on the psychometric test). The assumption of the a fortiori inference is that the differences in talent required to pass the composition and literature exams are only quantitative, but it is the same type of talent. By contrast, if the talents in literature and composition were qualitatively different from one another, then we would have to describe the level of literary talent in units of t and the composition talent in units of s, for example.

How exactly does the a fortiori inference proceed? The column inference proceeds as follows: we look at Table 2, and from the literature column infer that there is a difference in the talents of Reuven and Shimon in literature. For example, Reuven is talented at level 2 and Shimon only at level 1. Therefore Reuven succeeded in literature and Shimon did not. We now add the hidden assumption (the assumption of relevance, implicit in the very construction of the table), according to which the talents required for composition are also measured in units of t. If so, looking at the upper composition cell teaches us that to succeed on the composition exam a talent level of 1 is sufficient (for Shimon succeeded in it, and that is his level of talent), whereas literature requires a talent level of 2 (and therefore only Reuven succeeded in it). In other words, the a fortiori inference proposes an explanation for the three data points in Table 2, and does so in terms of one type of talent: t. In this picture the differences among the students and among the subjects are only quantitative. We can now see that this explanation succeeds in explaining all the data. If we assume that Reuven has talent level 2 and Shimon level 1, and further assume that success in composition requires talent level 1 whereas literature requires level 2, then this model explains the three data points in the table. Now we ask, in light of the model, what is to be expected of Reuven on the composition exam? The answer will be that he is expected to pass, since according to the model we have arrived at, passing this exam requires talent level 1, while Reuven has talent level 2.

The big question is why we assume that this is indeed the same talent. Perhaps these are two different talents? Perhaps to succeed in literature one needs a type of talent measured in units of t, and to succeed in composition one needs a type of talent measured in terms of s. If we return to the data, on the assumption that these are two kinds of talent one can interpret the data of Table 2 as follows: Shimon has talent of type s and does not have talent of type t. Reuven, by contrast, has talent of type t, and it is not known whether he has talent of type s. So what can we say about Reuven’s result on the composition exam? Nothing. The question whether Reuven has talent of type s cannot be learned from the data of the table, and therefore, according to this proposed interpretation of the table’s data, our question (whether Reuven will succeed on the composition exam) cannot be decided.

The a fortiori inference is based on the assumption that it is more reasonable to adopt the model according to which this is the same type of talent (or more precisely, that there is a connection between the two types of talent, which improves prediction). The reason for this is the principle of simplicity. Such a model is simpler than the model that assumes that these are two different talents (that is, that there is no connection between them). Therefore the result of the a fortiori inference is 1 (for, as we saw, the assumption of one talent gives that result).

We can now also understand why a column refutation, as in Table 3, does indeed completely refute the a fortiori inference, on both of its sides (the columns and the rows). Once we have two more data points of this sort, it is clear that there must be another type of talent operating in our field, for the talent required for English is certainly not the same as that required for literature (since the results are the opposite). But if we already have two different talents, t for literature and s for English, and it is clear that each of our two students has only one of them, the important question for predicting the value of the unknown (Reuven’s result in composition) will be which of these two talents is required for success on the composition exam. The table does not provide an answer to this question, and therefore our mystery (the question mark) cannot be decided. That is the reason that when the Talmud finds a row or column refutation to an a fortiori argument, it does not try to "turn it around," but immediately determines that it fails.

Talmudic A Fortiori: Formal Analysis

To explain the inference of a fortiori, we begin with the following two tables:

Student/Exam Literature Composition Shimon 0 1 Reuven 1 0 Table 4a. A Fortiori with 0 Filled In

Student/Exam Literature Composition Shimon 0 1 Reuven 1 1 Table 4b. A Fortiori with 1 Filled In

In each such table we have filled the unknown slot with a different result, 0 or 1. We must now find which of the two expresses the simplest model. We shall look for a model that explains each of them and compare the models. What we get is:

• The data of Table 4a are all explained by the following model: Shimon has ability a; Reuven has ability b; literature requires ability b; composition requires ability a.
• The data of Table 4b are all explained by the following model: Shimon has the relevant ability at level 1; Reuven has it at level 2; literature requires level 2; composition requires level 1.

One immediately sees that the model that explains Table 4b is the simpler one, because it contains only one parameter. Therefore, according to Ockham’s razor, 4b is the preferred table. Hence the result of the a fortiori inference is the one entered in the missing slot in Table 4b. The answer is 1, and therefore our prediction is that Reuven will pass the composition exam.

A Column Refutation: Formal Analysis

The very same technique serves us in analyzing the table of a refutation to an a fortiori inference. As an example we shall discuss the column refutation. In the first stage we fill in the two tables:

Student/Exam Literature Composition English Shimon 0 1 1 Reuven 1 0 0 Table 5a: Column Refutation with 0 Filled In

Student/Exam Literature Composition English Shimon 0 1 1 Reuven 1 1 0 Table 5b: Column Refutation with 1 Filled In

The simplest model for each table:

• Table 5a: Shimon has ability a; Reuven has ability b; literature requires b; composition requires a; English requires a.
• Table 5b: Shimon has both ability a and the relevant graded ability at level 1; Reuven has the relevant graded ability at level 2; literature requires level 2; composition requires level 1; English requires ability a.

The notation here means that Shimon possesses both ability a and the additional relevant ability.

Comparing the models, we see that both are two-parameter models, and therefore in this case neither table is preferable to the other. The conclusion is that in the absence of additional information we have no reasonable prediction for Reuven’s result on the composition exam, and the question remains open. This is exactly what one should expect from a refutation.

It is very important to note that this whole process assumes nothing about the nature of abilities a and b, and does not try to identify them. The ability required for literature may be patience, creativity, concentration, linguistic command, interpretive ability, or any other ability, and of course also some combination of all these. Our inference does not depend on locating and identifying the abilities in question. More generally, in the analysis proposed here of the a fortiori inference, we assume nothing about the content or identity of the parameters. Our model enables us to predict the results without needing that. The only thing we do is an analysis in light of the data in the table, in order to locate the number of relevant parameters operating in the field, without needing their identities and contents.

When one deals with other tables it turns out that we must resort to a more complex criterion of preference. Likewise, I am not describing here in detail the algorithm by which one can proceed from the data in the table to the theory, that is, to the simplest model, which is the map of parameters that explains the table. Here we have no room to enter into all this, and the interested reader is referred to the sources mentioned above.

"The Common Factor": Scientific Generalization

To complete the picture I shall bring here just one more analysis of one additional inference, for this is the inference that underlies scientific generalization (induction). In the jargon of Jewish law it is called "building a paradigm from two texts," or "the common factor." How is such an inference structured?

Suppose we have data about three students: Yossi, Reuven, and Shimon passed the literature exam. Yossi and Shimon also passed the composition exam. The question is whether Reuven will also pass the composition exam. A simple analogy says yes. If there is similarity among them in ability with respect to literature, and if composition is similar to literature, then Reuven too will pass the composition exam. We begin with data about two students plus an assumption about their similarity to a third student, and infer a conclusion about the third. In exactly the same way, if we have data about a book and a pencil, both of which fall to Earth. Our question is whether a chair too will fall to the ground. Since we are drawing an analogy among them, the conclusion is that it too is expected to fall.

But now we must complicate the picture a bit. Suppose Yossi has better achievements than Reuven and Shimon in grammar, and Shimon has better achievements than Reuven and Yossi in English. The picture now becomes more complicated, since it is no longer clear whether one can still conclude that Reuven will succeed in composition. In the same way, one can ask: if the pencil has a special property that it writes (which the chair and the book do not have), and the book has a special property that it is rectangular (which the chair and the pencil do not have), is it still correct to conclude that the chair too will fall to the ground?

The data table for these cases is exactly the same, and so we will present it in terms of the students:

Student/Exam	Literature A	Composition B	Grammar C	English D
Yossi	1	1	1	0
Reuven	1	?	0	0
Shimon	1	1	0	1

Table 6. Argument by analogy from two texts: data

We can look at this table as follows: when we examine the relation between Shimon and Reuven (the four lower-right cells), we see that this is a table of argument by analogy. However, the two lower cells in the leftmost column are an objection to it. The same applies to the relation between Yossi and Reuven, only this time the objection is the two upper cells in the grammar column.^[7] This means that we cannot infer from Shimon to Reuven because Shimon has high ability in English, and we cannot infer from Yossi to Reuven because Yossi has high ability in grammar. Thus we cannot infer from the pencil to the chair because the pencil has a special property (it writes), and likewise not from the book, because it has a special property (it is rectangular).

In the scientific context we know that if both the pencil and the book fall to the ground, we will tend to infer that the same will be true of the chair. Why? Because they have a common property, namely that all of them have mass. This is exactly what emerges from the analysis of Table 6. All the students share a kind of ability that we will denote by 1, and it is what is responsible for success in composition, so our prediction is that Reuven will succeed in composition. The simple filling-in is 1, exactly as in the scientific context.

From Table 6 one can arrive at a model that determines what study skills each student has, and which of them are relevant (necessary to pass the exam) in each subject. In this case, what emerges is the following model:

Subjects	Students
Literature: 1 Composition: 1 Grammar: 2 English: 3	Yossi: 1,2 Reuven: 1 Shimon: 1,3

We immediately see that all three students have a shared ability, 1, and this is precisely the ability responsible for success in composition (and also in literature), and therefore our expectation is that Reuven will succeed on the composition exam. That is also why it was possible to infer from success in literature to success in composition. What we have here is the same type of talent. The theory we found in fact explained to us the analogy on which it had been implicitly based. This is in fact the process of abduction, since in this mechanism we succeeded in extracting the theory from the data (the cases), and once it was in our hands we applied it to a future case (that is the prediction). If in the end Reuven fails the composition exam, then this theory has of course been empirically refuted. But this is how one constructs it from the data, and therefore this is a procedure of abduction. As we have seen, abduction is not a necessary inference, and so a future experiment can refute the theory we found by means of it.

Note that in the parallel physical case (the book, the pencil, and the chair, and the falling to the ground), the property common to all of them, 1, is mass. In the process of abduction we discovered that all three objects share the common property of having mass, and it is this that is responsible for falling to Earth.

Summary: abduction as a "theological" argument

In every case we begin with a data table that contains the cases, or the situations. These are the empirical facts. One cell is missing, and this is the prediction. We want to know what will happen in that situation (will a chair fall to the ground), and we try to infer this from the data we have observed (that a pencil and a book fall to the ground). This inference is basically a kind of analogy, from known situations to a new situation that resembles them. As we have seen, performing an analogy presupposes a theory, and therefore in order to infer the desired conclusion we are actually performing abduction, within which we extract from the data the simplest theory (we saw that the principle of simplicity is a foundation of abduction) that explains them. From this theory one can predict what will happen in the missing situation, that is, perform the analogy (the chair will indeed fall). The analogy from the data to the missing situation presupposes a theory, and the abduction we performed is an explicit exposure of that theory, and a use of it in order to perform the analogy (to reach the conclusion about what will happen in the missing situation).

Therefore, what has been described here is nothing but the logic of abduction. What is done here is a "theological" argument that reflects a process of scientific generalization. If the facts are such and such, what theory can offer us an explanation for them? Instead of going along the axis of physical causation, that is, deriving the cases/situations from the theory, we go along the abductive axis and derive the theory from the cases/situations.

In principle, this logic can be extended to tables of any size whatsoever, that is, to problems of any degree of complication and any level of difficulty we may want. This is a complete logic of analyzing situations and finding the theory that explains them. It can be used in law, science, Jewish law, everyday life, and in general.

Is this analysis necessary? Is the theory derived uniquely from the data? Seemingly yes, since we saw that there is a completely mechanical and algorithmic way to get from a data table to a theory and to the result in the missing cell (the result of the analogy). But all of this is based on the assumption of simplicity, which is itself not necessary. If one does not assume simplicity, one can propose a great many models (in fact, infinitely many), each of which explains the data in the table. Moreover, even if one adopts the principle of simplicity, there is not always a single solution. Sometimes there are several different models that have the same degree of simplicity and all explain all the data. Therefore it is not correct to say that the model is uniquely determined by the data (the situations). This is abduction, and as we have seen, it is not a necessary inference like a valid logical inference (deduction).

This algorithm also does not give us an explicit identification of these theoretical parameters. What exactly is 1? Even if the process of abduction leads us to the conclusion that there is a parameter common to all the objects, 1, as long as we have not identified it, the construction of the theory is not complete. In the physical context we identified it with mass, but how did we arrive at that? A theory is supposed to determine what those parameters are that are responsible for every physical state. It turns out that this identification is not a purely logical procedure but depends on interpretation. Later in the notebook we will enter a little into this process, and we will see the problems David Hume found in it, and the solutions Kant proposed for them. But I will not enter into details here, since what matters for our purposes is that identifying these parameters is another non-necessary component in the abductive process of finding the theory from the situations.

If so, abduction is a "theological" argument, but not a valid logical argument. It is an example of a move from the "philosophical" direction to the "theological" direction, except that unlike the previous chapter, where we dealt with deductions, here we did so with invalid inferences.

Part Two

The physico-theological argument from a "philosophical" and a "theological" perspective: the argument from epistemology

In chapter 4 we will present a formulation of the physico-theological argument from the opposite, "theological," angle, first formulated by the American philosopher Richard Taylor. In the chapter after that we will expand this argument and present an argument from epistemology. In chapter 6 we will present this expansion from another angle, the mathematical character of the universe, and chapter 7 will be devoted to the implications of this argument for the relation between rational thought and belief in God. In chapter 8 we will move on to discuss several objections to the argument from epistemology.

1. The physico-theological argument from the opposite perspective

Introduction

In the previous notebook we presented various versions of the physico-theological argument, which took us from certain premises to the conclusion that there is a God. In this part we will present an argument that works in the opposite direction. An initial version of this argument is presented in the book of the American philosopher Richard Taylor, Metaphysics^[8]. In my book Two Carts and a Balloon in note 21 I described Taylor’s argument, and around it (and also in note 25 and around it) I even proposed a broader and more sophisticated version of his argument, which will be presented in the chapters that follow.

It is likely that along the way it may perhaps appear to the reader that I am ignoring the possibility of evolutionary explanations, so I will say already here that for didactic reasons I am ignoring them until chapter 8, and there we will deal with them in detail. We will see there that evolution attacks this argument from a somewhat different angle than it does the usual physico-theological argument (that was what we dealt with in notebook 3), and therefore the response here to this challenge will also be somewhat different.

Taylor’s argument: the parable

One of the common arguments for the existence of God is the physico-theological argument. This is an argument that starts from the fact that the world is complex and ordered, or from the fact that it appears purposeful and directed toward various goals, and concludes from this that there is someone who arranged and organized it. As we saw in the previous notebook, the main assumption here is that a complex organ cannot come into being by itself, spontaneously.

There are several defensive arguments against a proof of this kind. What many of these modes of defense have in common is that they accept the claim that perhaps a complex thing can come into being by chance. Taylor proposes a different variation on this type of proof, one that remains valid even for those who do not accept the ordinary "philosophical" proof, that is, those who are prepared to accept as plausible the assumption that a complex thing can come into being by chance. As we shall see below, in the terminology defined in the previous chapter, what we have here is really a "theological" argument.

We will begin with a quotation from Taylor’s book, which brings a parable as an example:

Suppose you are traveling in a railway carriage, and at one of the stations you look through the window and see on the slope of a small hill next to the train a large number of white stones scattered in a pattern like the following: ‘Welcome to Scotland.’ It is obvious that you would not doubt for even a moment that it is not an accident that the stones form this pattern. In fact, you would be quite certain that they were arranged in this way with the intention that they convey a meaningful message. Nevertheless, you are unable to prove, solely on the basis of observing their arrangement, that they were arranged by a being with intentions. It is entirely possible—at least logically—that no directing hand stands behind this pattern, and that it is nothing but the fruit of the activity of lifeless nature. It is possible that the stones came to this interesting arrangement entirely by chance: for example, that over a period of hundreds of years each and every stone rolled down the hill until it finally found itself in its particular location relative to the others. For it is clear that the fact that something has an interesting and impressive shape or structure, and therefore looks as though it was planned in advance, is not proof that it was indeed planned. There can always be another explanation…^[9]

But here we come upon the important point, which is easy to miss, and it is that if, on seeing through the train window the group of stones arranged as described, you were to arrive at the conclusion that you are at the gates of Scotland, and if the only reason for this conclusion—whether or not it constitutes good proof—were that the stones form the pattern they form, then you could not consistently assume that the arrangement of the stones is accidental. In fact, you would assume that they were arranged in this way by an intelligent and purposeful being or beings, in order to convey a certain message that has nothing to do with the stones themselves. Another way to express the same idea is to say that it would be irrational on your part to see in this arrangement of stones evidence that you are at the gates of Scotland, and at the same time assume that they came to be arranged in this way at random, that is, as a result of the ordinary operation of natural forces of a physical character. If, for example, they came to this arrangement after each of them rolled down the hillside over the years until it finally happened to reach the place it reached, or if they were simply scattered in this way by an earthquake, a storm, and the like, then their arrangement can in no way serve as evidence that you are at the gates of Scotland, or as proof of anything else not connected with the stones themselves.

His claim is that two paths are open to the traveler: either to adopt the assumption that the stones were arranged by chance, and then continue sitting in his place until he hears the announcer declare that the train has arrived in Scotland, or to assume that the stones were arranged intentionally by an intelligent factor in order to convey to the passengers the message that they are indeed at the gates of Scotland. If the stones were arranged by chance, they could indicate any information whatever, and this has no connection to the real information, that is, to the state of affairs in the world itself. The third possibility, according to which the stones were in fact arranged spontaneously without a directing hand and at the same time we begin packing our suitcase, that is, assume that we are at the gates of Scotland, is of course not open to any rational person.

Later in his discussion Taylor brings another example, describing archaeological excavations in which a stone covered with interesting signs is discovered. These signs can be interpreted as though they were formed by chance or intentionally. Later an expert arrives who claims to identify the language in which the signs on the stone are written, and offers the following translation: "Here fell Cimon, leading into battle a handful of Athenians against the armies of Cyrus." In this case, two theoretical possibilities are open to us: either to insist that the signs on the stone were formed by chance, and then we cannot infer from these findings that there was a man named Cimon, or to infer that this is indeed the content of the inscription and assume that the signs were not formed by chance but were written in order to convey this information. It is clear that there is no logical possibility of assuming that the signs were formed by chance and nevertheless learning from these stones that there was a man named Cimon who fought against Cyrus and his armies.

Taylor’s argument: the application

From here Taylor moves to the application. Our sense organs are complex (they have low entropy. See the previous notebook in chapter 2) and amazingly sensitive. In addition, they are strikingly similar to things designed by humans, although in many cases they even surpass every human product in their sensitivity. He then goes on to argue that the route of natural selection and long-term random processes is indeed still open to us in principle, and therefore theoretically one can assume that despite their complexity they came into being by chance. Here we have in fact adopted the approach that challenges the usual physico-theological argument. And yet there is a reverse version of the argument with which it will be hard for us to cope.

Let us continue with the quotation:

As a result, the complexity, sophistication, and apparently purposive organization of our sensory organs do not constitute decisive grounds for the assumption that they are the result of some purposeful activity. A natural and non-teleological explanation of them is possible, and in the opinion of many it is already in our hands (He is referring, of course, to the theory of evolution. See the previous notebook for a detailed discussion.).

But the main point, to which attention is only rarely paid, is that we do not merely marvel at these structures and wonder how it came about that they are such as they are. We do not merely see them as amazing and astonishing things and construct hypotheses about their origin. In fact, rightly or wrongly, we rely on them in order to discover those things that we take to be true and to exist independently of these organs themselves…. Our senses and all our faculties may have been accidental in their origin, but then they also would not tell us anything. Yet the fact remains that we trust them without even reflecting on it. Seeing something is often regarded, almost by itself, as a good reason to believe that the thing exists, and it would be ridiculous to claim that we infer this from the structure of our eyes or from hypotheses about their evolutionary origin. The same applies to our other faculties…

We are not claiming here that our senses cannot make mistakes, or even that we ought to trust their testimony. The point is that we do trust them. We do not merely believe that our senses are extraordinarily interesting. We do not merely believe that they produce interesting phenomena within us, or that they merely produce beliefs in us. We assume, rightly or wrongly, that they are reliable guides for discovering truth and for discovering what exists independently of our senses and of their origin. And we continue to hold this assumption even when they are the only guides available to us….

If we do assume that they are guides to discovering certain truths that have nothing to do with themselves, then it is hard to see how we can believe, in a way consistent with that assumption, that they emerged by chance, or that they are the ordinary result of the operation of forces devoid of intention, even if their operation continued for ages and ages.

Taylor is making a "theological" argument here. Even if the complexity of our eyes in itself does not indicate that they were created in a purposeful process (not spontaneously, by an external factor), as the challengers claim, every such challenger must still ask himself whether he trusts his eyes. Is the fact that he sees something enough to convince him that this thing really exists out there? If so, let him go back and examine himself: if he truly believes in a spontaneous process that is responsible for the formation of the eyes (evolution), then there is no way to justify the trust he places in them. Exactly as someone who believes that the stones on the hill were arranged in a random process cannot place trust in the message they convey to us, since on his view it is mere coincidence. The connection between the shape of the stones and the state of affairs in the world can be anything whatsoever (if any). So too, someone who thinks the eyes are the fruit of blind chance cannot place trust in the information they convey to him. Their structure is accidental, and as such we have no guarantee that the information they convey to us is reliable. They could have come into being in any other way and turned any information in the world into any form in our consciousness. In fact, they could even fabricate an image with no source in the world itself. The important point is that, regardless of the actual reliability of our eyes, we have no way to know this merely from our seeing. The eyes in themselves cannot be a reliable source of information for someone who thinks they were formed in a spontaneous process. Even if in practice they were wonderfully reliable, we would have no way of knowing that.

The nature of Taylor’s argument

Taylor’s argument is a "theological" argument. It begins from the conclusion that our eyes are complex and that we trust them, and works backward from that to the assumptions that lead to this trust: that the eyes were not formed spontaneously but intentionally by an intelligent factor. The parallel "philosophical" argument is the following: if the eyes were formed spontaneously, the information they convey to us cannot be trusted. That is: atheism implies skepticism^[10]. The ordinary converse is not correct: if the eyes were formed intentionally, then they can be trusted (faith implies rationalism^[11]). The question is: what was the intention of whoever formed them intentionally? Perhaps he wanted to confuse or mislead us. But by denying the consequent we obtain the corresponding "theological" argument, which is indeed a valid argument: if we have trust in our eyes, then clearly, at least in our own view, they were not formed in a spontaneous process. That is: rationalism implies faith.^[12]

Again, one could say that this is failed pragmatism: because it is not comfortable for me to be a skeptic, that is, not to trust my eyes, I prefer to adopt a worldview of intentional and planned formation. Seemingly my trust in my eyes has no basis, and in order to justify it I assume premises (that the eyes were built by an intelligent factor) that lead me to the conclusion that this trust can indeed be given. This is intellectual dishonesty, for an honest person who believes in spontaneous formation ought simply to give up trust in his eyes. Giving up his understanding only because the conclusions that arise from it are not comfortable for him does not seem reasonable. This is the place to clarify once again that this is not necessary at all. If my trust in my eyes is intuitive (and not mere convenience), then I have exposed the fact that implicitly hidden within this intuition is a belief in intentional formation.

Now, of course, someone may come and ask on what that hidden belief is based. What is the basis for my belief in such a formation? Do I have scientific or other evidence for it? That is another question, and we are not dealing with it here. In a "theological" argument we merely expose to ourselves what we believe. The answer to that question apparently lies on the "philosophical" plane. I arrive at my trust in intentional formation because of the ordinary physico-theological argument. The "philosophical" formulation proves from the complexity of the eyes and the universe the existence of an external, creative, and directing hand. But that is another discussion, which we dealt with in the previous notebook. Here I succeed in proving to my interlocutor that despite his denials, he does implicitly accept the physico-theological proof. The "theological" argument reveals to my interlocutor that in fact he cannot deny that he implicitly adopts the "philosophical" argument.

Summary: the logical pincer movement

The picture I have described here is in fact an attack in a pincer movement against the atheist. First, I present to him the physico-theological proof in its usual "philosophical" formulation: the world is complex and it is unlikely that it was formed spontaneously, and I discuss with him all the objections we dealt with in the previous notebook. At the end of the discussion, my interlocutor claims that he still does not accept the physico-theological argument, because in his opinion it is possible for a complex thing to come into being by chance, spontaneously. To that I return and answer him from the other side with Taylor’s argument, which is in fact a "theological" argument, and which proves to him from the trust he places in his eyes that he himself apparently does not accept the assumption that a complex thing is formed spontaneously, and therefore he must retract his opposition to the physico-theological proof. In other words, when he argued against the physico-theological proof that in his opinion a complex thing can come into being by chance, he was being dishonest, or at least unaware of his own assumptions on the matter. And if now he begins to wonder why he really trusts his eyes, after all there is no real basis for it, I have no answer for him. What matters is only that he understand that he must choose: either to abandon trust in his eyes, or to admit to himself that he does in fact accept the physico-theological proof (that is, he assumes that the complexity of the eyes proves that they were not formed spontaneously, and therefore he places trust in them). There is no third possibility. The option of believing in spontaneous formation and at the same time trusting the eyes does not really exist, just as in the case of the passenger on the train he cannot assume that the inscription of stones was formed by chance and at the same time place trust in it.

Of course, he can still say that the trust he places in his eyes is nothing but a psychological habit and has no great significance. In other words, he is essentially agreeing that one ought not trust the eyes, except that this is how he lives. He truly does not commit himself to the claim that they reliably reflect what is happening in the world itself, but he has no other option. He is simply built in such a way that he trusts his eyes. To this claim I of course have nothing to answer. Its meaning is basically that the atheist has discovered about himself that he is an unconscious skeptic. Still, the "theological" argument helped him discover something else about himself. Either he will discover that he is a skeptic (not about God, but about his tools of perception), or he will discover that he believes in God.

One thing our atheist will certainly learn from this: exactly as in the case of the train to Scotland, the third possibility, namely trust in the information conveyed by the eyes together with atheism (that is, the assumption that a complex thing can come into being by chance), is not coherent. He must decide which of the two he is giving up. Is he an atheist, and then he must be a complete skeptic (not only about the existence of God), or is he a believer, and then he can also trust his eyes? Only he can and should make that decision. At this point the believer withdraws from the discussion and is no longer a party to it. A "theological" discussion does not come to persuade, but to expose what a person is already convinced of. Therefore such a discussion does not end in victory. In principle, one should present the argument with its two possibilities and withdraw, leaving the interlocutor to choose which of the two possibilities he finds himself choosing to believe. In a "theological" discussion I merely place him before a mirror that helps him expose his own thoughts more clearly. Nothing more.

After the discussion, the atheist must examine himself well. Does he really think that his trust in his eyes is only a psychological habit and not a reflection of the state of affairs in the world, or does he have trust and insist only so as not to lose the theological argument? That, of course, only he can examine within himself, and only he himself has any interest in doing so. As we have seen, a "philosophical" argument aims at conversion, but a "theological" argument is an exposing argument (not a converting one). It is neither my desire nor within my power to convert his views. When I present a "theological" argument, I can only help a person examine himself better, and discover whether he is an implicit believer or an implicit skeptic. The decision is his alone.

A note on the cosmological argument from the opposite perspective

In the previous notebook we presented the cosmological argument in a "philosophical" formulation. Now, of course, we can translate it too into a "theological" formulation. One can deny the principle of causality and be an atheist. One can also accept the principle of causality and be a believer. But one cannot accept the principle of causality and remain an atheist. Therefore there too one can formulate a thought experiment that confronts the atheist with these two alternatives and forces him to choose one of them. This is the "theological" formulation of the cosmological argument, exactly as we did here for the physico-theological argument.

1. The argument from epistemology

Introduction

In this chapter we will expand Taylor’s argument, and show that it really does not deal specifically with the eyes, but with the whole of our cognition and rational thought.

How can one accumulate information about the world?

One of the questions that has troubled philosophy, in one formulation or another, from time immemorial is how knowledge about the world can be accumulated. Here we will present it on two successive levels: trust in the senses, and trust in cognition, that is, in the processing of sensory data.

The more extreme formulation of the question concerns our very trust in our senses. Skeptics ask why the fact that our eyes show us something wins our automatic trust. Is it not possible that this is a deceiving demon, or simply a deception? In fact, there is no need to speak about deceptions at all. One can say that the senses deceive us only if in principle they can be trusted, but at times they fail and confuse us. The question here is much harder: what is the basis at all for assuming that one or another of our senses presents the world to us reliably?

Usually this question does not really trouble people, and not even philosophers. Some because they do not have a philosophical temperament, others because we have no real way to handle it (how would we check whether our senses are reliable or not?), and others think it is self-evident and needs no explanation. They will add that every explanation has to ground claim X in claims Y that are more self-evident. But we have no assumption more self-evident than trust in the senses. Is there anything we trust more than our own sight?

But in the previous chapter we saw that this is not a bizarre philosophical question but a very hard question that cannot really be answered. The fact that our eyes show us something says nothing in itself about the world itself, since it is possible that this is an arbitrary mechanism formed in a blind process. The only feedback we receive about the reliability of the eyes comes from the eyes themselves. If they are not reliable, that feedback is not worth much. If someone believes that our mechanism of vision came into being by chance and without a directing hand, then on his view there is no real basis for the assumption that they can be trusted.

Many will surely say that we do have feedback about the eyes, namely data we receive from the other senses. Hearing or touch can provide feedback on what we see with our eyes. For example, we see a wall before our eyes, and now we move toward it and touch it. The sense of touch confirms for us that there really is a wall here. Here, then, we have external and independent feedback about the reliability of the eyes. The same applies to cross-checking with the data of the other senses.

But the difficulty can be extended to our whole sensory system. What is the basis of our trust in the sensory system as a whole? How do we know whether the entire sensory system that presents us with some picture of the world—sound, sight, taste, touch, and smell—is not one great illusion? Beyond merely casting doubt on each of the senses separately, we all know that behind all the senses stands our brain, which processes the data of all the senses and organizes them into one large and comprehensive picture. If so, we will now ask Taylor’s question about this whole system (the senses + the brain), and not only about the eyes: what is the basis of our trust in it? To that we can no longer bring any external feedback, for we have no contact with the world outside the senses, and the senses cannot ground our trust in themselves. If indeed we assume that this whole system is a chance creation, then there is no reason to assume that it is reliable. And here again we arrive at the conclusion that even if we do not actually have proof that it is reliable, if we trust it, this implicitly indicates that we believe in some factor that takes care of its reliability and of the fit between it and what is happening in the world itself. This is again a "theological" proof of the existence of God, as we saw in the previous chapter. In fact, this is an expansion of that argument, and we will call it here "the argument from epistemology." The very fact that we trust our cognition indicates that implicitly we assume the existence of a factor responsible for its reliability. The possibility of an evolutionary explanation will be discussed later.

A skeptical query

One could ask the same question about other claims that seem certain to us. For example, the three basic assumptions of logic: the law of identity (everything is identical to itself, or every proposition is equivalent to itself), the law of non-contradiction (it is impossible for a proposition and its negation to be true simultaneously), and the law of the excluded middle (either a proposition is true or it is not; there is no third possibility). The same applies to claims in simple arithmetic, such as 2+3=5, or to the axioms of geometry, or to the assumption that two magnitudes equal to a third magnitude are equal to one another (one of the basic assumptions of mathematics—an extension of the law of identity). Regarding all of these too, one can seemingly ask what is the basis of the trust we place in these claims. Is it not possible that they are mistaken? Maybe it is all just a deception?

Two kinds of skeptical questions

It is important to understand that all these are questions entirely different in kind from the one we asked above about our trust in the senses. These are two completely different kinds of doubt. To sharpen the point, let us note that in Jewish law a distinction is made between two kinds of legal doubt. Suppose that two identical pieces of meat lie before us, one kosher and one non-kosher, and we do not know which one is kosher and which is not. In such a situation, regarding each piece of meat there is a 50% doubt that it is non-kosher. This is a doubt that in Jewish law is called a case in which "the prohibition is fixed" (=there is a definite prohibition present in the situation). Another situation, considered one in which "the prohibition is not fixed," is when one piece of meat lies before us and we do not know whether it is kosher or non-kosher. Here too, seemingly, there is a 50% chance that it is non-kosher. And yet Jewish law distinguishes between the two situations. In the first situation, one of the two pieces is in fact non-kosher, that is, there is a real basis for the doubt. In the second situation, we are the ones raising the doubt, but it has no source in the situation itself. The piece of meat itself may be perfectly kosher, and the suspicion has no basis.

Of course, one could continue and distinguish between a situation in which the doubt about the piece of meat arises because of concrete considerations, and a situation in which we do not have definite information and there is no concrete reason to doubt. An example of this can be taken from a child growing up in a home with two parents, where we naturally assume that he is indeed their son. True, there is a possibility of assuming that he was adopted, kidnapped, or simply happened to end up there by chance, but as long as we have no reason to doubt, we do not doubt. True, we have no concrete information, but in order to define a situation as doubtful, a concrete reason is required that arouses doubt. From the standpoint of Jewish law, such a consideration is enough to punish the child if he harms his parents, and the claim that perhaps he is not their son will not avail him unless he brings a concrete reason that awakens this doubt in us. This is in fact a case of presumption, where a certain state of affairs is presumed to be as it is, and about this the Talmud says (Kiddushin 80a), "We flog on the basis of presumptions; we stone and burn on the basis of presumptions." A state of presumption is enough to make fateful decisions, and baseless doubts cannot undermine this.

Another example is Bertrand Russell’s celestial teapot (see the notebook on the ontological argument, chapter 10). Russell describes a situation in which a man appears before us and claims that a small transparent teapot is orbiting the planet Jupiter. We have no information about such a situation, and the fact that we do not see it says nothing, since it is small and transparent and cannot be seen, and yet most of us would not regard this as a case of balanced doubt (a 50% chance that there is such a teapot). The reason is that there is no apparent reason that arouses in us the possibility that such a teapot really exists. This is a situation of lack of information with respect to which two possibilities arise, and yet it does not lead to a balanced doubt. See on this the words of Rav Kook, in his work Ein Ayah, Shabbat 30b, where the Talmud itself deals with a case in which a man comes and claims before Rabbi Judah the Patriarch that Rabbi Judah himself is an illegitimate child born of that man and Rabbi Judah’s mother. Rabbi Judah the Patriarch treats that claim with complete dismissal, and Rav Kook explains this by saying that no concrete argument was raised here that would awaken doubt.

Back to the "theological" argument

The skeptical query regarding the various claims brought above rests on shaky ground. There is no concrete reason to cast doubt on them, and therefore although a person may raise a skeptical claim about them, it will be a very weak claim. Our trust in all these claims is self-evident. For example, anyone who understands the concepts 2, 3, addition, and equality understands that 2+3=5 must hold. Questions such as: who told you? perhaps it is not true? appear in this context to be pulled out of thin air, and therefore we are rightly not troubled by them. The same applies to the basic laws of logic and the other examples I brought.

But the question about the eyes is a much harder question, for it definitely has a basis. If indeed our assumption is that the eyes were formed by chance, then the probability that they correctly reflect the state of affairs in the world is negligible. This is not a query that stems from the absence of information, but from positive information. If we have an assumption (information) that the eyes or our senses were formed by chance and without a directing hand, what is the probability that this blind chance created reliable sensory instruments? Think of a box containing a collection of parts from a disassembled television set, and now some blind and random mechanism (a blind monkey, or a passing storm) gathers them arbitrarily and randomly and connects them in some way. What is the probability that we will get a working television? The number of ways to connect those parts is enormous, and the possibility that in a blind and random process they would be connected into a functioning television is negligible. Incidentally, this is exactly Hoyle’s Boeing argument that we encountered in the previous notebook, except that here it is presented in the opposite, "theological," direction: if I begin from the assumption that the eyes were formed in a random process, the chances that they function reliably are negligible. And by denying the consequent: if I assume that they are reliable, then it is clear that I implicitly assumed that they were not assembled in a random and blind process.

Therefore the question of what is the basis of my trust in my eyes, and in my sensory apparatus in general, is a much stronger question than a mere query raised without basis regarding a claim that is solid and self-evident. It is exactly like the difference between the two kinds of queries we presented above. Of course, this question exists only if we assume that the process by which our senses were formed was random. If there was an intelligent factor there that is responsible for this complexity and fit, that would answer the difficulty, and that is exactly the argument we called above "the argument from epistemology." We will now continue and expand it even further. The question of evolution and the other objections to this argument will be dealt with later in the notebook.

The question of scientific rationality

Until now we have dealt with the question of trust in the senses. But contrary to what many think, our empirical conclusions are not exhausted by collecting data from the senses. We will now see an expansion of the argument from epistemology, which concerns our rational thought in general. I will present the philosophical background here only as briefly as I need for the argument, and the interested reader is referred to the fourth part of my book Truth and Not Stable. In fact, virtually the entire book touches in one way or another on this point.

Already David Hume, one of the British empiricists of the eighteenth century, pointed out that the laws of nature are not really based on observations alone. Observation by its very nature deals with particular cases, and after the observations there always comes the generalization that creates from the facts we observed a theory, or a general law. Hume asked what justifies our trust in the generalizations we make, for a given collection of facts can be generalized in very many ways. We choose one of them, usually the one that seems simplest to us among them (see above in chapter 2). What guarantees that what seems simple to us is also the correct one? Why should such a generalization work at all?

Hume raised a similar question regarding the principle of causality. In notebook 3 we pointed out that the principle of causality is also not really learned from observations. When we observe a person kicking a ball and see that the ball flies away, all that can be said with certainty is that first there was a kick and afterward the ball flew. The temporal precedence between the events is a product of pure observation, but the conclusion that the kick is the cause of the ball’s flight has no observational basis whatsoever. In fact, this example indicates that the concept of causal production itself is a product of our mind. We have not encountered it anywhere directly in our senses. Hume, as a thoroughgoing empiricist, wondered what justifies our trust in the general principle of causality (that everything has a cause), and in causal interpretations of specific events we have observed (such as the kick and the ball). As stated, there is no empirical justification for this, since we have no way to observe a causal relation between events. We see temporal precedence (first A and then B), and perhaps also consistent temporal precedence (that B always happens after A). But in order to infer that A is the cause of B, we must assume further premises beyond temporal precedence (for example, that A caused B). Therefore the question whether A is the cause of B cannot be answered by purely empirical tools. It is a matter of interpretation.

Let us present הדברים in a more focused way through an example. Suppose we are examining the question of the relation between force and acceleration. To do this, we take a body whose mass is m and apply to it forces of different magnitudes, and each time we check what acceleration it develops. We plot the results on a graph, where the horizontal axis is the acceleration a and the vertical axis is the force F. The line connecting the points is in fact our generalization, that is, the law of nature.

The resulting picture is as follows:

Looking at the drawing shows us that the five specific results lie on a straight line, and therefore the obvious generalization is to draw a straight line connecting them. Moreover, measurement shows us that its slope is exactly the mass of the body being measured. In such a situation, the scientific community decides that the relation between force and acceleration is linear, and the coefficient of proportionality is the mass. The law of nature we found in this experiment is F=ma, which is in fact Newton’s second law of mechanics.

However, it is a simple mathematical fact that there are infinitely many other forms of generalization for these five results, all of which fit all five. In other words, there is an infinite number of continuous curves that will pass through the five particular facts, that is, the five given points on the graph. Let us note that the number of possibilities is not merely large, but infinite. One of them is drawn as a dashed line on the graph above, and of course there are infinitely many such possible curves.^[13]

How are we to choose among the different possibilities? What is in fact the correct theory, or the correct general law, for the results of this experiment? As stated, every beginning physicist understands that he should take the simplest possibility among them, namely the straight line. But what is the justification for this decision? What guarantees that the simple is also the correct? This is in fact a reflection of Hume’s problem of induction, since it illustrates for us the transition, that is, the generalization (induction), from the specific empirical observations (the points on the graph) to the general law (the graph).^[14] It also illustrates well the problematic nature of this transition. And again, not only is this generalization not necessary (because there are many other possible ones), it does not seem to have any justification at all. Why on earth choose precisely the simple line?

The problems of induction and causality described here briefly posed no simple challenge to empirical science. All the rational thinking that underlies science suddenly found itself lacking an empirical or logical foundation.

A pragmatist solution

One can propose a pragmatic solution here, that is, to claim that the general law is really not something whose truth we are asserting. It is a law that passes our basic test, since it explains all the known facts, and among the generalizations that meet this requirement it is the simplest, and therefore we choose it. There is no claim here that it is true, but only that it is convenient. As long as it works, that is, as long as it meets the criteria of fitting the facts, there is no reason to abandon a convenient theory in favor of a more complicated theory.

This is a very common view in philosophy of science, which in various formulations basically holds that the theory claims nothing about the world, but rather constitutes a description that organizes all the information in our possession efficiently and conveniently. We are not saying that force is indeed directly proportional to acceleration as a law of nature; we are merely content with saying that in the cases we observed this always held. By the same token, all the other curves that pass through all the points shown on the graph above also held, of course, but the straight line is the simplest among them. According to this view, the experiment is not an instrument for learning about the world. It teaches us only what we saw regarding the specific object and the specific force we observed. Nothing more. The theory that is derived from generalizations about the specific observations is nothing but an efficient way to organize the specific observational information we have accumulated so far. In itself it says nothing about the world. We could have organized the information in many other ways, but if there is no other reason, it is convenient for us to choose the simplest. According to this approach, the simple is not regarded as a criterion of the true and the correct, but it is of course the most convenient and efficient. There is more than a scent of pragmatism here, as that was defined in the first part of the notebook.

Standing opposite this pragmatic conception is an opposite conception that sees theory too as a claim about the world, and experiment and observation as instruments for discovering the truth about the world. The general law, or theory, that is derived from the observations is learned from them. The purpose of the experiment is to teach us the theory, that is, the correct general law. Admittedly, no one claims that a scientific law is a certain proposition, since a scientific theory stands open to tests of refutation and can of course fail them. But as long as it has not failed, we believe that it describes the world correctly (and not merely conveniently and efficiently). Its simplicity is a reasonable measure of its truth, at least so long as it has not been proven otherwise (that is, so long as it has not been refuted in experiment).

Kant’s formulation: the synthetic a priori

In my book Truth and Not Stable I described the historical move whereby until the beginning of the modern era rationalism held sway, that is, the conception that logical considerations are a legitimate instrument for knowing the world (see notebook 1). At its foundation lies the conception that there is some sort of fit between the form of our thinking and the way the world itself behaves. Afterward, a strong critique of that approach arose, and at the beginning of the modern era empiricism arose and replaced rationalism. The feeling was that now we were finally on safe ground. The age of rationalist speculations was over, and now science was sticking to facts and observations. And indeed, in parallel with this philosophical revolution, science advanced more and more, thereby strengthening the feeling that we had reached our destination and our rest.

But then David Hume arrived, one of the outstanding empiricists, with the collection of skeptical problems he raised. Suddenly it became clear that empiricism too is not free of problems, and its intellectual infrastructure is not necessarily better than that of rationalism. Causality and induction, two of the most basic tools of scientific and empiricist thinking, received painful blows in Hume’s philosophy. Indeed, Kant, who is regarded by many as the greatest philosopher of the modern era, said of David Hume that he awakened him from his dogmatic slumber. What he meant was that Hume showed how far empiricism had not really solved the problems, and that it too required a philosophical infrastructure in order to ground it, and this had not yet been done.

When Kant set out to solve the problems Hume posed, he began by redefining them. First, he introduced two distinctions between different types of propositions: the distinction between a priori and a posteriori propositions, and the distinction between analytic and synthetic propositions. The first distinction concerns the question of how we come to know the proposition in question, that is, it concerns the plane of cognition: a posteriori propositions are propositions that are learned from observation, that is, from experience. For example, the sun rose this morning. By contrast, a priori propositions are known to us without the need for experience (they are prior to experience, a priori), for example, two magnitudes equal to a third magnitude are equal to one another. The second distinction concerns the character of the propositions themselves: analytic propositions are propositions that can be derived from the definition of the concepts involved in them. This is in fact the result of conceptual analysis. For example, every triangle has three angles. One can say that an analytic proposition does not contain information beyond what is implicit in the concepts that appear in it, that is, it does not add any new information. By contrast, synthetic propositions are propositions for which conceptual analysis is not enough in order to know them. For example, there are human beings taller than 1.80 meters.

What is the relation between these two distinctions? Seemingly they are independent, since the first concerns the way in which we come to know the proposition, whereas the second concerns the propositions themselves. The first distinction belongs to the field of epistemology, whereas the second belongs to logic (the structure of the proposition and its nature).^[15] But when you examine these two distinctions through examples, you very quickly discover that they actually overlap. That, at least, is what people thought until Kant. Every analytic proposition is a priori, since if it follows from the definitions of the concepts involved in it, why would we need experience in order to know it?! And every a priori proposition is analytic, since if it is known to us without experience, it is probably the result of analyzing the concepts involved in it. These two claims are enough to prove an identity between the distinctions (exercise for the reader: prove it).

Now Kant returns to Hume’s problems (induction and causality) and formulates them in the new terminology he developed here. When we look at some law of nature, it is always a synthetic proposition, since it cannot be derived from conceptual analysis alone; otherwise it would be mathematics and not science. If so, we would expect it to be a posteriori, that is, built on experience. And indeed, modern science really does build the laws on experience. But as we saw above, this is not precise. Experience brings us specific facts, such as values of force and the acceleration that develops from it. But from where does the general law, the theory, or the law of nature come? That is always built on generalization, and perhaps also on considerations of causality. Thus observation yields the points on the graph, but from there to the theory there is a non-empirical process: generalization. We make different generalizations and choose the simplest among them. This is not an analytic procedure, since the generalization is not contained in the particular facts on which it is built; and on the other hand, it is not itself an experimental or observational procedure, but a purely intellectual one. It takes place within us and not out of any interaction with the environment. Generalization is an a priori procedure. We thus learn that all the laws of nature are synthetic propositions (which contain information about the world, beyond the concepts involved in them) on the one hand, but on the other hand experience alone is not enough in order to reach them (although experience is of course involved in this), that is, they are a priori. Therefore Kant concluded that the laws of science belong to the category of the synthetic a priori. But as we saw above, this category does not really exist, since seemingly everything synthetic is a posteriori and vice versa. Kant was basically claiming that all the problems Hume raised can now be formulated in a completely general way: How are synthetic a priori propositions possible? This is Kant’s problem of the synthetic a priori, which is nothing but an overall translation of the collection of Humean problems.

On thought and cognition: fit between the human being and the world

Let us try for a moment to understand the meaning of this formulation. A synthetic proposition is a proposition that contains information about the world, or rather that adds information about the world (beyond what is implicit in the concepts or what we directly observed, that is, beyond the particular facts, or the points on the graph). On the other hand, as Hume showed, the laws of nature, which are synthetic propositions, become known to us in a way that includes elements of thought and not only pure observations. If so, it turns out that we are actually accumulating information about the world by means of thought (beyond observation), and that is seemingly impossible. After all, empiricism and modern science taught us not to rely on thought as a tool for knowing the world. The essence of empiricism, which replaced the naive and failed rationalism amid great fanfare, is that in order to know something about the world one must observe it. This approach brought about the emergence and progress of modern science.

And suddenly it turns out, not by someone else but by one of the greatest empiricists, David Hume himself, that empiricism suffers from exactly the same problem. It is only a different garment for the rationalism that was rejected in its favor. In fact, we are once again walking along paths paved within our minds, and the feeling that we are sticking to observation and experimental facts is nothing but an illusion. We are not really empiricists but hidden rationalists.

We have once again returned to the most basic philosophical problem that accompanied rationalism. It turns out that the generalizations made by empiricism also assume that there is a fit between our thinking and the world, and therefore the questions that empiricism itself hurled at rationalism and claimed to offer a solution for immediately return to it like a boomerang: how do we know? On what is this wild assumption based? The forms of my thinking are derived from the way I am built. I could have been built entirely differently, and then I would think in different ways. So why should the fact that I think in a certain way lead me to the conclusion that this is indeed how the world behaves? Why assume that there is a fit between the way I think and the way the world itself is conducted?

The "theological" solution: the argument from epistemology

The only solution that can be proposed for this difficulty is a "theological" argument in the style of Taylor’s argument from the previous chapter, and it proceeds as follows. If we thought that our thinking was formed in a blind and random process, it would not be logical to assume that it functions reliably, that is, that its products really reflect what is happening in the world itself. As we saw in Taylor’s argument about the eyes, here we extend this to the whole form of our rational and scientific thought. Our abilities to generalize, to identify causal relations, and in fact to define the concept of cause itself and to be aware of the principle of causality—all of these are themselves products of our way of thinking. If this were the product of a blind and random process, there would be no logic in trusting any of it, that is, in assuming that what is produced by our rational thought (the theories, or the laws of nature) is correct, that is, corresponds to the way reality itself behaves. From here, two paths open up: 1. to give up this trust. 2. to continue to trust rational thought, and thereby in fact to assume that our thinking, just like our cognition, was not formed in a blind process.

This is exactly Taylor’s argument, except that this time it does not revolve only around our eyes, and not only around the whole of human sensation (sensory cognition) as we suggested earlier, but also around all our rational and scientific thought. Our trust in rational thought is based on the assumption that these tools were not formed in blind and random processes. There is an intelligent factor that formed them, and this is the basis of our trust in them.

We have arrived here at the broadest formulation of the argument from epistemology. We moved from the eyes to the totality of our sensation and finally to all rational thought. Our ability to think and know the world in this way implicitly assumes the existence of an intelligent factor that created it and that "guarantees" its reliability. As we saw in the previous chapter, even someone who does not declare himself to be a believer in such an entity, the very trust he places in rational thought indicates that he has an implicit belief in the existence of such a factor, perhaps not consciously. The logical move and the analysis of this argument are completely parallel to what we saw in the previous chapter regarding Taylor’s original argument, and I will not repeat that here.

In order to complete this argument, we have to examine the alternatives. Perhaps there is another explanation for the fit between our thought and the world? Only after we rule out the alternatives will we be able to say that there is no escape from the assumption that at the foundation of rational thought there lies an implicit belief in the existence of an intelligent factor that is responsible for it and for its reliability. Surveying all the possibilities is beyond what can be done here, and therefore we will make do with sketching the principal lines.

On the "theological" character of the Kantian consideration

It is worth paying attention to Kant’s formulation mentioned above. When he asks how synthetic a priori propositions are possible, he states that the wording of the question is this, and not whether they are possible. He assumes that they are possible, since his trust in rational and scientific thought was firm and clear, and therefore he takes the opposite route. Such propositions are certainly possible, since all the laws of science are of this kind. Now he asks what our trust in them is based on, that is, how can it be that they are possible? Thus the greatest philosopher of the modern era declares here consciously and before the whole world that he is acting in a "theological" way, from the conclusions to the assumptions, and not the other way around. So what will those who rail against "theology" answer?…

At the beginning of the first chapter I brought the distinction between philosophy and theology, as though in philosophy one starts from assumptions and derives conclusions from them, whereas in theology one starts from conclusions and derives assumptions from them. I argued there that in philosophy too, in many cases, the conclusions are assumed and the assumptions are derived from them. The clearest example is Kant’s consideration described here. Kant himself does not ask whether synthetic a priori propositions are possible, but how they are possible. Despite the great difficulties Hume raised with regard to such propositions, he assumes that they exist and merely goes backward and looks for a conceptual framework that will justify this. He does not start from the framework and derive from it the existence of synthetic a priori propositions, but takes the opposite, the "theological," route. Therefore I argued that the more important distinction is not the one between theology and philosophy, but the distinction between "theology" and "philosophy" as directions of argument. This is the thread that runs through the entire course of this notebook.

Kant’s own solution

The solution Kant proposed is based on a distinction between the world and things as they are in themselves (the noumenon) and the world and things as they appear to us (the phenomenon). His claim was that the laws of science, and our rational thought in general (including the principle of causality and induction), deal only with things as they appear to us and not with things in themselves. This is how he explained our ability to apply processes of thought to describing the world. In fact, they do not describe the world but the "world" as it appears to us. I will not enter into the details of this proposal, since, as many have already remarked, it did not succeed in presenting a real solution to the problem. The interested reader is referred here to the discussion in my books Two Carts and a Balloon and Truth and Not Stable.

A bird’s-eye view of the miserable state of epistemology

Shmuel Hugo Bergman, in chapter 9 of his book Introduction to Epistemology,^[16] surveys all the attempts proposed throughout the history of philosophy to answer this difficulty. In that chapter there appears an illuminating description of the philosophical contortions surrounding the "miracle" of the fit between human cognition and the world outside us, but in the end he finds no philosophically adequate answer to it. All the thinkers, including Kant himself, define this as a "miracle" or a special "grace." But for some reason they are not willing to acknowledge the giver of that grace, that is, the implicit assumption at the basis of this miracle that there is an intelligent factor responsible for it. Of such a case the Sages said: "The beneficiary of the miracle does not recognize his miracle."

The field of philosophy gives the impression that there are many varied philosophical systems, and that anyone can adopt whichever one seems right to him. Moreover, there is really no way to decide among them. Every philosopher with his own method, and each of us with his own opinion. Unlike science, which subjects theories to empirical tests of refutation, philosophy is condemned to wander among all the possibilities and not advance. Therefore it is so important to focus and sharpen the following point: with regard to the utterly fundamental question of the fit between the human intellect and the world, there are not many philosophical approaches. Only the Kantian answer seriously attempts to answer this question, and as stated, it too fails to do so. I have already mentioned that many philosophers have challenged and continue to challenge Kant’s determinations and proposals, but I do not know of any who offers an alternative to these determinations, that is, another explanation for that wondrous fit between human cognition and the world (what Bergman calls in the title of that chapter the world’s "intelligibility"). Astonishingly, throughout the history of philosophy no other alternative grounding for human epistemology has been proposed, but the obvious way out of an intelligent factor that takes care of this is contemptuously rejected by many.

Even Bergman, there in his book, when he describes how epistemological thought remains in incomprehensible perplexity at this point, does not even mention the possibility of an intelligent factor, except in one place in the chapter, and even there only by way of negation. And so he writes there (page 182):

Yet if all these attempts have failed, then Hume’s claim remains in full force. The principle of the regularity of nature, the supreme principle of science in general and of natural science in particular, this principle that lies at the foundation of every inquiry (induction) in science, remains without proof.

I would note that "lack of proof" in this context is too weak an expression. After all, we all trust our thinking and the fit between it and the world, despite the fact that there is no reason in the world to do so. This is not a matter of something unproven, but of something absurd and devoid of logic. At the beginning of this chapter we distinguished between two kinds of doubt: one based on lack of information and one based on contrary information. The question of the fit between our thinking and the world is not based only on lack of information. After all, if we assume the blind and arbitrary formation of our brain and our sensation, there is no reason in the world to assume that they are indeed reliable. It is not only that we have no proof for this claim, but that there is a very strong argument against it.

Bergman goes on there and writes:

If we do not wish to cut the Gordian knot of proving the world’s intelligibility by means of a metaphysical assumption, such as God’s guarantee (Descartes) or pre-established harmony (Leibniz) or the activity of the intellect upon the sensation prior to consciousness (subjective idealism), then no other way remains before us but to regard the intelligibility of the world as a regulative assumption directing the path of science.

He rejects, without any argument, Descartes’ proposal of God’s guarantee, even though he himself repeatedly explains that this is the only proposal that can do the job. His conclusion, according to which this is only a guiding assumption and not a claim about the world as it is in itself, takes us back again to the realms of pragmatism, which we shall address immediately.

Here it is worth noting that Bergman himself speaks here in a "theological" way. He assumes a priori that God is not a relevant explanation (although this is the only explanation that exists), and now looks for another possible way out (and of course does not find one). I have written more than once that atheism is sometimes more "theological" (it clings a priori to its conclusions and looks for a de facto justification for them) than faith.

It is interesting to note that in another of his books, Thinkers of the Age, Bergman retracts this position and argues that only belief in God can provide a reasonable basis for the fit between cognition and the world, since this is the only reasonable basis for epistemology. There he truly understands that there is no other rational solution to this issue, apart from the solutions of Descartes and Leibniz (the main points of Bergman’s argument are summarized in the introduction to that book). This is exactly what we have called here "the argument from epistemology."

Back to pragmatism

We have already touched on the question of pragmatism above in chapter 1. We saw there that "theological" arguments give off a pragmatist smell, since we seemingly choose, in an arbitrary way, assumptions that lead us to the conclusion we want to occur. There we distinguished between three situations: the first is a philosophy that identifies the useful with the true. In the absence of truth, it defines the useful as true. This is a fallacy or just wordplay. There are people for whom some belief from a metaphysical source leads them to the conception that the useful is the true. They have information from some source, or a concrete reason to assume that the useful is an indication of truth. For example, if religious belief leads them to the conclusion that God governs His world in this way. A third, more clear-eyed possibility is to say that it really is not the true but the useful, without presenting this as an identity.

It seems to me that Bergman’s intention above is to make the third claim. The meaning of this, as many before and after him have argued, is that scientific methodology and rational thought are a kind of rules of the game, and therefore they are not to be discussed in terms of truth or falsehood. According to this approach, science does not seek truth, but products that follow from the methodology it has, for some reason, chosen to adopt. This methodology is not true in any sense, nor is it false. It is a system of rules that creates a language in which it is easy and convenient to organize the information in our possession. Therefore the laws of nature and the scientific theories that are created in this way are also only an organizing framework for facts and not claims about the world.

We already encountered this approach above in this chapter, and we saw there that it is grounded in consistent empiricism. Empiricism argued against rationalism that information about the world can be accumulated only by means of observations. If so, everything beyond what we observed is not worthy of being considered information. This consistent empiricism maintains that only specific facts that we directly observed are reliable information about the world, but the laws created by the generalizations we make from those facts (which, as stated, are not an observational means but a mental one) are only efficient ways for us to organize the observational information. If scientific methodology (like the principle of causality and induction) is an organizing set of rules, then the laws of science are nothing but a framework created by these tools within which we organize the information we have observed. According to this approach, the straight line drawn on the graph presented above is not a claim about the world. The scientific finding does not say that in the world there is a linear relation between force and acceleration, but only that the facts we have observed thus far display such a relation. The claim that there is here some general principle is only a manner of speaking and nothing more.

Is pragmatism really a solution?

This claim does not hold water, and one can see this easily through the example of the graph above. Pragmatism holds that the laws of science are organizing rules for information we have already observed, and not claims about the way the world behaves (including in other cases we have not observed). If that were true, then the generalizations we make would have to fail every single time. If the straight line on the above graph is merely an arbitrary product, one line among many other possible ones, then what is the chance that in the next experiment we conduct the relation between force and acceleration will also fall on that line? Of course, negligible. After all, the true line could be one of countless curves passing through the points we have observed. The straight line is only the simplest among them, but simplicity is not a criterion of truth. So how can we explain the fact that the predictions of scientific theories and laws are confirmed again and again in laboratory experiments? There are, of course, failures, and in certain cases the theory is replaced by another, more successful one. But the rate of successful experiments is certainly not negligible, whereas if the generalization were an arbitrary act (a game), we would expect almost no experiment to succeed. Every experiment we performed should have failed and led to the replacement of the theory, and so we would be moving in circles among different theories, jumping from one to another, but progressing in no sense whatsoever. This argument is discussed in greater detail in appendix B to my book God Plays Dice. In other words, remarkably, this "game" simply works. Again and again, the use of these "arbitrary" rules leads us to theories and laws of nature that are confirmed in laboratory experiments. Does this not mean that this is not an arbitrary game? Does it not mean that our principles of generalization reflect some truth, and that they are not merely arbitrary rules of the game?

Someone may now come and make this claim against the argument from epistemology. After all, this argument is based on the claim that we have no reason to trust our rational thought if, according to our assumption, it was formed arbitrarily and without a directing hand. Here, ostensibly, another possible answer arises, namely that we simply learned from experience that this works and therefore place trust in it. The fact that experiments testing our scientific generalizations stand up again and again to the empirical test is what causes us to trust these principles. If so, we have another explanation for why trust should be placed in our thinking, and we do not need to arrive at the assumption that there is an intelligent factor responsible for this.

But there is a double mistake here. First, we are using learning from experience in order to justify the validity of learning from experience. The induction that learns from what happened in the past to the future is itself based on induction that learns from the past to the future. This is, of course, a circular justification, and therefore it is philosophically inadmissible.

Second, even if we adopt the conclusion from our experience that this fit really exists and that all this works, we still have not answered the relevant question: why does all this really happen? After all, if our mind is the product of an arbitrary and blind process, there is no chance that its products would be so reliable. The fact that it works is a clear indication that its formation was not accidental. This is in fact the physico-theological argument in its "philosophical" form, which we dealt with in the previous notebook.

Let us note that the mistake here is very similar to the one we saw in the previous notebook regarding the anthropic principle. The physico-theological argument proves the existence of a directing hand from the complexity and tendency of the laws of nature in the world (which are directed precisely toward the creation of life). The atheist rejects this by saying that if these were not the laws of nature, we would not be here to wonder about it. We saw there that this is nonsense, for it returns us to the other side of the attack: how did such special laws really come into being, laws that allow life and human beings to come into being and live (and raise questions)? Does this not constitute an indication that there is a directing hand that created them?!

We once again see that the argument from epistemology is in fact an attack built in the form of logical pincers: if we trust our thinking, this shows that we have an implicit assumption that it is not the product of an arbitrary and blind process. And if we explain this trust by learning from experience (the fact is that it works), then this itself is the argument from epistemology: what is the explanation for the fact that it works? If it was formed arbitrarily, it should not have worked. Exactly as we saw in the summary of chapter 4, the "philosophical" argument and the "theological" argument are two arms that attack atheism in a pincer movement. The honest atheist must do one of two things: either give up his trust in rational thought and in his cognitive tools, or retract his atheism.

1. The book of the universe is written in the language of mathematics

Introduction

In this chapter we will look at the argument from epistemology from another angle. Galileo is credited with the saying that the book of nature (or the universe) is written in the language of mathematics. This saying presents the wonder that quite a few scientists and philosophers have dealt with: mathematics, which is an artificial language created in light of our tools of thought, succeeds very well in describing what is happening in the world. Already here we can say that in fact this is another expression of that same fit between the form of our thinking and the conduct of the world, and so it seems at first glance that here too a physico-theological argument is hidden.

Sharpening the question

Galileo’s question has received countless repetitions and formulations, and quite a few attempts at an answer. I know of fewer attempts to sharpen the question itself. Is it a wonder that the English language succeeds in describing what we wish to describe? Usually we do not see this as a great "miracle." The language was created for that purpose and built in a way that suits this goal. The very emergence of a language and the ability to communicate between people is indeed a kind of wonder, but that is not what we are dealing with here. This is just one more astonishing human ability, and it can certainly be added to the collection of phenomena (rational thought and sensory cognition) that constitute the argument from epistemology. So why is the fact that the mathematical language is suited to describing the book of nature perceived as more astonishing? To understand this, it is important to distinguish between science and mathematics, and between two different roles of mathematics: as a field that stands on its own and as a servant of scientific discourse and research.

In a nutshell, one can say that mathematics is a field whose essence is a meticulous logical and systematic examination of collections of concepts (and their definition), basic assumptions, and rules of derivation. In number theory we examine the properties of numbers and the basic operations on them, and we try to ground this on a defined and relatively small collection of basic rules. The same is true of geometry, which examines the properties of space by constructing a logical structure containing basic concepts (point, line, area, triangle, angle, and the like), axioms (most or all of which describe the space with which we are dealing), and rules of inference. The same is true of the other fields of mathematics.

By contrast, in the scientific context mathematics serves as a kind of language. We are accustomed to describing the laws of science by means of mathematical equations, where the variables are the magnitudes and properties dealt with in the relevant scientific field. This is especially prominent in physics, where all the laws are formulated in the language of mathematics. Is there any wonder in this? It seems not especially. Exactly as we saw regarding the English language, so too the mathematical language is built by physicists in order to describe the phenomena about which they want to speak and which they want to examine. Therefore there is no great wonder in the fact that the mathematics they use succeeds in doing so. It was developed for that purpose.

Moreover, in principle language is not essential to any scientific field, including physics. We could have engaged in physics by means of a completely different language, mathematical or otherwise. Moreover, it is only reasonable that other creatures endowed with forms of thought different from ours would have developed a different language in order to do so, and perhaps would have succeeded in this no less than we do.

Radical feminist criticism claims that men’s success in physics is the fruit of a male plot. Physics is simply built in a masculine way, and therefore there is no wonder that men succeed in it more than women.^[17] The same applies to minorities who think in a different way and therefore succeed less in exact science or in any other field. Not to mention the psychometric exam, which also absorbs many criticisms of this kind (that it is biased, because it is adapted arbitrarily, and perhaps also conspiratorially, to certain types of populations and forms of thought). Many are outraged by this criticism, and Gadi Taub even writes that he would not want to fly in an airplane built on the foundations of female physics. What he means is that physics is not the fruit of a plot. There is one physics, and its foundation lies in physical reality, that is, in reality itself. The fact that it is structured in a certain way is not the fruit of a plot, but simply a fact that is given to us and not in our hands. A different physics would simply be false. Is that not the meaning of referring to physics as an "exact science"?

Despite my lack of sympathy for these poor criticisms, somewhat surprisingly my answer is no. In principle, the very same physics could have been formulated in different terminology, and even in a different language, and then perhaps different people would have done better at it. One can raise the possibility that this is not a different physics, but a different formulation of the very same physics. The facts would not change, but they would be described within a completely different conceptual framework, perhaps even without mathematics at all.

As an example, think about a description of geometry, or of the properties of two-dimensional space, in different coordinate systems. In a Cartesian system we describe every point by means of an ordered pair of numbers that represent the projections or components on the X-axis and the Y-axis. This description was proposed by René Descartes (Cartesius), and therefore it is called a Cartesian description. But one could just as well describe the point by means of a different pair of numbers, for example: its distance from the origin, and the angle formed between the line from the origin to it and the X-axis. Such a description is called polar, and it turns out to be completely equivalent to the Cartesian description. Every point has a unique representation in terms of each of these descriptions.^[18] Now someone may come along and claim that his form of thought is polar. He cannot operate within a Cartesian framework and therefore finds geometry difficult. If we translated all our claims into the polar language, he would be a flourishing and very successful mathematician. Is such a claim absurd? Not at all. It would be the very same geometry, and every theorem that was true in the polar description would be true in the Cartesian one, and vice versa, and yet these are two different languages. Theoretically, all this might perhaps be described in non-mathematical or entirely non-formal terms. A person with a different kind of mind would describe geometry in his own language, and if mathematics were not present in his mind, he would not use it as the language for describing geometry or science. But he would be speaking about the very same geometry and the very same science.

For example, Newtonian mechanics is based on an analysis of several fundamental physical quantities: position, time, velocity, acceleration, force, momentum, energy, angular and linear momentum, and so on. All of this begins with position and its mathematical derivatives (velocity and acceleration). If the system of basic concepts we used were different, perhaps something totally unfamiliar to us, there is no obstacle to our obtaining a description of those same phenomena in different terminology and by means of utterly different laws and tools. Even in our own physics the same problem can be handled in several ways. Some prefer an approach by means of momentum and energy (conservation laws), while others prefer Newton’s laws of motion (the relation between force, velocity, and acceleration). These are equivalent descriptions, but it is certainly possible that one creature would be very gifted in research that uses the language of the laws of motion, while another creature would do better with a description in terms of momentum and energy. This happens even between two human beings like us, and certainly when we are speaking of two different kinds of creatures (as is well known, "Men are from Mars and women are from Venus").

These matters can be connected to a field that has been developing greatly of late: the study of multiple intelligences. The basic assumption there is that different people have different kinds of intelligence. Some of the conceptions there are utterly mistaken, and some are based on political correctness (so everyone comes out equally talented and equally successful. What’s wrong with that?), but there is still one correct point there: different people can handle the same problems with different tools and in different languages. Therefore, the feminist criticism of masculine physics is not absurd. It is entirely possible that there is another formulation of physics within which דווקא women would succeed and advance more. Of course, instead of criticizing they should simply find this alternative formulation, that is, prove its existence constructively, and not merely whine and claim that it exists (an obviously non-constructive claim). But at the level of principle, this really could be true.

If we return to the question of the use of mathematics in research and in scientific discourse, we return to the starting point. It is a language, and obviously it was developed by human beings because that is how we and our thought are built. Therefore it is no wonder that this language is suited to its scientific uses. We developed it for that purpose, just as we developed English or Hungarian.

A demonstration of the two functions of mathematics

I mentioned that mathematics is also an independent field that deals with collections of concepts, rules, and their properties. Mathematicians are not scientists, since their claims do not stand the test of empirical falsification. There is no way to refute Euclidean geometry, or number theory, scientifically by submitting them to an empirical experiment.

To be sure, some readers will certainly raise an eyebrow, since these fields apparently make claims about the world, and therefore those claims certainly can be true or false. For example, number theory yields 2+3=5. Can this not be tested experimentally? Of course it can. One simply takes two oranges and puts them into a bowl, then adds three more oranges, and counts how many oranges are now in it. If we find five, we have corroborated the law 2+3=5, and if not, then we have refuted it. Geometry too describes the properties of our space. Therefore, here as well, one can simply check empirically whether the sum of the angles in every triangle we draw is indeed 180, or not.

In chapter 4 of my book God Plays Dice I explained why this is not correct. Thus, in mechanics we apply forces to a body and it turns out that their sum does not obey the laws of arithmetic. For example, two forces act on a body: one force of 2 newtons northward and another of 3 newtons eastward. What is the total force acting on the body? It turns out not to be 5, but something between 3 and 4 newtons. Has the claim 2+3=5 been refuted here? Certainly not. What has been refuted here is the implicit assumption that arithmetic is the mathematical tool that correctly describes the addition of forces in mechanics. It turns out to be an unsuitable tool, and we must use a calculus called vector analysis, in which there are different laws of addition. The same is true of geometry. According to general relativity, Euclid’s laws of geometry do not hold exactly in our world (although they are a pretty good approximation in most of space). Does this refute Euclidean geometry? Certainly not. It only means that it is not the tool that correctly describes our world (our space is "curved").

These two examples demonstrate three things: 1. Mathematical fields have an independent existence that is not subject to empirical tests of falsification, since they do not deal with our world. 2. Mathematics is a successful language that correctly describes broad parts of our reality. 3. And yet, even if these mathematical laws are apparently "refuted" empirically, we will not give them up and we will not say that they are untrue. They are true, just not in our world. Where, then? In some Platonic world that describes our way of thinking. Here we will have to replace the language.

If so, the independent existence of mathematics is due to the fact that it deals with relations among forms, ideas, and concepts in some Platonic world. There it is certain and eternal and cannot be refuted. This is not at all surprising. It is the relation among the concepts and ideas, and it follows from an analysis of them themselves (these are analytic propositions^[19]). Its use in science is in the role of a language, and therefore it may or may not be suitable for that purpose. In mathematical terminology, we would say that science may be a model of the mathematical theory, and it may also fail to be such a model.

The way to check whether a certain mathematical field is suitable to serve as the language for a certain physical field is by means of observations. If it turns out that this physical field satisfies several fundamental principles, and contains several concepts that are defined in a certain way, then a mathematical analysis may show us a great many additional properties that will necessarily also hold in the physical world. For example, if our space satisfies the axioms of Euclidean geometry (as stated, according to relativity it does not), namely that parallel lines do not meet and that only one straight line passes through any two points, and so on, then one can show by mathematical analysis that the sum of the angles in every triangle we draw will be 180, and also that in every right triangle we draw the Pythagorean relation among the squares of the side lengths will hold, and so forth. An entire collection of geometric theorems developed by mathematicians throughout history will at once turn out to be true of our world. This is the great advantage of mathematical language. It is enough for us to check five properties of our space, and from them we can infer countless further properties that must hold in it.

Back to the question of the book of nature and mathematics: another look at the argument from epistemology

We can now ask whether there is nonetheless something surprising here. The fact that mathematics is what it is is not surprising at all. It is the relation among these concepts and ideas. Moreover, the fact that geometry correctly describes (approximately) our space is not surprising either. If our space does indeed satisfy the axioms of geometry, then it is no wonder that it also satisfies all of its theorems. After all, they necessarily follow from the axioms.

What is surprising is that more and more fields that were developed independently in mathematics find applications in various scientific disciplines. Reality serves as a model for quite a few mathematical theories. Here we must distinguish between two different cases: a. Geometry was developed מתוך looking at space, so it is no wonder that it was found useful in describing it. The same is true of number theory. b. But group theory, Hilbert spaces, or Minkowski transformations are fields that were developed in mathematics without any practical orientation. And yet, after some time, it turns out that they are very useful in various branches of physics.^[20]

To understand the nature of the difficulty, one must remember that mathematics basically expresses the way our thought is structured. If it is not born from observations, it is probably created from our reflection on principles of thought and our conceptual analysis of various concepts found in our mind. And yet, these structures, whose source is our thinking, are found to correspond to ways in which the world itself behaves. So we have again returned to the fit between our thought and the world, and to the argument from epistemology. The mathematical language in which the book of nature is written joins the set of marvels that express the fit between the way we think and the world. As stated, if thought is the product of a blind and accidental process, it is unlikely that such a fit would obtain between it and the world, that is, that it would be reliable.

1. Objections to the argument from epistemology

Introduction

In this chapter we will deal with possible objections to Taylor’s argument, and in fact to the argument from epistemology in general. Most of the objections are a mirror image of the objections to the physico-theological argument (in the "philosophical" formulation) that we dealt with in the previous booklet, and so we will not dwell on them again here. Our aim here is mainly to sharpen still further the relation between "philosophical" and "theological" discussion, through the similar yet still different ways of addressing objections in these two kinds of discussion.

Two main directions of objection

We have already noted that the argument from epistemology is a "theological" formulation of the physico-theological proof. It is based on the fact that we trust our sensory cognition and our rational thinking, and that this trust is not justified if one assumes that our thought and cognition developed in a blind and accidental way. A random formation can create any sensory and cognitive system whatsoever, and therefore the chance that reliable systems would arise (systems coordinated with the world itself) is negligible. Hence, if we do place such trust in our sensation and thought, this means that we have a belief (implicit, and not always conscious) in the existence of an intelligent factor that created this thought and cognition and saw to it that they would be reliable (that is, in accord with the way the world itself operates).

There can be two directions of objection to the proof for the existence of such a coordinating factor: 1. Trust in the senses and cognition because of accumulated experience. 2. Evolutionary arguments. In this chapter we will address these two objections briefly.

1. The first objection: trust as a result of accumulated experience

We already mentioned that, ostensibly, the atheist can argue that although he does not understand how the senses arose, and in his opinion this happened in a blind and arbitrary process, he still has justification for the trust he places in the senses, since his accumulated experience shows that this indeed "works." On the basis of this reasoning, one can ostensibly justify trust in the senses and in cognition generally without recourse to belief in a coordinating factor.

Rejections of the experiential objection

We have already dealt a bit with this objection, and explained that it contains a double mistake. The first is that it is a circular argument. The second is a mistake similar to what we saw in the previous booklet in the discussion of the anthropic principle. Even if we accept learning from accumulated experience, that does not relieve us of the need to wonder how it happened that our senses and thought really do work with such high reliability. After all, the chance of such a thing happening by accident is negligible. This is precisely the "theological" argument (the inverse counterpart to Hoyle’s airplane and Paley’s watch, which express the regular, "philosophical," physico-theological argument). We saw that the two formulations in fact attack atheism in a philosophical pincer movement, created by the "philosophical" and the "theological" formulations. This objection is directed against the argument from epistemology, and it runs straight back into the ordinary design argument: even if we accept experience as the basis for our trust in the senses, that still does not solve the question of how it really came about that our senses, which were produced blindly, work reliably. Here we have returned to a kind of physico-theological proof.

But beyond that, there are also several refutations on the merits. Even if reliance on accumulated experience were a good refutation of the argument from epistemology (and it is not, as we saw in the previous paragraph), this very claim that learns our epistemology from accumulated experience suffers from several flaws.

First, it does not seem that our trust in the senses increases with the years. If this were a matter of accumulated experience, we would expect a young child, who has only a little experience, to have less trust in his senses and in his thinking. In reality the opposite happens: as we grow older we understand that our thinking and sensing sometimes deceive us, and therefore we must not place unqualified and uncontrolled trust in them. It seems that we are born with this trust, and it is self-evident to us. It is not the result of accumulated experience, although experience can of course strengthen the innate trust that we have.

Second, and I have already noted this as well, every experience that succeeds and confirms our trust in our senses and thinking is itself the result of that very trust. I see that my sense of sight works when I touch the object that I saw and thus become convinced that it really is there. If so, there is a reliance here on an additional assumption of trust in the sense of touch. Therefore I suggested treating the entire cognitive system as a single whole, and then asking what the basis is for our trust in this system. Of course, in that case we will not be able to bring any experimental proof for it that is independent of the senses themselves.

Third, our trust in accumulated experience is itself one of the parts of rational thinking. To sharpen this further, Hume’s questions about induction cannot be answered by saying that we trust our inductions because they worked in the past. This very learning from the past to the future is itself based on the principle of induction, and one cannot use it when trying to justify the principle of induction itself. It is a circle with its tail in its mouth. If our inductions are mistaken, then this justification for using induction is mistaken too, since it was also learned inductively from the past.

2. The second objection: the argument from evolution

Just as in the ordinary physico-theological argument, here too the atheist can argue that the basis for trusting our cognition and thought is the evolutionary process. In fact, the argument from epistemology assumes that if the formation of our cognitive and thinking tools was accidental and blind, it is unlikely that what was formed would be reliable and coordinated with what happens in the world. But evolution can offer an explanation of how a blind and arbitrary process secures a fit between human cognition and the world. Sensation and correct cognition have the highest survival value, and therefore one may assume that if we have survived until now, this is thanks to the fact that we were endowed with excellent cognitive and rational abilities. This seems to be a sufficient basis for adopting the information they convey to us. Evolution is what "takes care" of the fit between us and the world, and there is no need to assume the existence of an intelligent factor that did and does this.

In the "philosophical" formulation we saw that this objection does not hold water. Among other things, we explained there that evolution operates within a rigid system of very special laws that make such a process possible. The objection from evolution at most pushes us one step back to the question of who is responsible for that special system of laws, and that is how we formulated what we called there "the argument from the laws." But here our concern is with the "theological" formulation. The argument from epistemology is based on the assumption that accidental formation does not create a reliable system, and evolution shows that this is possible. Once we have reached the conclusion that evolution is a correct scientific theory, and certainly a possible one, we have a basis for the trust we place in the senses, and there is no need to assume the existence of an intelligent factor in the background. This can be joined to the claim of accumulated experience, and one can say that thanks to evolution we trust accumulated experience without necessarily needing the assumption that an intelligent factor exists.

A further sharpening of the second objection

Evolution may perhaps offer a possible explanation for why the senses are reliable, but the question posed by the argument from epistemology is not why the senses are reliable, but how we know that they really are. Even if our senses were in fact reliable, it is still unclear how we ourselves know this. What revealed to us the fact that our senses are reliable? As in Taylor’s formulation, even if there is a possible and plausible explanation for why the stones arranged themselves on the hillside without an intelligent factor, that is not enough to give that arrangement of stones our trust as an informational source. For us to trust the stone inscription, we must know from some independent source that this really is the mechanism that arranged the stones, and in addition we must know that this mechanism also sees to it that there is a fit between the content of the inscription and its location. In other words, we must know that this inscription really conveys to us the information that we are at the gates of Scotland.

But this argument can perhaps be rejected, since evolution is indeed such an explanation. If the evolutionary process is indeed as we understand it, then it really does see to it that our abilities will fit the world and thereby help us survive. This is a mechanism that not only creates eyes and a brain, but creates them in such a way that they will function well and reliably. That is the essence of the evolutionary explanation. It does not deal only with the coming-to-be of complex things, but with the fact that they are useful and function better in survival struggles.

A preliminary clarification

Before the discussion, we must preface that we are not seeking an explanation for the psychological phenomenon of placing trust in the senses and in thinking. Such a phenomenon can be a mere instinct that was created in us for some reason in the evolutionary process. Just as we may have a fear of the dark, and one can probably find various psychological explanations for how it arose (in the past robbers and predators ambushed us mainly in the dark), that does not justify this fear now. Such a justification would not mean that the fear reflects some real state of affairs (that there really is someone lurking for us somewhere in the dark). Likewise, even if we had an evolutionary explanation of how our trust in our senses and thinking arose, this would not constitute a justification for that trust. The question is not whether such trust exists as a psychological phenomenon. Of course it exists, and no one denies that. The question is why we think this trust is justified. If we are given an evolutionary explanation that shows how this trust arose, not only does this not constitute a justification of the trust, perhaps the opposite: it even gives us another reason to suspect that this is an illusion. Evolution implanted such a trust in us, but precisely because of that we have no independent way of knowing whether it is justified. Add to this the fact that we are creatures who are highly self-aware, and we know that evolution is what probably implanted such a feeling of trust in us. If so, we ought to suspect that trust itself and regard the trust dwelling within us as a mere illusion. The fact is that although we are aware of evolutionary processes, we have no suspicion toward our sensing and our thinking. It is not only that we have such trust; none of us casts any doubt on it at all.

From the assumption that our senses and thought are complex and reliable, one can build a regular physico-theological proof, that is, a "philosophical" one. This would be an argument that proves the existence of God from the complexity and reliability of our sensation and thought. But here we are moving in the opposite direction. The argument from epistemology is not based on the question of whether we have good and reliable senses and thought, nor even on the fact that we feel that they are indeed such. The question that the argument from epistemology asks is whether this feeling, that is, this trust, is justified, and how we know it. Alternatively, if we think it is justified, what does that presuppose?

We should note that in the next part of the booklet we will deal with the validity of morality, and there the focal point will be the distinction between a moral feeling and the claim that morality is valid and binding. There we will see that there is a difference between explaining why we have a moral feeling (which may be evolutionary), and the claim that there is an obligation to behave morally (which has no connection to evolution and cannot have one). There we will realize just how important this clarification is for understanding the course of arguments of a "theological" nature in general.

A second clarification

At the beginning of the discussion it is important to understand (and we already explained this in the previous booklet) that even if we adopt this objection, it does not refute the existence of God but at most this argument for Him. Even if the theory of evolution is correct, there still remains the possibility that God is what drives it and underlies it, that is, that He secures the fit between us and the world by means of evolutionary processes. If so, even after this objection the question of God’s existence remains open. But that is the nature of a proof. Clearly, an objection to it does not refute the conclusion, but at most this particular path to it. Here our concern is with examining the argument as such, and therefore we ask whether such an objection really does refute the argument from epistemology or not. I think it does not, and we will now see this through several rebuttals.

The circularity in this objection

The first rebuttal is that our trust in scientific theories in general, and in evolution in particular, is also based on our trust in sensation and rational thought. One who does not accept scientific thinking and the processes of scientific generalization and inference will not accept the theory of evolution either, since it was created by them. Therefore, when we come to explain our trust in scientific generalization, we cannot hang it on the theory of evolution. Darwin’s own trust in his cognition (before he discovered evolution) is what gave us the theory of evolution. This is of course an indication that our trust was not born with our acquaintance with evolution and does not depend on it. The opposite is true: our awareness of that theory depends on it. Any of us who asks himself why he trusts his senses will not be able to answer honestly that it is because of evolution. On the contrary, his trust in evolution was born from his trust in scientific procedures, that is, in our rational thought and scientific cognition. And again, evolution may have created the reliability of the senses, but it cannot be a sufficient explanation of why we trust them. We will now sharpen this further.

Trust in the senses throughout history

Someone who is unfamiliar with the theory of evolution, or alternatively a person who lived five hundred years ago when this theory was not yet known in the world, clearly did not trust his senses and cognition any less than we do today. So how did he explain to himself his trust in his senses and his thought? Was that person irrational? Did such a person harbor a feeling of trust because of evolution, but have to conclude that it was an illusion? Again, it can be said that this trust is a product of evolution. Even if the person was not aware of it, evolution implanted this trust in him. But our question here is not about the reliability of the senses themselves, nor even about our trust in them as a psychological phenomenon. Our question is about the validity of our trust in them, or how rational this trust is from our point of view.

The other side of the same coin is that when we teach a student or any other person today the theory of evolution, it is perfectly obvious that the strength and basis of his trust in his means of cognition will not change. It follows that the reliability of epistemology in our eyes does not depend on our belief in the theory of evolution. There is indeed room to say that this trust is based on the theory of evolution, but it need not necessarily be conscious to the person. We, as observers from the side, know that that person’s trust in his senses is based on evolutionary processes, even though he himself may not be aware of this. But that explains the presence of the feeling of trust within him, not his belief in the validity of that trust, as we clarified above.

It seems to me that if we say this, we present all the generations before Darwin as irrational. What did they think when they tried to give themselves an account of their trust in their senses? The evolutionary answer was not available to them. Rational and intelligent human beings of that period should have decided that they had no trust in their senses (that is, that this trust, which of course did exist in them as a psychological phenomenon, was nothing but an illusion). It seems that none of them denied that they did in fact trust their senses. My assumption is that those generations were not less rational, only less educated in certain respects (they did not know the theory of evolution). Therefore my conclusion is that even if none of them explicitly gave himself an account of this, the very fact that this question did not trouble them shows that they had an implicit belief in some coordinating factor, even if only implicitly. And since trust in the senses and its roots have not changed from then until our own day, it is likely that this is our basis as well.

And what about the theological explanation?

One can raise this argument against the alternative that hangs this trust on belief in God as well. After all, even when a person does not believe in God, his belief in his senses and in his rational thinking is not impaired.^[21] If so, what advantage does the explanation that hangs trust in epistemology on belief in God as a coordinating factor have over the evolutionary explanation?

Here there is an important difference between these two explanations. The claim of the argument from epistemology is that belief in God is found implicitly in every person, even if he denies it. He encounters and meets God unconsciously, and therefore he also assumes His existence without being aware of it. In contrast, trust in evolution ostensibly ought to depend on conscious knowledge of it, since we are dealing with a scientific theory whose source is observation. In order to become convinced of it, one must observe it and go through all the processes of scientific inference and formulation. In fact, this is the main point of the argument with which we are dealing here. The argument from epistemology tries to show a person that belief in God as a coordinating factor has long been present within him already. We are not trying to persuade him to begin believing, as is done in the "philosophical" formulation of the argument (as in the previous booklet). It is hard to say the same thing about a trust that we have in a scientific theory before we have studied it and encountered it.

The absoluteness of trust in the senses

Another rebuttal is based on the fact that our trust in the senses and in cognition is so absolute that it is not plausible to hang it on an evolutionary process. Evolution is a random process, and the outcome of a random process, even one with a character of natural selection, cannot be so airtight and unequivocal. Think for a moment about a situation in which you arrive in an unknown region, the only datum about which is that evolution operated there. Would you stake your money on the outcome of that process being completely reliable? Very doubtful. Our trust in vision is perfect. A person is not at all willing to accept the possibility that what he sees does not really exist. Therefore the conclusion is that it is highly implausible to build such trust on an evolutionary process.

Beyond that, there is also the consideration of the length of the process. After all, evolution is a long and complex process, throughout which the creatures that are produced become more and more sophisticated. Unsuccessful intermediate forms disappear, and other, better ones come in their place. When these fail in the struggle for survival, they disappear and are replaced by others. How do we know where we are situated in this process? Are we already at the point where our vision and our thought are perfect? And even if so, let us again remember that the argument from epistemology is "theological," that is, it does not ask whether our sensation and thought are reliable, but how we know that they are. An evolutionary explanation can at most persuade us that we are on the track toward reliable sensation and thought, but we assume that we are already there. We have full trust in our sensation and thought as though the entire evolutionary process had already come to an end. We are the pinnacle of creation. This is truly the antithesis of the evolutionary picture, which sees the human being as some incidental stage in this process.

And in general, who has guaranteed to us that the human being really has high survival value? We have no evidence that he will not become extinct at some stage or another, perhaps even very soon. After all, every mutation existed at some stage of the process and later became extinct. It too could have thought that it had high survival value, and as a result trusted its senses (and precisely because of that become extinct, since they were not reliable). It seems that there is not a sufficient basis for the assumption that our structure really does have high survival value. In any case, it certainly does not justify such perfect trust.

One can raise here the claim about sensory errors. For example, the phenomenon called "Fata Morgana," in which a person in the desert sees sights that do not exist in reality. If so, trust in the senses is indeed not so perfect. The same is true of seeing at a distance, or at night, where we know that our vision is not so perfect. If so, the argument about the reliability of the senses is ostensibly not so clear-cut. Indeed, our trust in the senses is not quite so decisive and unambiguous.

But this is a mistake. Even when a "Fata Morgana" occurs, every person always looks for explanations of why his vision failed. This is considered a pathological phenomenon, and therefore we seek explanations for it. Sometimes we attribute it to a mental state, or to the fact that it was night, or to deceptive distance, or to vapors that distort the sights around us in the desert, and so on. All these are rational explanations for it. No one entertains saying: "What’s the problem? Our vision does not have to be perfect. We are still not at the end of the evolutionary process, and so our vision sometimes deceives us." Our basic assumption is that vision ought always to work, and that only certain problems cause failures in vision. In light of the evolutionary assumption, the human being should have accepted with equanimity the fact that his senses sometimes betray him as a result of our still being in the middle of the evolutionary process. After all, this process is still not over. Moreover, these failures should also have appeared under varying circumstances, and not always when we are in the desert, or in the dark, or at a distance, or in any specific situation. In an evolutionary description, such failures should be expected even with a normal sensory structure, without any special problem. But with us, when failures of vision appear, we rush straight to the doctor. It is obvious to us that something has malfunctioned in us, since our vision in itself is perfect.

Do reliable sensation and thought provide optimal survival value?

Another rebuttal to this objection is based on the fact that maximum survival value is not necessarily obtained by correct vision but by useful vision. Accurate perception is not always what has the highest survival value. Sometimes a person survives better if he does not know reality as it really is. A sick person will sometimes survive better if he does not know his condition accurately. If someone close to a person has died, it is sometimes preferable (at least from the standpoint of survival considerations) that he not know this. A person walking at a great height and afraid, though there is no chance he will fall from it, ought not to see the depth beneath him. In such circumstances, do our senses indeed stop showing us reality properly, as should happen in light of the evolutionary process based on survival considerations? And in general, there is a maximal range to our vision. Was it determined by survival considerations or by other limitations? Clearly, if we saw farther we would have a greater capacity for survival.

Summary of the rejection of the second objection

The conclusion that emerges from all these arguments is that every person who is not a complete skeptic, and apparently almost none of us are such, assumes belief in God as a coordinating factor implicitly at the base of the trust he has in his senses and in his own cognition. After the theory of evolution was discovered, those who want to rid themselves of the compulsion to believe in God try to hang their hopes on the evolutionary tree, but as we have seen this is a circular argument that also lacks real support. The basis and force of this trust remain today as they were before that, and therefore they probably reflect an implicit belief in a coordinating factor.

1. Summary: the relation between rationality and faith

Introduction

In this chapter we will summarize the argument from epistemology and its meaning. Here we will look at the relation between rational thought and faith.

Rational thought and faith

There is a common assumption that religious faith does not go together with rational thought. Many atheists certainly think so, but surprisingly many believers agree with them on this as well. A common saying is that where philosophy ends, faith begins. When various philosophical difficulties arise concerning religious faith, many take comfort in the idea that faith is above rational thought, and therefore is also not subject to the criticism of rational thought. The strict ones will add that if we could know and understand, it would not be faith but knowledge.

In the introduction to my book Truth and Not Certainty I defined fundamentalism as a view that places some principle, religious or otherwise, above critical thought. If so, what was described above is fundamentalism. At the end of that book I proposed a different view, according to which faith is simply knowledge, and it is exposed to rational criticism, and is even based on rational modes of thought, and of course is also not certain, like every conclusion of human rational thought. In this chapter I would like to summarize what emerges from this booklet and from the previous one regarding the relation between rational thought and faith.

The "philosophical" and the "theological" formulations

In light of everything we saw in the opening chapters, it is clear that Taylor’s argument, and also its expansion that we have called here the argument from epistemology, are arguments of a "theological" character. The "philosophical" formulation of the physico-theological proof places the existence of God on the basis of rational thought. We saw there that if one wants to avoid this conclusion, one has to give up some of the basic principles of rational and scientific thought, such as the second law of thermodynamics (or rather the logic that underlies it. We saw there that one could have managed with the law itself), the principle of causality, our trust in the power of scientific generalization, and more. We saw there that the conclusion that there is an intelligent factor responsible for the laws of nature and for the modes of behavior of our world arises from rational inferences that are very similar to scientific generalizations. The path from specific observations to the general law is completely parallel to the path from the character of the universe (complexity, fit, and the like) to the intelligent factor responsible for it. All these are in fact abductive inferences. Rational modes of thought led us to the conclusion that there is a God. In the "theological" formulation of the proof (the argument from epistemology), we saw the same thing from the opposite angle. Here we saw that God is what stands at the basis of our modes of rational and scientific thought. Without Him they have no validity. Here the relation is the reverse: only if there is God does rational thought have validity. God is what leads us to trust rationality.

This is precisely the relation we saw in chapters 2 and 3 above between "philosophical" arguments and "theological" arguments. We saw there that if the philosophical argument is: , then the "theological" argument is: . If A is that one should trust the validity of rational thought, and B is that there is a God (or an intelligent factor), then the "philosophical" argument takes us from rationality to God, while the "theological" argument takes us, by denying the consequent, to the conclusion that if there is no belief in God then one should not grant validity to rational thought.

In both of these moves we assume rational thought, that is, A. In the "philosophical" move we derive B from it, according to the first implication above. But in the "theological" move we proceed by way of negation: admittedly, it is not certain that there is a God, and perhaps we have no indication, and for the purposes of the discussion certainly no proof, that He exists, but if we give up His existence, that is, assume , then we necessarily arrive at the conclusion that there is no trust in rational thought, that is, . But this contradicts our assumption that A, and therefore we have here a reductio proof of B.

This effect resembles the difference between cause and purpose. Faith in God constitutes a rational basis for our other beliefs, whereas they constitute only an indication toward Him. Either way, rational people must believe in an intelligent factor responsible for what is happening here, what we call God. Alternatively, they can remain atheists, but then they will have to give up their trust in rational thought, that is, stop being rational.

The book of nature and mathematics

In chapter 3 I discussed non-deductive modes of inference, in which this reversal is also expressed. I explained there that these are the modes of inference that stand at the basis of our rational and scientific thought. This is how we infer theory from observations (abduction). We also saw that the basis for all this logic is the principle of simplicity, that is, the principle of Ockham’s razor. We have already wondered more than once why we should assume that simplicity is a criterion for truth, or indeed why what appears simpler to us often turns out, in many cases, to be what works in the world itself.

In the argument from epistemology, we saw that belief in the existence of an intelligent factor is the basis for our trust in scientific inference and scientific thought. The meaning of this is that the wondrous fit between the criterion of simplicity and the way the world itself operates is another reflection of the fit between us (or our thought) and the world. The argument from epistemology teaches us that this fit is based on an implicit belief in an intelligent factor responsible for it.

Chapter 1 dealt with logic and chapter 2 with science. "Theological" arguments in both these domains necessarily led us to an implicit belief in an intelligent factor responsible for them. The fact that the book of nature is written in mathematical language is one indicator of the existence of this factor, and it operates in the logical-mathematical, analytic domain discussed in chapter 1. Science is the second indicator of its existence, and it of course operates in the a posteriori or synthetic domain discussed in chapter 2.

Conclusion

In the previous booklets we noted that every argument in favor of God’s existence assumes a certain definition of Him. We have reached the stage at which we must discuss the question of who the God is whose existence we have proven in this booklet. Here we are not speaking about a God responsible for the complexity of the world (as in the physico-theological argument), but about a factor responsible for the fit between our thought and the world. This is a God focused on us rather than on the world, since He enables us to understand the world and function within it. One can say that this is essentially the God of rationality. To set faith in this God in opposition to rational thought is outright absurd. As we have seen, belief in Him is derived from rational thought, and indeed constitutes a condition for it. Without it there is no rationality.

We should note that although there is indeed, within religious faith, and especially in the transition from deism (= the philosophical God) to theism (= the religious, revealing, commanding God), a non-philosophical step, it is difficult to reach the revelation at Sinai and the meaning of putting on phylacteries by philosophical tools, which by their very nature are universal. After belief in God at the philosophical level, we must take steps of a different character in order to arrive at a more concrete religious God, but in the next booklet we will try to show that even these steps do not depart from rational thought and from rationality in general.

In the next part of this booklet we will already deal with the first step toward a commanding and more concrete God, the one that underlies moral obligation. We are still in the universal domain (we are not speaking of religion and particular commandments but of the imperatives of morality), but we are already speaking about a kind of commands and demands addressed to us, beyond the abstract philosophical belief with which we have dealt until now.

Part Three

The argument from morality

1. What is morality?

Introduction

In this chapter we will try to examine the nature of a rather elusive concept: morality. There are very many disagreements about it, and there are even those who doubt its existence, and certainly its validity. There are utilitarian approaches that ground morality in certain utilities, others speak about maximizing the good in the human being himself, in humanity, or in the world generally, and there is hedonism, which holds that a person should do what gives him the greatest pleasure. Egoism thinks that a person should act in a way that maximizes the various outputs he derives, and so on. Here I do not intend to examine which of all these is correct (except perhaps indirectly), and in this chapter I will also not ask what the source of morality’s validity is, nor even what criterion defines an act as moral or immoral. The only question I will discuss here is a categorical one, and it concerns the definition of the domain itself: what is morality at all?

To sharpen this, let us ask ourselves in what sense all the approaches described above are speaking about the same concept. Are Reuben, who holds that a person should act in order to bring the maximum utility to himself, and Simeon, who claims that he should maximize the good or utility for other human beings, and Levi, who thinks that he should do what gives him the greatest pleasure, even speaking about the same thing? Is there a disagreement between them, or are they speaking about different concepts? Ostensibly, these are different approaches regarding the question of what morality is and what the moral imperative is. But what is this morality, that is, what is the common thing over which the dispute is waged? One may perhaps ask this differently: ostensibly everyone agrees that one should do what morality obligates, but as long as we have not defined the concept of morality in a way accepted by all, one cannot really say that they are speaking about the same thing, and so it is also unclear whether there is any disagreement between them at all. Perhaps it is simply a dialogue of the deaf.

Initial characterizations

A person wants to make money, and in his estimation an investment in a certain security will yield him a handsome profit. He decides to invest in the stock market. Is this a moral act? Or perhaps an immoral one? Most of us will agree that on its face this is not an act that belongs categorically to the domain of morality. It is neither moral nor immoral, but neutral (perhaps depending on what that person later does with the money he earns). This is an action intended to fulfill an economic interest, not an action in the moral sphere.

Another person invests all his energy in helping the needy, but he does so because someone else promised him that if he did this for a month he would be given a huge sum of money. Is that a moral act? Not necessarily. Here too, in essence, we are dealing with the fulfillment of an interest. Again, there is no immoral act here, but it is hard to give that person moral credit for what he is doing. Everyone would do it with exactly the same zeal if they were promised the same sum of money. There is no real difference between him and a person who puts the same energy into his work as a building contractor or engineer.

A third person underwent hypnosis that programmed him to act in a wonderfully moral way, and afterward, all his life, he invests inexhaustible superhuman efforts in helping everyone around him. Are these moral actions? Many of us would say no, because he did not decide this but was programmed to do so. The matter resembles a robot that would do the same thing because of a program we planted in it. No one would say that such a robot acts morally.

A tycoon donates charity from his wealth to various social causes. This act too usually does not win high moral appreciation, and for two reasons: 1. Very often he does it for the sake of publicity and glorifying his own name. 2. He has a great deal of money, that is, the cost of his act is not high from his point of view.

The first example points to the type of acts we are talking about, that is, the definition of the domain to which moral questions belong. The following examples speak about the motivations and motives of the person who performs the acts and the way they are carried out. Bottom line: in terms of types of acts, an act is moral if it benefits human beings and immoral if it harms them. If it is neutral, then it is amoral. With regard to our evaluation of moral acts, we require that the person do the thing not in order to satisfy some interest of his own (to earn money, honor, or publicity), and that he do it by his own decision and not out of some kind of conditioning or programming. In addition, the moral esteem due to him is higher insofar as there is some cost to his doing it (that is, insofar as there is some difficulty for him in doing it). Ultimately, he must do the act out of a moral motivation. The intention underlying the act is very important for our moral evaluation of it.

What shall we say about a person who performs the act in order to gain the satisfaction of being a moral person? Many will say that this is a moral act, and the satisfaction is at most a harmless bonus. Perhaps it is even useful, since it will help him continue doing good. So why should we not say the same about financial profit? That too will help him continue doing good. After all, what matters is what the person does, and the motivations should be left to him. If he profits as well, what is wrong with that?

It seems that this is not correct. After all, we are still dealing here with acting for the sake of a self-interested goal, except that the interest is not money but satisfaction. How is that different from acting for money? Or from philanthropy for the sake of publicity, prestige, and power? All of these are benefits, and they are even worth money (a person is willing to pay a great deal in order to feel satisfaction and pleasure, that is, these are compensations equivalent to money^[22]).

To sharpen this further, I will bring here a parable once told by Amnon Yitzhak. The city rabbi got up early in the morning and slaughtered a sheep in the middle of the main road, covered it with a prayer shawl, and began wailing tearfully and crying out at the top of his voice over the righteous man who had died. The people woke up and looked out the window, and when they saw the scene they came down and joined the heartbreaking funeral procession, bitterly mourning the "righteous man" who had died. When they reached the cemetery and removed the shawl in order to bury the "righteous man," they saw that it was a sheep and became enraged at the rabbi. He did not understand what they wanted from him, and explained: "Whenever I rebuke you for not observing commandments and for various transgressions, you answer that you do not understand what I want from you. You explain to me that you are righteous people, since you do not rob and do not harm anyone. Perfectly righteous. If so, by this criterion this sheep too is perfectly righteous. It did not rob and did not harm anyone…" The meaning is that the act itself does not define a person as righteous. No less than what he does, the reason and the motivation for why he does it are important. Likewise, it is very important to ask whether he chose this, or whether he acts because he was programmed to act this way. A sheep cannot be considered a moral entity, because it acts by its nature and does not choose to act this way. It has no possibility of acting in any other way.

Double action

To sharpen this further, I will quote here from the introduction to the book Dewdrops, by the first Sochatchov Rebbe. There he discusses the meaning of the demand to study Torah "for its own sake":

And while speaking of this, I recall what I heard: that some people stray from the path of reason regarding the study of our holy Torah, and say that one who studies and develops novel insights, and rejoices and delights in his learning, this is not Torah study quite so much for its own sake as if he were to study simply, with no pleasure at all from the learning, and only for the sake of the commandment. But one who studies and delights in his learning—his own enjoyment is mixed into his learning as well.

Those "mistaken" people think that when one enjoys and delights in study, it is not considered studying Torah for its own sake, that is, for the religious purpose of serving God, since it is done in order to satisfy a personal interest (the enjoyment). Study "for its own sake" is only study alongside which there is no satisfaction and no interest whatsoever, including enjoyment. This conception is similar to what we saw above regarding a moral act done for the sake of personal satisfaction. If there is satisfaction, then that contradicts the morality of the act. A moral act is supposed to be done "for its own sake," and not for the sake of any personal goal, however lofty it may be.

However, the author of Dewdrops flatly rejects this, and writes:

But in truth this is a well-known mistake. On the contrary, this is the essence of the commandment of Torah study: to be joyful, glad, and delighted in one’s learning; then the words of Torah are absorbed into his blood. And since he enjoys the words of Torah, he becomes attached to Torah [see Rashi’s commentary on Sanhedrin 58a, s.v. ‘and clings’]

And in the holy Zohar, it is said that "both the good inclination and the evil inclination grow only through joy: the good inclination grows through the joy of Torah, the evil inclination…" And if you say that because of the joy he has from the learning it is called not for its own sake, or at least both for its own sake and not for its own sake, then this joy only detracts from the power of the commandment and dims its light, so how would the good inclination grow from it? And since the good inclination grows from it, certainly this is the essence of the commandment.

If so, it is clear that enjoyment of study deepens it and increases its value, and it also leads him to persevere and study more and more. Therefore one cannot say that study with enjoyment is study not for its own sake. By the same token, moral action that has satisfaction alongside it is only better, since it will help people persevere and behave morally, and will deepen their bond with morality and internalize it within them. Is this really so? Is the fact that such action has the potential for perseverance enough to define it as moral action?

Up to this point these are the famous words of the author of Dewdrops. But now he adds one more sentence that is less well known:

And I concede that one who studies not for the sake of the commandment of study, but only because he has pleasure in his learning, this is called study not for its own sake—like one who eats matzah not for the sake of the commandment but only for the pleasure of eating; and regarding this they said, "A person should always engage… not for its own sake, for from…" But one who studies for the sake of the commandment and delights in his learning, this is study for its own sake, and it is wholly holy, for the delight too is a commandment.

That is, a person who studies not for the sake of the commandment but only because of the pleasure really is studying not for its own sake. Everything said above applies only to a person who studies for the sake of the commandment, that is, his motivation is solely the commandment, but as a result of the study he also has satisfaction, delight, and pleasure. There is nothing wrong with this; on the contrary, it intensifies the value of the act and the spiritual benefit that it contains. But if the motivation for the study is the delight and pleasure—then we are indeed dealing with study not for its own sake.

The same applies in the moral context. If the person’s motivation is a proper moral motivation (see below), then there is nothing wrong with his also having satisfaction and pleasure from the moral action. On the contrary, there is great moral and spiritual value and benefit in this. But if this satisfaction and pleasure are his motivation for moral behavior—then we are not really dealing here with moral behavior, but with actions intended to satisfy his various interests.

There may perhaps be room to discuss what happens if that person has two motivations in parallel: both morality and satisfaction.^[23] Is this still moral behavior? It seems that it is. If without the moral motivation he would not have done the act at all, then it seems clear that this is a moral act. But even in a situation where he would have done it for the sake of the satisfaction, there is room for the view that so long as there is moral motivation in the background of the action (and certainly if he would have done it even without the satisfaction), we are dealing with moral action.^[24]

The essence of moral action

The conclusion so far is that an action can be considered moral only if it is not done in order to satisfy any interest whatsoever. This is an action that has no self-interested motive at all (except perhaps as an accompanying motive). So why, really, does the person do it? Ostensibly there must always be some reason why he acts as he does. Is it not true that in the background there always stands some interest, money, honor, or just spiritual satisfaction? Can a person perform an act with no motive at all?^[25]

The required conclusion is that the essence of moral action is action flowing from a decision to be moral. Nothing more. When one asks the person, Why did you do what you did? he should answer: "Just because." Or in other words: "I wanted to be moral, and so I did it." If he has ulterior motives, interests, or even if the motive for the action is spiritual satisfaction and pleasure, that disqualifies the action.

It is important to sharpen that the moral motive itself (= the good will) is not an interest. The person does not gain something as a result of his act, not even a feeling of satisfaction (even if he has satisfaction, that is not the reason why he did what he did). He does the act simply because in his eyes it is the right act. There are those who will say that there are no such situations. A person always acts for the sake of satisfying some interest. I do not intend to argue with this claim, but it is important to understand that one who thinks so has no morality or moral behavior in his world. My arguments here are addressed to those who think that all these things do exist.

Kant on the moral act

Kant devotes three of his books to ethics: Critique of Practical Reason, Groundwork of the Metaphysics of Morals, and Religion Within the Bounds of Reason Alone. Various remarks on ethics also appear in his book Critique of Judgment (which deals mainly with aesthetics). Kant’s contribution in the field of ethics is regarded as no less central than his contribution in the field of epistemology. We dealt with his move in the field of epistemology in the previous part of this booklet, and the main argument from epistemology was based on the question of the synthetic a priori, which belongs to that field. In this part of the booklet we are dealing with his parallel move in the field of ethics.

Our point of departure is Kant’s conclusion concerning the essence of moral action. He devotes broad sections of those books to it, and ultimately arrives at a conclusion that appears already in the opening sentence of his book Groundwork of the Metaphysics of Morals:

Nothing can possibly be conceived in the world, or even out of it, which can be called good without qualification except a good will.

According to Kant, a good act has moral value only if it is done from the good will, that is, a sense of duty or commitment to the moral principle, which by definition is a categorical imperative, that is, an absolute, unconditional imperative. A good act that is not done from the sense of moral duty (respect for the categorical imperative) but from my inclinations or from any other motive may perhaps contribute to general happiness, but it is devoid of moral value. This is completely parallel to what we saw above. In the next chapter we will see that the religious value of an act, like its moral value, derives from performing it מתוך commitment to the relevant system: in the religious domain to the divine command, that is, accepting Him as God, and in the moral domain to the moral imperative.

According to Kant, the categorical imperative does not demand results from the person, and it is not based on the character of the acts in question. A person need not succeed in creating a better reality or in actually contributing to human happiness. Kant claims that the moral worth of an act depends only on the intentions of the one who performs it, and on no fact whatsoever. The objective moral law demands of us respect for the law of reason that the act tries to realize. That "respect for the law of reason" (more accurately: commitment to the law of reason) is also called the good will. Kant argues that the good will is the only thing that confers moral value on an action. Let us sharpen this further: according to Kant, the desire to benefit another person is also not a motivation that defines an act as moral. Only the desire to be moral can be a moral motivation. Admittedly, the definition of morality (what one should will in order for it to be a moral will) may perhaps be an action that benefits another. That is the content of the imperative, but not the motivation by virtue of which one responds to it. The response is by virtue of commitment to the imperative itself.

The naturalistic fallacy

Kant devotes broad portions of his ethical writings to the absolute independence between norms and facts. He argues that to hang the moral value of an act on some fact is a fallacy (the naturalistic fallacy). Therefore moral theories that hang the moral value of an act on certain outcomes (such as utilitarian theories) are categorically mistaken. Morality is not derived from any fact whatsoever.

For example, when I say that it is forbidden to hit another person because it causes him suffering, I have fallen into the naturalistic fallacy. The fact that hitting causes suffering is a factual claim. The prohibition on hitting is an ethical-normative claim. One cannot derive a normative claim from a factual claim. In order to validate the argument, we must add another assumption: that causing pain is morally forbidden. This is a bridge principle that connects the fact (that there is suffering) to the judgment (that this act is forbidden). Now the conclusion really does follow from the premises.

The moral judgment of some act cannot depend on facts about the person acting, nor on facts about the world or about any other person. Morality is indifferent to facts, and facts are transparent from its point of view. The only important thing is the good will, that is, the motivation of the person who performs the act. Below we will sharpen this further. Let us now turn to examine the content of the categorical imperative.

The categorical imperative

What is the content of Kant’s categorical imperative? After a rather complex line of reasoning, Kant reaches the conclusion that some categorical imperative must lie at the basis of morality, and that commitment to this imperative is the essence of morality. He must now define the content of that imperative. Another chain of considerations leads him to an explicit formulation of the content of that categorical imperative. Scholars have found several different formulations of this imperative in Kant’s writings. One of the best known is the following:^[26]

Act only according to that practical rule which, in accepting it, you can also will to be a universal law.

That is, your behavior should not be derived from who you are or from some specific state of affairs. It should be a general practical law. The supreme measure of the morality of an act is whether we would want it to become a universal law. Below we will clarify this further.

In a much later formulation, the philosopher John Rawls spoke about what he called the "veil of ignorance," saying that a person should make a moral decision when he:^[27]

does not know his place in society, his class position or social status… what fortune has befallen him in the distribution of natural assets and natural abilities, his intelligence, his strength, and the like.

This is a more concrete expression of Kant’s requirement that the imperative be general and unbiased, and also independent of circumstances.

Despite the general formulation, Kant himself already showed that concrete imperatives relevant to different specific situations can be derived from this general law. For example, he argues that it is forbidden to lie even in a situation where the lie is useful, because I would not want there to be a universal law that permits people to lie. There are many objections to the possibility of deriving concrete instructions from this law, and the question of how to define a general law is also very far from simple (perhaps there is room for a general law permitting lying when the lie is useful), but we will not go into all that here.

As I already noted, the moral act must be done out of commitment to this imperative. An act that fits the content of the imperative but is not done in order to obey it (out of respect for it) is not a moral act. For example, a person who does not lie when lying would be useful to him, but does so because he fears being caught, or because his good name may be harmed, or for any other reason (including the pleasure and satisfaction of being a truthful person), is not behaving morally. Moral behavior exists only when one does not lie because of respect (that is, commitment) to this imperative and not for any other reason.

Schiller’s criticism: another look at double action^[28]

Kant essentially demands that a person free himself from his inclinations and from the various influences on him, and choose his path not from inclination but from respect for the law, or from duty and the good will alone. He distinguishes between the legality of the act and its morality. The act is lawful when its content conforms to the demand of the moral imperative, but it is not done out of respect for the law, rather from other motives. The good will is free in the sense that it is not founded on inclinations and sensual influences but on a free decision.

Against this conception stands the well-known poet Friedrich Schiller. Despite his admiration for Kant, and especially for his moral theory, he opposed Kant’s sharp distinction between inclinations and moral action arising from free decision, and thus he writes in his playful verses:^[29]

Gladly I serve my friends,

Yet I do so from inclination.

And so my heart is always troubled,

That I am not righteous in my actions.

Decision:

There is no other advice: you must strive to despise them,

And then do, with revulsion, what duty commands you.

Bergmann rightly comments there that this criticism is based on a mistake. Kant did not forbid doing the thing with inclination participating as well; he only forbade doing it out of inclination alone. He means, similarly to what we saw above from the author of Dewdrops, that if the inclination is the reason we do the thing, then indeed we are dealing with an act that has no moral value (it is lawful but not moral). But if the motivation for the act is the good will, and alongside it there also appears inclination, there is of course nothing defective in that.

The categorical imperative and considerations of outcome: teleology and deontology

The categorical imperative deals with the criterion by which one can determine whether a given act is moral or not. It does not speak about the utility and consequences of that act. This can be seen from two aspects:

1. The motivation. A morality of outcomes exists even among sheep. This is teleological morality (telos—end/result; teleios—complete), that is, a morality that examines and judges the act in terms of its consequences. According to the teleological approach, the moral act is supposed to bring about the optimal result. But as we have seen, morality in its essence is not teleological but deontological (volitional, decision-based), that is, the moral act is judged mainly according to the moral will that served as the motivation for doing it.
2. A practical difference. Even in practice, as a matter of fact, the moral act is not necessarily the act that brings about the best results (morally). The motivation is respect for this imperative itself, and it is conditioned by nothing. As we saw above, the moral value of an act does not depend on any facts and is not derived from them. Results too are facts. One cannot say that some act is good because it brought some benefit or happiness to someone. The happiness that was achieved is a fact, and as such it cannot determine the moral value of the act.

At first sight it seems that we are dealing here with two essentially different conceptions of morality and its aims. The teleological conception sees morality as a means to achieve a more perfected social state. Morality is a means, and the goal is the repaired social state. In contrast, according to the second conception, the aim of morality is not only the attainment of a perfect social state but also the perfection of the individual person. The moral person is a more complete person, and the aim of the moral act is to perfect the doer and not only the society within which he acts. We will return to this point later, and also in the fifth booklet.

Up to now I have dealt mainly with the first aspect of the difference between morality and utility, the importance of moral motivation. I will now elaborate on the second aspect as well, the practical difference between a moral act and an act whose aim is the attainment of utility (telos).

The question of moral utility^[30]

From the formulation Kant proposes for the categorical imperative, it is very easy to become confused and think that Kant is trying to ensure that things go well for all of us, somewhat like the biblical commandment "Love your neighbor as yourself," or in the Talmudic formulation, "What is hateful to you, do not do to your fellow." Here too there is an instruction to do what we would want everyone to do to us, and ostensibly that is an equivalent formulation to the Kantian imperative. According to this interpretation, Kant is basically instructing you to do to others what you would want them to do to you, because if you do not do that to others, then they also will not behave toward you as you would like. But that is not the meaning of the Kantian imperative. Such a consideration is a kind of consequentialist consideration, or utilitarianism, or a theory of maximal good, and Kant rejects all such considerations outright. The categorical imperative offers a criterion that determines the morality of an act, without any connection to the consequences that actually arise from it. The goal is not to improve the world, or to attain some result, but to behave morally. This is not only the motivation from which a person is supposed to act (as we saw, solely out of respect for the categorical imperative, and not in order to achieve anything, even something moral and important), but also the definition of the content of the imperative itself.

I will try to sharpen this here by means of several examples, in which we will see that the categorical imperative instructs us to act in a certain way even though the consequentialist consideration does not lead there.^[31] For example, a person is considering whether or not to evade income tax. On the one hand, it is clear that a shortfall of one hundred shekels in the public coffers is utterly meaningless. No person will be harmed, not by the tip of his fingernail, if I evade tax in the amount of one hundred shekels. Every budget item will be fully implemented, and the entire effect of my act is at most the movement of some digit or another far beyond the decimal point in the budget ledger or in the bank account on the computers of the state treasury. There is not the slightest shred of practical effect here. It is important to understand that this is not a negligible effect but a total absence of effect. In other words, a pure consequentialist consideration ought to lead me to the decision to evade tax: I gain one hundred shekels and no one else is harmed.

Many will argue against me: and what will happen if everyone does as you do? This, of course, is an argument that keeps us within the realm of consequentialist considerations. I will, of course, answer that that would be very bad, and therefore I very much would not want it to happen. But why does this bear on my decision? After all, when I evade tax, I obviously hide this from everyone, and therefore my act will not influence in any way the decision of any other person, just as the acts of others do not influence me (and are not known to me either). Therefore, even if everyone evades tax, from my point of view it still does not matter, because one way or another they will do what they decide to do without any connection to my decisions (none of us will know about the other). So every citizen in Israel will decide independently whether or not to evade tax, but these decisions are made within the private domain of each of us, and are not influenced by what I decide to do.

To sharpen this further, I will describe it this way. When I consider, on consequentialist grounds, whether or not to evade tax, I examine the expected results of my act in the two possibilities: if I do not evade tax, there will be x shekels in the state treasury. By contrast, if I do evade tax, there will be x-100 shekels in the state treasury. The size of x is of course determined by the decisions of all the citizens (how many evade tax and how many do not), but all these decisions do not affect the delta, that is, the difference between the results of my two possible decisions. That difference is always 100 shekels, regardless of the decisions of everyone else. And my decision is determined only by the difference. x is irrelevant (so long as it is large enough, of course; and if it is so small as to be on the order of magnitude where the absence of 100 shekels can be felt, then in any case we are long past that point and the state has long since ceased to exist). So even after the argument of what will happen if everyone else does as I do, the consequentialist consideration remains as it was. Therefore the answer of proponents of consequentialist morality is that from my point of view it is indeed right to evade tax, and from a moral perspective there is no obstacle to doing so. The state treasury will not feel it at all, and for me this is a significant sum; the conclusion is that there is moral justification for evading as much tax as I can.^[32]

Now Kant’s categorical imperative comes and tells us that we must do what we would want to be a universal law. Would I want there to be a universal law that people evade tax as much as they can? I already said that I would not. If so, according to the criterion of the categorical imperative, this act is not moral. It is important to understand: this is not the claim that the consequences of this act would be severe. That is not a consequentialist consideration. The categorical imperative speaks about a philosophical criterion that examines the act and determines whether it is moral or not, with no connection whatsoever to the question of whether such behavior is actually likely to become a universal law or not. This is not an evaluation of facts or outcomes, but a kind of thought experiment. I think about a hypothetical situation in which my behavior is the universal law, and I ask myself whether that is a world that seems worthy to me or not. If not, then the categorical imperative forbids me to behave that way, quite independently of the fact that there is in fact no consequential effect to what I do. In practice it will not bring about any damage, and yet it is still an immoral act.

Interim summary: benefit and morality

To sum up, we saw above that the motivation for moral action is not benefiting another person, but responding or committing oneself out of respect to the categorical imperative. Now we see that the content of the imperative too does not necessarily lead to such benefit. The definition of an act as moral does not depend on the degree of benefit it will actually bring. The benefit at issue is a hypothetical benefit examined in a hypothetical situation, and it serves only as a criterion for the moral goodness of the act as such. Benefit is not the purpose of the act (it is not determined to be moral because that is the result it will achieve), nor is it the motivation for doing it.

Here it should be noted that many do not agree with the Kantian severance between the definition of the moral act and the outcome (the benefit). They claim that an act is moral only if it actually benefits. But even according to this conception, it is clear that the disagreement is only over the content of the imperative, while the philosophical framework is certainly correct. A moral act is only one that is done by virtue of commitment to the imperative (whatever its content may be). What is done from other motives cannot be considered a moral act. One can adopt a different content for the imperative (such as performing acts that benefit) on the same theoretical ethical basis.

One implication of this is that even according to the conception that a moral act is an act that actually benefits, it is basically enough for us to have an act that tries to benefit. The question of success, that is, whether the act actually brought the hoped-for result or not, is another question, and it plays no part in the moral evaluation of the act. If it was done out of the correct motivation (that is, out of commitment to the moral imperative), then the act is moral even if it does not succeed in bringing about results in practice. According to this conception, it is clear that it must be done for the sake of bringing about the result, but success is not important. Even according to this conception, the motivation is what determines the moral judgment of the act, and that is what matters for our purposes.

The paradox: in the final analysis, Kant’s categorical imperative does have a practical result

After all the discussion in which we showed that the moral consideration according to Kant is not intended to bring about any result, it is interesting to point out that in practice it actually does so, and perhaps even better than any other consideration. To see this, let us return to the example of tax evasion. The Kantian consideration is supposed to cause everyone who adopts it not to evade tax even if there is no consequentialist consideration forbidding this. If Kant’s categorical imperative did not exist, then we would expect every citizen to evade tax, since as we saw the action of each individual person by itself has no effect whatsoever on the state of the general coffers. But in such a case the general coffers would very quickly become empty. True, no individual has the ability to influence the situation, but in practice, after each individual separately had made his decision, that is what would happen. The only way to save the coffers is that each of us individually should behave according to Kant’s categorical imperative, which defines the morality of acts in a non-consequential manner.

Absurd as it may seem, although none of us has any effect whatsoever on the state of the coffers, and although the goal of the imperative is not to save the coffers but the moral behavior of each of us, obedience to the imperative is still the only way that actually saves the public coffers, that is, brings about the hoped-for practical result.

An analogy to the prisoner’s dilemma

This situation is completely parallel to what is called in game theory the "Prisoner's Dilemma." Let us now look at a common version of this problem. The police arrest two criminals who committed a crime together and separate them for questioning. If the police manage to secure their conviction, each will go to prison for 15 years, but for lack of evidence they will be tried for a lesser offense carrying one year in prison for each. The police do not have enough evidence to prosecute them, so they offer each of them a deal: testify against the other, and as a reward the witness is promised a reduced sentence. If both prisoners accept the police offer, each will go to prison for five years, and if only one of them testifies while the other remains silent, the witness goes free immediately and his companion is jailed for 15 years. This situation can be summarized in the following table, which summarizes the sentences that will be imposed on Prisoner A (red) and Prisoner B (blue) according to their actions:

		Prisoner B
		Silent	Informs
Prisoner A	Silent	One year, one year	15 years, zero years
	Informs	Zero years, 15 years	Five years, five years

All these facts are known to both prisoners, but they cannot communicate with one another, and therefore neither knows which strategy his companion chose. The dilemma facing each of them is whether to remain silent or testify. Prisoner A looks at the table and says to himself that regardless of the tactic B chooses, it is better for him to testify, because in every case, if he testifies his punishment will be less than if he remains silent. Hence informing is his dominant strategy. Prisoner B, of course, analyzes the situation similarly. Their rational decision leads both of them to choose to testify, with the result that both go to prison for five years. But we must now note that had they both chosen to remain silent, each would have gone to prison for only one year.

The paradoxical nature of the Prisoner's Dilemma stems from the fact that a rational decision leads to a result that is not the best for both of them. To reach the best result for both, the players need cooperation, that is, a joint decision to remain silent. But they must make that decision without communicating with one another. Each one separately is supposed to understand that it is better for both of them to form a coalition of silence and decide accordingly without an explicit agreement with his companion. But when Prisoner A chooses the strategy of silence, he must trust that his companion will do the same. If the companion talks, he will get fifteen years and his companion will go free. Of course, even if the prisoners are able to communicate with each other, so long as they do not sign a binding agreement that somehow guarantees that those who sign it will act in accordance with their declaration, the strategic choice to remain silent is risky. It depends on the second person choosing the same path.

This dilemma illustrates a situation that is not uncommon, in which cooperation would bring greater benefit to both sides than an approach in which each side acts on its own. Beyond that, and no less important for our purposes, the decision each person makes to cooperate with his companion has to be made without communication between them. In this sense, the situation in the Prisoner's Dilemma resembles the one described above regarding income-tax evasion. There too, the rational decision each citizen makes individually is to evade taxes. But if everyone makes that decision, that is, if it becomes a universal law, we will all be harmed (the state treasury will be empty). Therefore a reasonable way out is to act as though we had all signed a social covenant of cooperation.^[33] This is exactly the effect we pointed to above: ironically, conduct in accordance with the categorical imperative also brings about the best practical result.

Closing the circle: deontological = teleological

Actually, the necessary conclusion is that despite the distinction we drew above between teleological morality (whose goal is the attainment of social benefit) and deontological morality (whose goal is human perfection), here we have reached the conclusion that even in its deontological definition morality is nonetheless intended for the repair of society. This is not a necessary conclusion, for although we have seen that deontological morality optimally brings about social repair, that does not mean that this is indeed its purpose. But it is more reasonable to think that if this is the case, then morality really is meant for that. This reunites the common intuitions that see morality as an instrument of social repair with the understanding that morality is deontological in its essence. We have seen that the perfection of the individual person also brings about a repaired society.

Thus the deontological conception is what brings about the telos, even though these are still two different goals (repairing society and repairing the person who performs the act). We will return to this point in the fifth notebook when we discuss the question whether morality can be the purpose for which we were created.

1. The meaning of command in Jewish religiosity

Introduction

An entirely parallel move to the one we encountered in the previous chapter also exists in the Torah-religious context. There too the question arises how we should assess the religious value of a given act, and as we shall see here, the answer is quite similar.

Example: the essence of religious worship^[34]

The Gemara in Sanhedrin 61b brings a halakhic dispute between Abaye and Rava:

It was stated: One who worships idolatry out of love or fear—Abaye said: he is liable; Rava said: he is exempt. Abaye said: he is liable, for he has worshiped it. Rava said: he is exempt: if he accepted it upon himself as a god—yes; if not—not.

According to Abaye, one who worships idolatry for reasons such as love and fear is an idol worshiper in the fullest sense, but Rava holds that he is not considered an idol worshiper until he accepts it as a god. As a matter of law, as in all disputes between Abaye and Rava (except for the six signaled by the mnemonic Ya'al Kagam; see Bava Metzia 22b and parallels), the halakha here is ruled in accordance with Rava.

The difficulty raised by Rava's words is obvious. If a person does not worship this idol out of love or fear, then why does he do so at all? According to Rava, how is one who wants to worship idolatry in the fullest sense supposed to act? Moreover, worship out of love and fear is the very essence of religious worship. We are accustomed to the demand to love and fear God, and out of that to serve Him. So why, when these pure motivations are directed toward idolatry, is this not a full prohibition of idolatry? In other words, what is that "acceptance as a god" that, according to Rava, is the condition for the act to count as complete idolatry? Is loving or fearing the idol not accepting it as a god?

Not for nothing does Rashi there explain it as follows:

Out of love and fear—out of love of a person and fear of a person, and he did not conceive of it in his heart as divinity.

The case is about someone who worships idolatry out of love and fear for some person. For example, he wants to please him and give him satisfaction, and therefore worships his god. Worship of idolatry by accepting it as a god is when one loves or fears the idol itself. Other Rishonim and halakhic decisors explain this passage likewise. Despite the strain this places on the language of the passage, these commentators chose to explain it this way because of the difficulty we raised above. Love and fear are the highest religious motivations, and when they are directed toward an idol this is certainly idolatry in the fullest sense.

Rambam too, in the Laws of Idolatry 3:6, rules in accordance with Rava, but he states it as follows:

One who worships an idol out of love, for example because he is attracted to this image on account of its craftsmanship, which was especially beautiful, or who worships it out of fear of it, lest it harm him, as its worshipers imagine that it benefits and harms—if he accepted it upon himself as a god, he is liable to stoning. But if he worshiped it in its customary manner or by one of the four forms of worship out of love or fear, he is exempt. One who embraces an idol, kisses it, honors it, sweeps and sprinkles before it, washes it, anoints it, dresses it, shoes it, and anything similar among these acts of honor, transgresses a negative commandment, as it is said: 'You shall not worship them'; and these things are included in worship. Even so, he is not flogged for any one of them, because they are not explicit. And if its customary mode of worship is one of any of these acts, and he did it in order to worship it, he is liable.

He cites Rava's formulation in its plain sense. If a person worships idolatry out of love or fear, he is exempt until he accepts it as a god. He does not specify that this refers to love and fear of a person, and it appears from his wording that he means to explain the Gemara as its plain wording suggests.

And indeed, the Raavad there already comments on this:

And we explain it as love of a person and fear of a person, not love of idolatry nor fear of it.

And indeed, the Kesef Mishneh there comments on this:

As for what he wrote, 'And we explain it as love of a person, etc.,' our master saw fit not to explain it that way, because fear of a person is coercion, and the Merciful One exempts one who acts under coercion. How then could Abaye say that he is liable even if he did not accept it as a god? Rather, 'out of love and fear' means out of love of idolatry and fear of it, as our master wrote.

That is, Rambam must indeed be read literally: one who worships out of love and fear of the idol itself is exempt. He explains that the reason is that worship out of fear of a person is idolatry under coercion, and therefore one is exempt for it. And what about idolatry out of love of a person? Here he is silent. We will explain this below.

How are we to understand Rambam's position? What is this "acceptance as a god" that constitutes full religious worship? How is it different from love and fear of the idol? It seems that Rambam understands that if a person worships an idol because he fears it or loves it, this is an ulterior motive. Genuine religious worship is surrender without any side reason. I worship it because, if it has commanded, one must obey. This is the meaning of the "acceptance as a god" of which the Gemara speaks and which Rambam also mentions. To worship someone because one fears him or loves him is worship for the sake of personal satisfaction, a kind of interest, and as such it is not pure religious worship. Perhaps that is also what the Kesef Mishneh meant above. We saw that he defines worship out of fear as coercion, and he does not explain at all why worship out of love of a person is not an idolatrous offense that incurs liability. Clearly, even in the case of fear his intention is not mortal danger, which would be actual coercion, for then we would be dealing with laws already discussed at length elsewhere in Rambam (coercion to worship idolatry). His intention is to say that both fear and love are ulterior motives, interests, and therefore worship motivated by these is not worship of religious value. These are actions for the satisfaction of interests. The basis of the act is my feelings (love and fear), not feelings of duty. From this we may infer that "acceptance as a god" means worship out of commitment that does not depend on any interest. To do it simply because it is the right thing. I act this way because of a sense of duty to the divine command. The action is done because God commanded, and not for any other reason.

As an aside, it would seem that these matters apply to an idol, but no less so to the Holy One, blessed be He. Religious worship toward Him, too, ought not to stem from love or fear, but from accepting Him as God, that is, from a sense of duty. True, according to all opinions there are commandments to love God and fear Him (see Rambam's Sefer HaMitzvot, positive commandments 3-4), but these are two commandments out of the 613, not the motivations for His service. The basic motivation is accepting Him as God, though alongside it there should also come love and fear of Him. Moreover, there are indeed sources in which love and fear are seen not only as commandments but also as reasons to serve Him (see Rambam, chapter 10 of the Laws of Repentance,^[35] and many others), but these are at most secondary motivations, added to the fundamental motivation of accepting Him as God. Exactly as we saw above in the words of the Aglei Tal about a situation of dual motivations.

Comparison to the picture from the previous chapter

The picture we encountered here is completely parallel to our conclusion regarding the moral act. A moral act or a religious act is not judged solely in light of the act itself. Motivation and intention are no less important. Bottom line: an act is judged as a moral act if it is done מתוך the motivation to be moral, and not because of some other consideration. So too, a religious act is judged as having religious value if it is done מתוך a motivation of religious commitment, "for its own sake," and not מתוך any other motivation. This is a fundamental principle in judging acts of normative significance, whether moral or religious.

A note on the centrality of command in the Torah and on Kant's relation to Judaism

From here we can understand the central place of command, that is, of halakha, in the Jewish religious conception. Yeshayahu Leibowitz used to say that intellectual principles and beliefs never constituted a criterion defining who is a proper Jew and who falls outside the fold. What has always defined Jewish religiosity is commitment to halakha, that is, to command.

Surprisingly, Kant himself argued that Judaism is a kind of social-political code and not a religion, since for him religiosity was connected more with moral feeling and religious experience. Obedience to law belongs to the universal ethical sphere and not to the religious aspect of our lives. Although his Jewish friends and students argued that Kant had not properly understood Judaism and tried to offer interpretive alternatives, it seems to me that Kant grasped its essence better than they did. If in Christianity religiosity is identified with religious experiences (= closeness to God) and religious feeling, the essence of Jewish religiosity is commitment to law. Kant, who looked at Judaism through a Christian lens, diagnosed it better than his Jewish friends did, but he described it in terms drawn from Christian religiosity. He correctly saw that commitment to law is the essence of Jewish religiosity, and in that he was right. But he defined this very thing as a social-political code rather than religion, and here he unwittingly used a Christian conceptual framework.

It is interesting to note that Rabbi Eliezer Berkovits, in his essay on the reasons for the commandments,^[36] points to a similar role for halakha. As a starting point he identifies (in my opinion quite mistakenly) halakha with morality, and argues that the purposes of halakha are only moral; but as a result he is forced to invent explanations for the whole array of commandments that seem entirely unrelated to morality (most of the commandments in halakha). He proposes that the totality of commandments comes to train us in Kantian obedience, so that when we come to fulfill the duties of morality we will be skilled in acting out of commitment. The explanation is dubious and also contains several mistakes in its understanding of Kant's morality, but it still takes for granted the centrality of commitment to command that stands at the basis of Judaism.

This is the reason that acceptance of the commandments is required in the process of conversion. The essence of Judaism is commitment to the halakhic-religious command, and without it there is no Judaism and therefore no conversion either.^[37]

The meaning of all this

In my article, Causing a Secular Person to Transgress,^[38] I took this conception one step further. I argued there that a person who does not believe in God (or even if he believes in God but not in the giving of the Torah and in the divine source of the command) cannot meaningfully fulfill commandments or commit transgressions. True, in the Talmud and the halakhic decisors there is a dispute over whether commandments require intention (to discharge one's obligation), that is, whether someone who performed a commandment without intending to discharge his obligation indeed fulfilled the commandment or not; but according to all opinions, commandments require faith. One who does not believe in God—his commandments are not commandments, and his transgressions are not transgressions.

Thus, for example, fulfilling commandments in the style of Ahad Ha'am—namely, keeping the Sabbath in order to preserve the national character of the Jewish people and its heritage (as in his well-known saying, "More than Israel kept the Sabbath, the Sabbath kept Israel")—has no religious value, because it is not done for the right reason (commitment to the divine command). Likewise, all the pioneers who gave their lives for conquering the land and draining its swamps did not fulfill the commandment of settling the Land of Israel, unless they did so מתוך commitment to the commandment of settlement and conquest of the land. Atheist pioneers cannot thereby fulfill a commandment. Likewise, the moral acts of atheists have no religious value (though not no moral value)^[39]. In all these situations the motivation and commitment to the command are missing, and therefore these acts should not be seen as acts of religious value. In fact, one can say that they are done for ulterior reasons (though not petty ones, but value-laden ones), namely for cultural and national benefit, or even moral benefit.

We once again find that the structure of moral and religious judgment is very similar. In both cases intention is critically important, no less and perhaps more than the act itself. And precisely because of this, a sharp distinction is also needed between these two systems. A moral act must be done out of commitment to the moral command, and a religious act out of commitment to the religious command. If one performs a religious act out of commitment to the moral command (in its secular sense, as we shall see below), it has no religious value. That is why I argued above that Berkovits (as well as many others) was mistaken in identifying halakha with morality. Even in commands that have moral content, there is still an important distinction in the motivation required for performing them. The source of validity and the motivation for performance are critical to the evaluation and judgment of such acts.

1. The proof from morality

Introduction

In this chapter we will present the proof from morality, and then we will see that here too we are dealing with an argument of a "theological" character.

On morality and autonomy

Let us begin with a distinction made by Ari Elon in several of his essays^[40] between the rabbinic Jew, whose identity is built and validated by the rabbinic establishment and halakha, and the sovereign Jew, who constitutes his own values. One of his essays opens with the following sentences:^[41]

A sovereign person is sovereign over himself. There is no Master of the Universe in his world, and he is not the master of the universe in the world of others. A rabbinic person is not sovereign over himself. He makes for himself a rabbi. The rabbi makes for him a god.

According to his approach, it seems that the criterion by which the sovereign Jew's values are measured is his own choices, that is, he himself. In my books I have more than once pointed to the importance of sovereignty, that is, autonomy, as a foundation for value judgment (moral or halakhic).^[42] An act not done out of free will cannot be considered moral or immoral. Choice is a necessary condition for moral judgment (therefore we do not judge the acts of sheep or of computers). But here I would like to qualify that claim and sharpen the fact that this is a necessary but not a sufficient condition.

According to Elon's proposal, a person who autonomously chooses the profession of hired killer deserves the same appreciation as Mother Teresa. Both chose their values and the ways to realize them autonomously. Does Ari Elon really think these two deserve exactly the same moral evaluation? I allow myself to guess that he does not. If so, the decision that professional murder is a worthy value and way of life is unacceptable, even if it was made sovereignly and freely (indeed, especially if it was made that way).

What, then, is the difference? It is quite clear that the difference is that Mother Teresa chose autonomously and sovereignly the right values, whereas the hired killer chose in the same autonomous and sovereign way the wrong values. It is obvious that if the measure for a person's moral judgment is the values he himself chose, then all of us will always count as morally righteous. There must be some external criterion involved in the moral judgment of a person or an act. Thus, in the background of the ethical evaluation a person deserves, two things stand: whether he chose his path and values sovereignly and freely, and what path it was that he chose in that way.

The question now arises: what is the criterion by which that standard itself is determined? That is, how is it determined which values are right and which are not? We have seen that the mere fact that the person chose those values is not a relevant criterion (for according to that criterion, the killer is just as moral as Mother Teresa). Alternatively, who decides that Mother Teresa's values are good and the hired killer's are bad? At the first stage, what is important here is to expose the illusion in Ari Elon's conception: even the sovereign person or sovereign Jew needs some external source to determine the standard for his values, since the question which values are worthy cannot depend on him. What the person himself can decide is only whether to choose those values and commit himself to them, but he cannot decide which values are worthy.

Thus the sovereign picture painted by Ari Elon is partial and inaccurate. A person cannot constitute values for himself. He chooses how to live and to which values to commit himself, but he is not the one who determines which values are the right ones. Therefore our evaluation of that person's path and personality also depends on some standard that lies outside him (which determines whether his values are right or not), and not only on the criterion of sovereignty. One may say that Elon's basic mistake is the identification he makes between morality and autonomy. The autonomy of the agent is a necessary but not sufficient condition for his morality, and it is certainly wrong to identify the two.

As an aside, it is now also clear that Elon's distinction between the rabbinic Jew and the sovereign Jew is empty of content. A rabbinic Jew can choose his values with the same degree of sovereignty as Ari Elon. What distinguishes them is not sovereignty but only the values they chose sovereignly. The difference is in the content of the choice, not in the mode of choosing. Ari Elon chooses secular moral values, and the rabbinic Jew chooses with the same degree of sovereignty moral and religious values. The more relevant distinction is between people who are sovereign and those who are not, and rabbinicity has nothing to do with it. The important distinction is between those who choose their values and others whose values and path are influenced by external factors (society, impulses, and so on). But both kinds of people exist among the secular and among the rabbinic alike.

But our concern here is not the question of what distinguishes rabbinic from sovereign, or believer from atheist. The point important for our purposes is that every normative system that judges people and acts must rely on some external source that determines which value is worthy and which is not. The moral and sovereign conception presented by Elon implicitly assumes the existence of an external standard, one not dependent on our choice and in fact imposed upon us, by which we examine whether some conduct is moral or not. A person who does not accept the existence of such a standard cannot constitute a consistent moral and value-based worldview. As we have seen, if one assumes that the person's choice is the only measure by which we may determine our evaluation of him, one empties moral judgment of meaning.

The proof from morality

We can now move to formulating the proof from morality. We have seen that to ground a coherent moral theory there must be an objective external standard that determines which values are worthy (= good) and which are not (= evil). These determinations exist regardless of our own choices. The question that arises is where they come from. Who is that objective factor that determines the difference between good and evil, and in fact created the very concepts of good and evil themselves? As stated, in the absence of such an external source, good and evil, morality and moral behavior, have no meaning—at most autonomy does. Thus morality proves the existence of an external factor that legislated it and determined the difference between good and evil. We shall call that factor God, and thus have proved His existence. The proof from morality claims that if moral and value judgment indeed have meaning, then there must exist a God who lays the foundation for that judgment. It cannot be based on us alone.

As with all the proofs in the previous notebooks, here too the God whose existence we have proved is a special sort of God: the moral legislator. But this God is a legislator who does not necessarily enforce His laws and does not necessarily grant them their special validity. This God only defines and determines them, and perhaps also gives us the ability to discern them (to distinguish between good and evil). He is the one who set the standard that distinguishes good from evil and determines the criteria by which we judge people and acts.

It is important to understand that in the conception we have described here, God is not the source of morality's validity. Morality is a kind of fact, though not a physical fact. It is a quasi-factual determination that says this act is good or that act is bad. At that point our autonomy as human beings comes in: we accept upon ourselves commitment to the good and to moral conduct. That element is of course ours alone. The definition of good and evil must come from outside, and afterward comes the good will that creates commitment to the good and to morality. Moral and value judgment compare what we chose with the standard, and the product of the judgment is the determination of the morality or immorality of the person or the act.

The "theological" nature of the proof

The situation in which we now find ourselves is that without God there is no meaning to morality and moral judgment. But this is only a dependency between two claims: "there is a God" and "moral judgment has meaning and validity." Can we prove the existence of God from this?

The picture we have presented leads us to one of two possibilities: 1. There is no God, and therefore indeed there is no meaning to morality or moral judgment. 2. There is a God, and there is meaning to moral judgment. But it is impossible to adopt a third worldview (that of Ari Elon), according to which there is no God and nevertheless moral judgment still has meaning. In the case of the train to Scotland that we encountered in earlier parts of this notebook, too, we could say that the arrangement of stones was created by chance and has no meaning, and we could say that it was arranged intentionally and indeed points to the entrance to Scotland. But there is no way to adopt the position that the arrangement came about by chance and yet points to the entrance to Scotland.

As we saw in that case, here too one can remain an atheist and deny the validity of morality. There is no unconditional proof here of the existence of God. But if some person accepts the validity of morality and moral judgment, he must posit the existence of God. So this is an argument of a "theological" character, since from the conclusion that moral judgment is valid we work backward and posit the existence of God. God is the basis of morality and not morality the basis of God. Clearly the connection between them depends on the direction of the argument: morality is an indication of God's existence, and God is the reason for morality's validity. Going from God to morality is "philosophical," and going from morality to God is "theological."

As we saw above in chapter 2, the relation between these two directions is of the form of denying the consequent. If we denote the claim "there is no God" by the letter A, and the claim "moral judgment has no validity" by the letter B, then the picture we described actually presents us with the relation A → B. We may now deny the consequent and obtain: ¬B → ¬A, that is, if moral judgment has validity, then there is a God. This is the proof from morality, and it is now clear that it has a "theological" character. A person can assume that value and moral judgment have meaning and believe in God, or deny both. But he cannot embrace morality and reject belief in God.

As we already saw in the first part, one could ostensibly accuse this argument of pragmatism, that is, of begging the question. We shrink from a world without valid morality, and therefore we create out of whole cloth, or invent, God as a basis for morality (opium for the masses). But as I did above, here too I will repeat that this is not pragmatism, or at least not necessarily. The assumption that there is valid morality already contains within it the assumption (or the "conclusion") that there is a God. Whoever is sure that morality is valid is necessarily a believer. We have not proved to him that there is a God; rather, we have exposed to him the fact that he is already a believer. Perhaps he was not aware of it, but the matter has been revealed to him through this "theological" argument.

The meaning of this theological argument is as follows: the moral atheist now stands before a mirror that presents him with the dilemma whether to give up his atheism and internalize the fact that he is a hidden and unconscious believer, or to give up his morality. The mirror reveals to him that, contrary to what he (and Ari Elon too) thought, there is no third possibility.

1. The proof from morality according to Kant

Introduction

Kant's ethics is identified with his humanistic conception, which sees the human being as autonomous and sovereign, that is, as one who legislates for himself. And indeed this is the spirit that blows through most of his writings, including those in which he does deal with God and His existence. In Bergman's words (p. 98):

It is a mistake to think that Kant bases the moral doctrine in any way on the existence of God. The categorical imperative remains fully in force whether we acknowledge the existence of God or not. The assumption of this existence is meant to explain to ourselves the direction of the world's development, but even if we had to give up the requirement of the existence of God, we would still be compelled to acknowledge our moral duty.

Kant and his interpreters continually twist between these two poles. On the one hand, morality cannot derive from God, since it is autonomous (coming from the law of our reason) and not heteronomous (imposed on us from outside); and on the other hand, Kant does indeed tie moral duty and moral conduct to God and to belief in Him.

The difference between the two books

In his books Critique of Judgment and Religion Within the Bounds of Mere Reason, Kant offers a proof from morality for the existence of God (in addition to the three described in the previous notebooks that are brought and discussed in the Critique of Pure Reason).

In the Critique of Judgment, Kant bases this on the harmony that must exist between the world and the moral command, and between moral conduct and the emergence of the good and human happiness (see Bergman, pp. 144-5). God is the guarantor of that harmony whose existence Kant assumes (this he calls "faith"). But Kant there explicitly stresses that we have no way to prove the existence of God as though it were a scientific-factual hypothesis. This is a belief required in order to constitute morality and moral conduct. There it is not a proof of the existence of God but an assumption of His existence. But in his book Religion Within the Bounds of Mere Reason he does offer an argument as a proof from morality for the existence of God (see Bergman, pp. 156-7).

Kant argues there that the laws governing a moral society cannot be the fruit of its own legislation and social coercion upon it. The reason is that action מתוך subordination to laws cannot be moral, since moral action is only action done solely מתוך the good will. One cannot legislate, and certainly cannot coerce, the motivations for action, but at most the action itself. In the terminology we already encountered above, legislation and coercion can produce "legality" but not "morality." Moral laws are not the fruit of the legislator's will; they are fixed in advance and grounded in themselves. These laws must be the products of a supreme lawgiver, whose moral duties and commandments are one and the same. He can also demand and even examine the motivations for action beyond the action itself (He searches the heart and the inmost self). Therefore a moral society is only a "people of God."

On the face of it, these things are very unclear. How does this fit with Kant's general approach, according to which morality must be autonomous and not heteronomous? Do we need God in order to validate morality or not? If there is a proof from morality for His existence, that is a sign that His existence is indeed a condition for morality. And if His existence is not a condition for morality, then how can Kant speak of a proof from morality for the existence of God?

Bergman there (p. 157) sums the matter up as follows:

In the Critique of Judgment as well as in Religion Within the Bounds of Reason, Kant faces the problem of how to infer the existence of God from the moral law without making the moral law itself dependent on God… The moral imperative must stand on its own authority, that is, be autonomous, and yet it must be understood as God's commandment. Kant opens his book on religion by saying that morality, founded on the concept of man as a free being, who by his reason imposes unconditioned laws upon himself, has no need of the idea of the existence of some other being above him in order to recognize his duty, nor of any other motivating incentive outside the law itself. With these words Kant detached himself from the outset from moral theories that ground morality in the existence of God and teach that the validity of moral laws derives from the existence of God. Morality therefore has no need of religion at all. Morality is not based on religion; rather, religion is based on morality… The moral society, which is the highest good and the purpose of creation, requires the existence of God, because its laws are built not on deeds but on the stirrings of the heart, not on legality, after the manner of the laws of the civil state, but on morality. These laws remain valid without any enactment of law, whether on the part of the members of society or on the part of the supreme divine lawgiver. The only lawgiver in this kingdom can be God as the highest moral being, so that we can conceive the moral laws, which stand in force by themselves, also as His commandments.

It seems to me that Bergman means exactly what we have been saying here. God is indeed a condition for morality. As we saw, He is not the source of morality's validity but its legislator (the one who created the distinctions between good and evil). Moreover, this argument is a "theological" proof and not a "philosophical" one. That is, one cannot prove the existence of God from here, but whoever accepts the validity of morality necessarily presupposes His existence implicitly. So there is a proof here, but it is "theological" and not "philosophical."

Morality does not need religion, since the insight that there is valid morality is understood by every person, believer and non-believer alike. Belief is the result of additional, "theological," self-examination by the person. He asks himself: how can there be valid morality if there is no God? It follows necessarily that at the basis of moral duty stands belief in God. Therefore acknowledgment of God is not required as a basis for moral commitment, for our eyes plainly see that many atheists are fully committed to morality. But such an atheistic position is not consistent. Belief in God is required so that moral commitment will be consistent. When we go from morality to God and not from God to morality, then indeed God is not a condition for moral commitment. That exists even before conscious belief. But when we probe within ourselves, we discover that an unconscious faith is hidden inside our moral commitment. Exactly as we saw in the earlier parts of this notebook, here too Kant is the father of these "theological" moves. Only here he went all the way to belief in God, whereas in our theory of knowledge he stopped one step earlier, at the stage where he firmly assumes the existence of synthetic a priori judgments and our scientific and inferential ability, without stating explicitly that at the basis of the matter lies an implicit belief in God. That move was described in the earlier parts of this notebook.

1. Analytical perspective

Introduction

In this chapter we will deal with the same topics, but from an analytical point of view. We will analyze the types of sentences and propositions that deal with ethics and morality, and through that again expose belief as an implicit assumption of ethics.

On sentences and propositions

In philosophy we distinguish between sentences and propositions. Aristotle defined propositions as sentences to which truth values can be attached (true or false). How do we determine whether some sentence is true or false? When factual propositions are involved, this is generally done by comparison with the relevant state of affairs in the world. If I assert the proposition "It is now light outside," I must examine the situation outside and see: if there is indeed light out there now, the proposition is true, and if not, it is false. There is another kind of proposition whose truth we have no practical way of checking. For example, "There are a billion ants in the world." Is this a factual proposition? It is reasonable to say yes,^[43] since it is true or false even if we cannot determine this in practice.

There are, of course, sentences that do not assert propositions—for example, questions or commands. When I ask someone, "What time is it now?" that is not a proposition, since it is neither true nor false. Likewise, when I command someone, "Do X," it is impossible to attach any truth value to that sentence. There are also fictional statements, such as "Every fairy has three wings." It is reasonable to say that here too we are not dealing with a proposition but with a sentence that asserts nothing.

Emotional and aesthetic propositions

And what about propositions such as "I love so-and-so"? At first glance, this is a factual proposition to be examined against my mental state. It is a report about a mental state, and therefore if I love him it is a true proposition, and if not, then it is false. And what shall we say about a case in which two people are arguing, one loves a certain person and the other hates him? According to our proposal, this is not really an argument. Both propositions are true, since each reports the mental state of a different person (Reuven loves that person and Shimon hates him). So why are there nevertheless such arguments? Because the proposition is not about reporting Reuven's or Shimon's mental state, but about what is fitting and unfitting: whether it is fitting to love that person or not. Is the proposition "One ought to love so-and-so" even a proposition? Can it be true or false? If not, then what is the point of arguing about it? The argument implicitly assumes that there is truth or falsehood here. But clearly we are not dealing with ordinary factual truth or falsehood, since there is no state of affairs in the world whose comparison with it will determine whether the proposition is true or false. We are dealing with a normative dispute.

Let me sharpen this further. Suppose Reuven says that one should love that person, and Shimon argues against him that the person is not worthy of love. This dispute may be over one or another of that person's traits—for example, when Reuven argues that he is kind-hearted and Shimon says that he is not. Here the dispute is about facts, not about norms. This dispute is settled by the tools of factual propositions: one checks the parties' positions against the state of affairs in the world (one checks whether that person is indeed kind-hearted)^[44]. If both agree that he is kind-hearted and still argue whether he ought to be loved, then we have a normative disagreement: should one love a kind-hearted person? Now let us look at that proposition itself: "One ought to love a kind-hearted person." Is this a proposition? What exactly does it claim? Against what are we to compare it in order to determine whether it is true or false? Is there any state of affairs whatsoever whose comparison with it can confirm or deny it? For this reason, many feel that we are dealing with sentences that are not propositions, and that such arguments rest on a categorical mistake. These are subjective sentences (describing Reuven's or Shimon's mental relation to that person) wrapped in the guise of objective, disputable propositions.

The same applies to aesthetic propositions. Reuven claims that this picture is beautiful in his eyes. Is he claiming something about himself (reporting feelings), or is his claim about the picture itself? Is Shimon, who claims that it is not beautiful, merely reporting a different mental state, or is there an argument here?^[45] Anyone who accepts the possibility of an aesthetic dispute or a dispute over artistic judgment must assume that these are propositions about the picture. The mental state of Reuven or Shimon is only a result of a stance toward the picture itself, and their dispute revolves around that.

Ethical propositions

Even if, with regard to mental-emotional sentences, we might be able to accept the position that we are not dealing with propositions but with reports of a mental state, in the moral sphere this is much harder. Think about moral sentences such as "It is forbidden to murder," or "One must help one's fellow." Are these propositions or not? Here too, if we wish to examine whether such a sentence is true or false, we have nothing against which to compare it, since there is no state of affairs in the world that will determine whether it is true or false. Seemingly, then, we are dealing with a mere report on a mental state and not with a real proposition.

But if we adopt here too the conception that these are not propositions in any objective sense, a rather grim conclusion follows: there is no more truth in the proposition "It is forbidden to murder" than in the proposition "It is permitted to murder." Moreover, by saying "It is forbidden to murder," I am not even pretending to claim something, but merely reporting my mental state and subjective feelings regarding murder. In such a picture, each of us can formulate his own position and decide whether, from his point of view, murder is permitted or forbidden, and these sentences then become subjective reports of a mental state. But there is no truth or falsehood here in the ordinary sense (as we saw with regard to factual propositions).

We thus arrive at an emptying of morality of all real content, apart from reports of feelings and mental states. According to this conception, when I say "It is forbidden to murder," I mean that there is within me a feeling of revulsion toward murder. The act of murder repels me. Can I have any real criticism of someone who does not have such a feeling within him? Certainly not. Just as, if I love a certain person, I cannot criticize someone who does not find such love for that person within himself. Everyone according to his own psychic structure and his own feelings of disgust.

If, however, we still think that moral propositions say something objective, that is, that a dispute about them has meaning and is not merely a report on the mental states of two people and nothing more, then we must assume that it is possible to attach a truth value to them. This means that if there are right and wrong in the moral world, or if the dispute has any point, then we are forced to see ethical sentences as propositions. The proposition "It is forbidden to murder" means that we are obligated not to murder. Therefore, one who is built differently and does not find this duty within himself is worthy of condemnation.

Prescription and description

The question now arises: what determines whether such a proposition is true or false? We cannot deny that there is no state of affairs in the world whose comparison with it will give us the truth value of such propositions. It is important to understand that the question here is not only how we can know whether an ethical proposition is true or false, but what the very meaning is of saying that an ethical proposition is true (or false). If there is no relevant state of affairs to which the proposition should be compared, then not only can we not know whether it is true, but there is no meaning at all to saying that it is true. A true proposition is one whose content matches a relevant state of affairs. Where there is no such state, there is no meaning to saying that a proposition is true. The implication is that in the domain of ethics we are not really dealing with propositions. On the other hand, if we accept the possibility of moral judgment, then we cannot be satisfied with the idea that ethical propositions are just descriptions of a subjective mental state. Therefore we must seek a meaning for the term 'truth' in the ethical context. Against what do we measure ethical propositions in order to determine whether they are true or not?

A common suggestion is to look at other people in society and see whether most or all of them think that murder is forbidden. But then we have once again turned the ethical proposition into a merely descriptive one. The fact that many people think murder is forbidden is a fact, like any other fact. An ethical proposition, or a normative proposition בכלל, is not a simple fact. A fact is neutral in terms of its normative charge. If it is now night, then it is night, whether that is good or not. A certain person is a murderer whether that is good or not. If some society encourages murder, then the proposition that that society encourages murder is true, whether murder is good or not.

For this reason, as we saw, Kant argued that it is impossible to ground the proposition that murder is forbidden—or any other ethical proposition—on some fact or facts. Factual propositions are neutral, whereas ethical propositions carry normative weight. The proposition "It is forbidden to murder" does not present me with a fact. It says that we are obligated not to murder, and that whoever murders commits a wrongful act. This is a proposition that cannot be regarded with indifference as though it were a mere factual description. The proposition "It is forbidden to murder" does not say that in practice we do not murder, or even that we think murder is forbidden. It states a moral fact: "It is forbidden to murder."

Grounding normative propositions in facts is a naturalistic explanation of morality, and therefore it involves a fallacy (the naturalistic fallacy described in the chapter above). The philosopher David Hume distinguished between sentences dealing with ought (the desirable, or fitting) and those dealing with is (the factual, the actual). Ethical propositions deal with ought and not with is. Therefore the proposition "It is forbidden to murder" is not a factual description—not of what some people think, and certainly not of what they do. According to Kant, it is not even a description of the consequences of murder (the suffering it causes, and so on). All these belong to the world of the actual, that is, to factual descriptions. Ethical propositions deal with ethical facts, not with physical, psychological, or other facts.

In analytic philosophy a distinction is made between descriptive propositions, which describe facts, and prescriptive propositions, that is, propositions that instruct us what to do. Factual propositions are neutral. They convey to us a fact or facts, regardless of our relation to them. Ethical propositions are supposed to arouse some attitude in us or move us to action (or deter us from action). One may say that prescriptive propositions are not neutral, but laden with some value-charge (positive or negative).

If someone comes and tells me that in a certain society, or even in all humanity, it is accepted not to murder—does such a sentence move me to action? Not at all. It is just a fact. I can accept that fact and at the same time support murder as legitimate. There is no contradiction here, since no prohibition follows from that description. I may think differently from the rest of the world, and there is no contradiction in that. By contrast, if someone tells me "It is forbidden to murder," I am supposed to draw operative conclusions from it (or dispute it). I cannot accept the claim that murder is forbidden and at the same time support murder. The sentence "It is forbidden to murder" not only describes; it is also meant to move (or restrain). The prohibition is a derivative of the ethical proposition. One who agrees that morally murder is forbidden and at the same time thinks that it is proper to murder simply does not understand the concept of a moral prohibition. The meaning of the existence of a prohibition is not a neutral fact, but that in practice one may not do it. In this ethical propositions differ from any other factual proposition.

Chaim Perelman, a Belgian philosopher of law, points out that when I tell Reuven not to murder because it is immoral to murder, I have said nothing. I have simply repeated the same thing in different words. If he knows that it is immoral to murder and he also understands what that means, nothing further needs to be added in order to dissuade him from murder.

Moral contemplation

The conclusion from the analysis we have made here is that ethical facts are different from ordinary (physical) facts. Physical facts are observed with the senses, and the mere fact that one knows them says nothing in the value-normative plane. It is a neutral fact. Moral contemplation, by contrast, which yields ethical propositions such as the prohibition of murder, is contemplation of ideas (a concept drawn from Husserl's teaching). I contemplate the idea of the good and understand that murder is forbidden. The ethical proposition "It is forbidden to murder" is true because it corresponds to what I see in my moral contemplation. That is the comparison I make in order to determine whether an ethical proposition is true or not.

Many believe that moral contemplation is performed inward, into our own soul. Some formulate this as contemplation of my conscience and what it tells me. But this is a mistake. If what I contemplated were something within me, then we would have returned to the conception that ethical propositions are descriptions of my own subjective mental state. Here again we see that there must be a standard in the objective world outside me in order to give meaning to my moral and value judgments. If moral and value judgment has any meaning at all beyond reporting a mental state, then it is clear that conscience is a cognitive instrument. It is the tool that allows me to contemplate the idea of the good and derive from it practical instructions regarding good and evil, or moral do's and don'ts.

And again the question returns: who created the idea of the good? If it is some abstract object that exists in the world outside us, it came into being somehow. Moreover, it is not just an ordinary neutral factual object. Therefore its existence cannot be explained as other facts are explained. It is an object laden with normative weight, which moves me to action (or restrains me from action). So who created it? That is the factor that defined good and evil and distinguished between them. If good and evil are merely the product of my own psychic structure, there is no room for moral judgment. As we saw in earlier chapters, any person whose choices are judged by a criterion that he himself chose and created is by definition morally righteous. Thus the analytic perspective we presented in this chapter is another reflection of what we saw above. If judgment on an ethical proposition is made only from within the person's own system, it is emptied of its special moral content. It becomes a proposition describing a person's conceptions, and its truth or falsehood is nothing but correspondence to his own worldview and not to any objective measure. Clearly, there is no possibility of blaming someone for being built differently from me.

A note on values and materialism

In my two books, The Sciences of Freedom and God Plays Dice, I pointed out that the very existence of norms and of good and evil is itself contrary to materialist conceptions. A person who conceives of the world as nothing but a material object will not be able to accept the existence of the distinction between good and evil. There is useful and useless; there is what causes suffering or happiness; but all these are facts. The normative dimension as a whole is irrelevant and cannot exist in a world that is entirely matter. Stones, or even merely biological creatures, do not allow the creation of norms and value and moral judgments. They are what they are because they are what they are. They behave this way and not otherwise because that is their nature (as in the sheep story of Amnon Yitzhak).

Thus a norm is something non-material and does not exist in a world that is only material. It is important to understand that I do not mean only that human beings cannot behave morally if they are made of matter (just as stones or sheep do not choose the good). I also mean that the categories of morality, good, or evil cannot exist in such a world. Those categories are not made of atoms; they are something else.

On the other hand, as we will sharpen further in the next chapter, this category is also not merely our nature and nothing more, for if it were it would lose its objective judging significance and become subjective. As we have seen, there must be some idea independent of us, and it is not merely a nature implanted in us. It is an idea that exists in the world as an idea, and our contemplation of it yields our moral judgments and decisions.

It is true that such an argument does not necessarily lead us to belief in God, but only takes us out of the materialist conception. But one of the foundations of disbelief in God is materialism. The feeling that one can generate morality and values by the human being himself, without dependence on God and without anything beyond matter, is philosophical folly (held by many intelligent people). See more on this in the next chapter.

Summary

At first glance, this picture seems to imply that God is the source of the validity of moral laws. But that is not necessary. It is also possible to argue that God here is the source of the laws themselves, and that their validity comes from themselves. He created the good and the evil, and defined the values that fall under each of these two headings. Every person who contemplates the idea of the good and understands the difference between good and evil and its meaning thereby automatically understands that he must act in a good way. This contemplation yields propositions that are not neutral like ordinary factual propositions. It yields propositions with value-charge, which move us to action.

Therefore God does not function here as one who commands us to be good. He created the distinction between good and evil and planted within us the ability to distinguish between them, and from that point onward the matter is in our hands. God only defined what is good and what is evil, and indeed the good and evil themselves. From there onward, it is our understanding and the commitment we have taken upon ourselves to conduct ourselves accordingly. The conclusion is that God is the external objective source that was missing in Ari Elon's theory of sovereignty.

1. Is there a moral atheist?

Introduction

From what we have said so far it follows that in an atheistic worldview there is no possibility of valid moral judgment, and from this one could apparently derive that an atheist cannot be moral. Among thinkers of the Mussar movement it was common to quote the verse in which Abraham says to Abimelech (Genesis 20:11):

And Abraham said, "Because I thought, surely there is no fear of God in this place, and they will kill me because of my wife."

At first glance this is an expression of that conception: without belief in God and fear of Him, there is no morality.

An empirical difficulty

On the other hand, our own eyes plainly see that there are many atheists who are no less moral than believing people, and perhaps more so. And conversely, there are believers who do not act morally. Does this theory stand the empirical test? The second claim is weaker, for belief is a necessary condition for morality, but certainly not a sufficient one. A person who believes in God can also choose evil and fail to commit himself to the good. The more significant question is whether an atheist really cannot be moral.

Before I go on to discuss these claims, I should only note that the moral theory presented here is not empirical. As we have seen, one cannot ground a moral theory in facts (the naturalistic fallacy). Facts, even those concerning human behavior, are neutral. When I say that people behave morally or immorally, I have given simple factual descriptions, but I have said nothing about their moral theory and certainly nothing about its validity. It is important to understand that we are dealing here with ethical propositions and their meaning, not with factual propositions. We will now see the application of this to our matter.

Is there a consistent atheistic morality?

My claim here is that within an atheistic worldview it is impossible to develop a consistent moral theory. Atheists can be good people, and there are quite a few כאלה. They can even devote all their days to acts of loving-kindness and helping others with great devotion. And still, there is no moral behavior here. I do not think that atheistic groups behave less well than others, and there is no principled reason their behavior could not even be better. The question I ask is what justification they can give for that behavior, and whether it is consistent.

When I ask the atheist why he does this, the answer will be: because that is the dictate of his conscience. If he is of the more rigorous sort, he will add that he is a sovereign Jew and not a rabbinic one, that is, he constitutes his own values. Then I will ask: and if someone else's conscience tells him to be a hired killer, do you have criticism of him? In my experience, at this point atheists divide into two groups: a. there will be those who say no, but they are built differently from him. It is pleasant and comfortable for them (and also seems right) to do good, whereas he is built in the opposite way. b. and there will be those who say that they certainly do criticize him, for although he chose his values sovereignly, his values are not the right values.

Regarding position a, I no longer need to explain that this is not a moral conception. A person who does something because he feels like it, or because that is how he is built, is not a moral person. He is a pleasant and agreeable person (in fact, he is a kind of sheep), but morality is obedience to some external command. A person who constitutes his own values is not essentially different from the hired killer, and those who hold position a even admit this.

By contrast, to those who hold position b I will now ask: who determines which values are good and which are not? If sovereignty is indeed the criterion (my choice is what gives these values and not others their good character), then as we have seen there can be no difference between Mother Teresa and a hired killer. Both chose their values. For moral judgment to be possible there must be some external factor that defines the killer as acting on the basis of evil values and Mother Teresa as acting on the basis of positive values. In an atheistic picture there is of course no such factor.

In fact, I am not claiming that there is no atheist who behaves well, but that an atheist who behaves well does not do so for moral reasons. If you like, there can certainly be an atheist whose conduct is moral, but his moral theory is not consistent. A person cannot be an atheist and answer consistently all the questions I have posed here without smuggling into the picture some external factor that defines and establishes the distinction between good and evil. That is God in the terminology of the proof from morality. The argument from morality places the atheist before a Sophie's Choice: either give up atheism (that is, recognize that all along he has been an unconscious believer), or give up morality and the ability to judge other people for their behavior. He can of course continue to behave pleasantly and agreeably, but he cannot criticize and judge others for their behavior, nor can he claim morality for himself.

Judgment as instinct

As noted, I already have some experience with such thought experiments. Faced with the cruel choice before them, and given their unwillingness to give up both atheism and morality and the possibility of moral judgment, they claim that they actually can judge others as good or bad while still being atheists. The same built-in instinct that tells them what is good and what is bad (their nature) also tells them to judge those who act differently as bad and those who act that way as good, to condemn those who do bad and praise those who do good. They have an instinct of moral judgment, and therefore they judge others.

This is a very strange claim. Just as behavior according to instinct is not morality, so judgment based on instinct is not judgment. You get stomach pains when you see a murderer, but stomach pains are a problem that calls for taking a pill, not for moral judgment. Why does the fact that I am built in a certain way allow me to judge someone? If I am built like a hired killer, I certainly will not judge him for his conduct. Moreover, how can one judge a person for being built differently from oneself? After all, he acts according to his understanding exactly as you act according to yours. If your measure of good and evil is the sovereign measure (what you chose), then that is exactly his measure too. As stated, in order to judge you must assume some external objective standard that is binding on both of you. The mere fact that you are built differently is just a fact.

In other words, I do indeed feel judgmental toward others who act differently from me, but one cannot give that feeling the meaning of judgment. It is an instinct, and as such it is not essentially different from hunger or fear. The atheist who judges instinctively is basically doing the same thing I do, and he probably feels exactly the same feelings about it. In my opinion he does so because he implicitly believes in God, even if it is difficult for him, or he refuses for some other reason to admit it. But if he nevertheless insists that he does not believe in God, then either he is inconsistent (for there is no moral judgment without belief in God), or he simply does not understand what judgment is, and mistakenly identifies it with instinct.

It is important to understand that even in this picture there is certainly room for moral instinct as a guide that directs our judgments. But judgment cannot end with instinct. By its very definition, judgment is not an act of instinct itself. Judgment must pass through a cognitive process of deliberation and decision. And to prevent another mistake: this is not because instinct is wrong or can be wrong, but because instinct, even if perfect, is not judgment. A sheep with a perfect moral instinct does not judge and cannot judge anyone. Exactly as a robot that produces an output containing a moral judgment of an act or a person, even if the judgment is entirely correct, is not judging. It is an automaton, exactly like the sheep or the atheist (according to his own conception of himself).

Moreover, many have already pointed out that a person who lacks the capacity for empathy, that is, to feel the other person, cannot behave morally. Empathy is a kind of instinct (that is, a feeling not derived from deliberation and decision), and nevertheless it is a condition for moral behavior. If a person does not feel another's suffering—for example, if his amygdala ("almond nucleus") in the brain, which is responsible for empathy, has been damaged—he does not understand at all that there is a problem in the suffering he causes. Therefore, even if theoretically he is a moral person, this will not come to expression. But again, identifying empathy with morality is a categorical mistake. The fact that I feel empathy is a necessary condition for my behaving morally, but certainly not a sufficient one. By the same token, the fact that I have eyes and can see is in many cases a condition for moral behavior. If I do not see someone, I cannot help him. Would anyone think of identifying morality with sight?

All these are further expressions of the naturalistic fallacy we encountered above. We saw there that morality cannot be derived from facts—neither facts about the doer nor facts about his environment or any other person. The fact that I feel something (see, or feel empathy) is a fact, and therefore one cannot derive a judgment from it (that is, that some act is morally good or bad). On the way from the fact to the judgment there must be some bridging principle (for example, that whatever I feel bad about is morally bad), and adopting that principle is in fact the essence of the judgment.

Feelings of disgust^[46]

Certain feelings of disgust are perceived by many of us as reflecting a moral problem. Jonathan Haidt gives several examples of this at the beginning of his book. For example, the neighbors' family dog was run over and killed in the middle of the night in front of their house. They had heard that dog meat is very tasty, so they cut up the body, cooked it, and ate the dog's meat. No one saw them doing this. Is there a moral problem with what the neighbors did? Most human beings will feel that there is some moral wrong here, even though many of them will not really be able to explain exactly what the problem is. Haidt gives another example there: every week A goes to the supermarket and buys a slaughtered chicken. Before he cooks it, he has sex with the dead bird. Afterwards he cooks the chicken and eats it. Is everything all right? Can we just continue as usual? Or is there something immoral in what A did? In both stories no one was harmed, the matter is entirely private (family or personal), and there is even an efficient use of available raw materials in order to increase the total amount of pleasure in the world. So what exactly is wrong with these acts?

There are people who feel no problem at all here. In their view morality is identical with the feeling of disgust. For them, moral judgment is nothing but the externalization of the disgust instinct they feel, that is, a report on a mental state and nothing more. The same applies to incest with the consent of both parties, eating human flesh, and so on. If morality is nothing but an expression of disgust, then all these are indeed immoral acts. But if judgment must also pass through our cognition, then more complex problems arise here.

Society as the legislating factor

Another suggestion commonly heard from atheists is that society defines good and evil. The external and objective factor that legislates values and distinguishes between good ones and bad ones is human society itself. It is an external and objective factor in the sense that it is neither me nor you. Seemingly this is exactly Rousseau's social-contract conception and that of his followers.

But this proposal too is very problematic. And if society legislates bad laws, such as the duty to murder every person under 1.90 meters tall—does that make those laws good? This is exactly the same problem as the sovereign individual who legislates for himself. According to this proposal, society is by its essence good, since it legislated what it legislated. But it is clear to all of us that society too is not above moral judgment, and that there can be good societies and bad ones. What determines whether a given society is good or bad? Objective standards that lie beyond it as well. And once again we return to the need for that external factor that legislates and validates the distinctions between good and evil and classifies values as good and bad.

On the Nuremberg Trials and the Euthyphro dilemma

Incidentally, this was exactly the revolution of the Nuremberg Trials. The defendants there argued that they had acted according to orders. The conception underlying that defense was precisely the one described above: if those were the laws and orders, then those were the standards by which a German citizen had to act. Morality and values are the product of society's decision. The implicit assumption is that action according to laws and orders is not subject to judgment, since legislation is what determines good and evil.

The great novelty of the Nuremberg Trials was that such a defense was not accepted. Society too, and the laws it creates, stand under moral judgment. The novelty there was even greater, for they were not dealing with morality but with law and legal judgment. The message that emerged from there was that even in legal standards, legislation is not the only measure of the legality of an act. Thus when we move to the moral plane, a fortiori legislation is not the only measure, or even the main one.

Society does not determine moral norms; rather, it is commanded to act according to them. Society must legislate the correct norms, not that norms are correct because society established them. In theological contexts people speak of what is called the "Euthyphro dilemma" (from the Platonic dialogue Euthyphro): is the good good because God commanded it, or did God command it because it is good? God stands outside and above all systems (He is the one who created them), and therefore in His case there is room for this question. But no other system—law, society, and certainly not the human being himself—can be regarded as the moral lawgiver that determines the standards for moral judgment and therefore stands above such judgment.

There is yet another plane to which the desperate atheist tries to flee in order to find an anchor for command and moral judgment: humanity as such. Moral laws and the distinction between good and evil are the product of belonging to humanity in general, and not to a particular human society. In this way one can also judge a given society if it acted contrary to universal human laws. But this is, of course, a fiction. Where did humanity enact such laws? Moreover, what are we to say about a situation in which all the human beings alive today behave immorally? Who is the factor that will judge them? Is universal human evil somehow above morality and moral judgment?

Creating this fictitious concept of a convention signed by all members of humanity does not really offer an alternative. From where does the obligation come to keep the conventions we signed? This is a veneer that tries to let us escape the need to speak of and recognize God as the moral lawgiver. But these pathetic attempts to flee the need for a moral lawgiver do not really succeed. People try to look for Him within us (in thought or instinct), in the society around us, or anywhere else, or in humanity in general; but any factor that itself stands under such judgment cannot be regarded as the lawgiver who creates the standards. Again and again we return to the proof from morality: either there is a God, or there is no morality.

The proof from morality and the proof from epistemology

There is a parallel between this move and what we encountered in the previous parts (the proof from epistemology). There we stepped outside our system of cognition and thought and exposed the fact that belief in God lies at its base. Here we stepped outside our moral system and exposed the fact that belief in God lies at its base. There we saw that evolution was presented as a possible rebuttal to the argument, and therefore we should not be surprised that the same is true here as well. The rejection of that rebuttal will likewise be quite similar.

An evolutionary explanation

Many people with whom I spoke about the proof from morality tried to propose evolution as an answer to the source of morality. We act morally and judge people and societies morally because evolution implanted in us the moral sense and tendency. Various explanations have been offered for this, almost all of them resting on the survival value of morality and cooperation among individuals. A society that cares for its members and in which each member cares for his fellows is a stronger society with a better chance of survival. Thus the evolutionary process created within us values and moral behavior. Once again evolution is presented as an alternative to God.

This argument suffers from so many flaws that it is difficult to detail them all here, so I will only try to point to them briefly. Almost all of them have already been clarified at earlier stages.

First, there is a scientific mistake here. Evolution ensures that behaviors useful for survival develop. But there is no reason to assume that it develops feelings and judgments. If a society had emerged whose members all behave well toward others, and whoever does not behave so suffers, that would be an evolutionarily plausible result. But there is no need whatsoever for the entire mental space that was created around the matter. Why should moral judgment, or a Kantian ethical theory, arise? It would have been enough for the tendency to assist others to be embedded in our genes. What survival requires are acts, not mental states. Evolution does not offer even the slightest shred of explanation for this.

Second, the evolutionary explanation, even if it were correct, explains how the moral feeling arose, that is, the tendency to help others. But as we have repeatedly seen, that is not morality. If someone explains his tendency to help others by a built-in instinct within him, evolution may perhaps explain how such an instinct came into being. But such an instinct is not morality. Morality is not acts, nor is it responsiveness to instinct (as with a computer or a sheep). Morality is the fruit of cognitive decision. Moreover, morality is a valid norm, not a pattern of behavior. Can an evolutionary explanation ground the obligation to be moral? It can explain how the moral tendency arose, but what if there is someone who does not respond to it or does not feel bound by it? He went through a different evolutionary path and does not have that same tendency, or he simply does not feel like responding to the tendency that is indeed embedded in him. Is there a defect in that? Can he be judged for it? And in general, what value or obligation is there in behaving as I was born just because I was born that way?

In fact, evolution deals on the factual plane (how a tendency or behavior was formed), whereas morality belongs to the normative plane (the desirable and not the actual). The fact that some tendency arose in me does not mean that I must behave according to it. Is a person who does not eat therefore immoral? The tendency to eat is also innate and inborn in us. What is the difference between it and the moral tendency? Is someone who was born overweight and tries to slim down immoral? He too is not adhering to the way he is naturally built. Is someone born in a religious home who decides to be secular, or vice versa, a moral offender? The fact that I am built in some way has absolutely nothing to do with the obligation to do or not do something. This is once again the same failure to distinguish between the desirable (ought) and the actual (is), or between facts and norms, which we called above the naturalistic fallacy.

Thus the evolutionary explanation can at most explain good behavior, but not obligation and moral behavior. It also cannot justify moral judgment. Those who rely on it confuse a sense of morality with moral obligation (or valid morality). If we return to the proof from epistemology, the difference between a sense of morality and valid morality is like the difference between a sense of trust in the senses and in thought, and a philosophical conception that they are indeed reliable. The former is instinct; the latter is a cognitive decision.

And perhaps the sense of obligation and judgment really are mere illusions?

Of course, one can claim that they are illusions. Even someone who thinks moral judgments are valid lives under an illusion. The truth is that these are only built-in tendencies. No problem. That is indeed one of the options. But then one should try to refrain from moral judgments, and certainly we should not take too seriously judgments coming from such a person. He is merely expressing feelings and nothing more.

I repeat once again that a "theological" argument only places us before a mirror. Either belief in God or non-valid morality. If someone chooses the option of non-valid morality, that is certainly a consistent choice. This argument cannot persuade him that he is wrong. The purpose of the argument from morality is only to say that if you really are an atheist, then you must necessarily see judgments as illusions and built-in, unjustified instincts. That is all. I have no way to convince someone that morality is indeed valid. Each person has to examine himself and his positions and make a decision. But once you have decided that there is valid morality and that in your view it is not merely an illusion, you must recognize that at least in this sense you are a believer.

A note on the Euthyphro dilemma

We presented above the Euthyphro dilemma, which sets two possibilities against one another: is the good good because God commanded it, or did God command it because it is good? Many thinkers have addressed this question, and Avi Sagi even devoted an article and a book to it. His conclusion is that, surprisingly, in Jewish thought we scarcely find the possibility that the good is good because God commanded it. Despite the theological difficulty involved in assuming that morality has validity independently of the divine command and of God altogether, it is this latter approach that is dominant in Jewish thought.

But now we must note that the proof from morality assumes that there can be no valid morality without God, who provides its grounding and gives it validity. There is no atheistic morality. Does that not rule out the option in the Euthyphro dilemma according to which the good does not depend on God? After all, there we assumed that the good does not depend on God. Does the proof from morality still allow the Euthyphro dilemma to stand, and in particular that option in the dilemma (which, as noted, is the prevalent one in Jewish thought)?

First, we must note that the dilemma proposes a separation between morality and God's command, not between morality and His will. What we assumed in the proof from morality is that morality draws its validity from God's will and not from His command. On the contrary, we saw that morality and halakha are two different categories, and morality belongs to the category of God's will and not His commands. Second, one may infer from the proof that in truth one cannot speak of morality in a way that precedes God, and therefore the dilemma is indeed illusory. The conclusion is that the second side of the dilemma is the correct one. And still, the dilemma has a narrower meaning: is morality part of God's command or part of His will? But it is true that morality cannot be valid and binding without God at all.

The assumption that morality can be valid without God at all, in effect grants moral principles logical validity. They possess necessity like the laws of logic, and therefore they precede God and he is subject to them. We have already seen that logic is valid by virtue of itself (and therefore God too is "subject" to it, that is, cannot deviate from it). This dilemma suggests that morality is like that as well. If one indeed adopts this conception, then the claim that act X is moral is necessary in itself and can precede God’s command.

It seems to me that perhaps such a possibility can be raised, but in a narrower way. Given the world as it is and the human beings created in it as they are, morality too is necessarily as it is (it cannot be otherwise). This is a necessary connection, like the logical necessity of the connection between premises and conclusion. But the decision to create precisely such a world and such human beings (the premises) is a free decision of God. In this sense, God precedes everything and nothing precedes him. He created the world, and from that the principles of morality are derived (necessarily derived, according to this suggestion). He cannot create the same world with different moral rules. According to this suggestion, this is a kind of logical necessity, and therefore God too is subject to it. But the decision which world and which human beings to create is his free decision. If he had decided to create them differently, then perhaps the relevant moral rules too could have been different.

In summary, according to the assumptions of the argument from morality, the Euthyphro dilemma—at least in its broad and sweeping formulation—is illusory. There cannot be a morality that precedes God, but at most (if at all) one that precedes his command. It draws its validity from the will of God and exists in this form only within the framework of the world he created.

1. The argument from meaning

Introduction

To conclude this part I will briefly present a formulation that extends the pattern of the argument from morality, dealing with meaning (instead of morality). The structure is entirely parallel to the argument from morality, and therefore I will only trace the stages of the argument schematically, without again entering into the subtleties and nuances. We have already done all of that with respect to the argument from morality, and as stated, the move here is parallel.

The argument from meaning

People experience a sense of meaning in their lives. Even those who do not find such meaning are frustrated by this, because they implicitly assume that their lives must have meaning. Viktor Frankl, in his book Man’s Search for Meaning, built an entire psychological doctrine on this principle. He offers people a kind of redemption through finding meaning in their lives.

But we must ask ourselves what meaning is at all. Can any object that exists in and of itself have meaning? Meaning is always the result of some comparison: striving toward some utopia that lies outside us and serves as a standard for us. People can find meaning in morality, in art, in the observance of commandments, and more. But all of these can have value only if there is some objective source of validity that gives them such value. A thing in itself is always meaningless. It simply exists and simply is what it is. It can have meaning only if someone infuses it with meaning. Someone who created it for some purpose, or at least someone with the authority to chart its path and give it meaning.

If so, we are back to God once again. If a person feels that his life has meaning, then implicitly he is a person who believes in God, in some being that stands at the foundation of the meaning given to his life. A person standing in a void, by definition, has no meaning in his life.

Does a person create meaning for himself?

To be sure, in Viktor Frankl this concerns various and diverse meanings that a person constructs for himself. A person who is in a difficult psychological state, in existential despair, is supposed to establish some meaning for his life. According to Frankl, a person is not supposed to "find" meaning somewhere outside himself. There is no objective and given meaning apart from that which the person himself generates and constitutes for himself.

This picture recalls the Kantian conception that sees the human being as a moral legislator (see the discussion in Ari Elon’s article at the beginning of this part). There too we saw that ostensibly the framework is humanistic, one in which the human being is the source of the laws and of the obligation they impose. But we noted that this cannot be so, and that behind human choice and decision there must stand some objective standard that determines, whether we like it or not, what is good and what is not. We decide whether to be committed to the good, but we do not determine what the good is. The same holds in the context of meaning. For meaning to have any validity, it must come into being in a way that does not depend on us. We decide whether to act in accordance with its guidance and toward its realization, or not, but we are not the ones who determine what it is. The moment we constitute meaning for ourselves, the matter resembles someone legislating the laws of morality for himself. The system loses its meaning, for whatever we decide to do is always the meaning given to our lives. Meaning becomes a tautology.

Two senses of meaning

The search for meaning as psychological therapy is of course not contingent on all this. A psychologist may speak of the autonomous constitution of meaning as a way to heal a person and bring him out of the crisis in which he finds himself. This is a psychological process, and as such it is evaluated in terms of usefulness or lack of usefulness, not in terms of right and wrong. Just as, in the moral context, a person may act properly and well because he feels like it, and not as a response to a moral command. He responds to the command of his heart, or of his conscience. But there too such conduct empties those acts of their moral significance. As we saw, this is a good, nice, pleasant person (like Amnon Yitzhak’s sheep), but not a moral person.

When I speak about meaning in the philosophical context, I mean meaning that has validity, meaning that is assessed in terms of right and wrong. Here it is not relevant to speak of meaning measured in terms of its therapeutic value.

The argument from meaning as a "theological" argument

The argument from meaning addresses a person who feels that his life has meaning in the philosophical sense, not a person who needs meaning as a therapeutic tool. If a person feels that his life has meaning in this sense, then he necessarily believes in God (even if only implicitly). And indeed, a person who does not feel this, or a person who gives a psychologistic interpretation to his sense of meaning, truly need not infer from it the existence of God. Exactly as a person who feels moral obligation but gives it a psychologistic interpretation (this is how I am built, and therefore I feel such an obligation) does not have to infer from this the conclusion that there is a God. In this sense, the proof from meaning too is a "theological" proof and not a "philosophical" one.

1. A look at the theological significance of "theological" arguments

Introduction

In the previous three notebooks we dealt with the three arguments discussed in Kant’s great critique, Critique of Pure Reason: the ontological, cosmological, and physico-theological arguments. Those three were arguments of a "philosophical" character. By contrast, in the present notebook we dealt with two arguments of a "theological" character: a "theological" formulation of the physico-theological argument, and the argument from morality. The latter appears in Kant’s books that deal with ethics. In this chapter I wish to place the argument from morality, and in fact "theological" arguments in general, within the general theological context, to identify their distinctive character, and finally also to say a few words about the move from deism to theism (that is, from philosophy to religious faith), which the next notebook will address.

The God of the first three arguments: deism

I have already noted more than once that every argument that proves the existence of God presupposes a different God, or rather a different definition of God. The ontological argument presupposes a God who is a perfect being (than which none greater can be conceived). The cosmological argument presupposes a God who is the source of creation (the creator of the world). The physico-theological argument presupposes a God who is the engineer and architect of the world, with its complexity and its laws. What do all these have to do with a religious, commanding God—that is, with the one who gave the Torah at Sinai? We will address this question in the next notebook. Here I wish to take only one initial step toward the answer.

It is enough for one of the proofs to convince us in order to reach the conclusion that there is a God (of the type with which it deals). But it is important to understand that even if one accepts all three arguments, there is no necessity to assume that these are different beings. It is quite possible that this is the same being, who is also perfect, also the creator of the world, and also its architect. One can even say that this assumption is simpler than the possibility that these are three different beings, and therefore, according to the principle of Ockham’s razor, it is preferable to the assumption that these are three different beings.

But these three aspects describe for us a God who is not connected to the world, nor to us. This is a deistic God, that is, a philosophical being whose relevance to us and our lives is very limited. Even the God of the laws described in the previous notebook is a God who created laws for some purpose, but once they were created, they are what drive the world. His involvement is no longer required. He may have created a world with laws that would lead it to produce human beings and animals, but does God want anything from those human beings? Is he interested in them at all? How can one proceed from here toward a commanding God, who is interested in interaction with his creatures?

The God of the "theological" arguments: theism

The two arguments presented in this notebook already take a small step toward an involved and commanding God, that is, they move us from deism toward a theistic conception.

The "theological" formulation of the physico-theological argument (the argument from epistemology, which was presented here in the second part) indicates that God saw to it that we would be able to understand the world and learn it. That is, he is involved in our lives in some sense. He built the world so that we could understand it and manage within it. This is a kind of involvement and interest in us.

The argument from morality already takes us a significant step further. Here he already expects from us a certain kind of behavior and rejects other behaviors. True, there are no religious or legal commands here, but there are moral demands. Here a normative God is already revealed, and not merely a physical or epistemic God. From here, the distance is shorter to a theistic conception that speaks of a God who reveals himself and commands a comprehensive system of commandments (of a different character, religious and ritual).

The God of the "theological" arguments: concretization of God

The perfect and creator God may be wise and omnipotent. But can we say anything more about him, or is he an abstract being about whom we can say nothing? It seems that the "theological" arguments not only bring us closer to an involved and commanding God, but also begin to color him in more concrete hues.

God who commands morality is endowed with certain attributes. A God who commands morality and expects us to behave morally is a compassionate and gracious God. He is interested in the good and in our behaving accordingly. This is already a more concrete statement about him and his attributes. In the argument from epistemology as well, a God is revealed who cares for us and for our ability to manage in the world he created. Again there is here some description of him as good and compassionate.

Summary

The philosophical toolbox we have used up to this point cannot take us all the way to putting on phylacteries or to the prohibition on eating pork. Philosophical tools can lead us to general philosophical conclusions, not to particular religious conclusions (why Judaism rather than Christianity or Islam?). And yet, we have seen here that the "theological" arguments brought us a little closer to a more concrete, "religious" God. From this point on, it is not clear how one can proceed. Seemingly, philosophy reaches only this far, and now "where philosophy ends, faith begins." But if, as I have tried to show so far, faith is not a substitute for rational thought but rather its product, then we must examine how it is nevertheless possible to proceed by rational means toward faith and the observance of commandments.

Even if it is possible to proceed further, it is quite clear that the tools will be less general and logical, and less abstract, than they were in the first four notebooks. From here on we will have to use tools of common sense, history, and the like. That will be the subject of the next notebook.

1. See more on this in the fifth part of my book Truth and Uncertainty. ↑

2. I am not entering into a precise definition of a negation that operates on the whole set of premises. It is easy to understand that for our purposes it means that at least one of them is false. ↑

3. For an overview and primary sources, see the English Wikipedia entry on Abductive reasoning. ↑

4. For the sake of completeness I should note that there too I qualified this claim, since the claim that there is a God can be seen as a claim based on observations that have already been confirmed in the past, and in that sense it may perhaps be viewed as a kind of scientific claim. ↑

5. For a more detailed explanation, see the fifth part of my book Truth and Uncertainty. There we saw that at the basis of scientific generalization, that is, abduction, stands the faculty we call intuition. I further explained there that this faculty is not a kind of thinking but a kind of cognition; that is, intuition is in fact a kind of observation (non-sensory) of the world and of the ideas that underlie it. ↑

6. Michael Abraham, Dov Gabay and Uri Schild, College Publications, London 2010. Two lectures of mine on this subject can be viewed on YouTube: https://www.youtube.com/watch?v=XEVSj1My5Ns

   https://www.youtube.com/watch?v=cuLA-UXYoM4 ↑

7. Those familiar with the terminology of Jewish law know that there are actually three different kinds of "common-denominator" inference. Here the inference presented is the one composed of two arguments from paradigm cases and the refutations of them, but there is also an inference composed of two a fortiori arguments and the refutations of them (there the upper and lower values in the right-hand column of Table 6 are 0), as well as an inference composed of an a fortiori argument and an argument from a paradigm case and the refutations of them (one value is 0 and the other 1, respectively). ↑

8. Richard Taylor, Metaphysics, translated by Yael Cohen, Adam Publishing, Open University, Jerusalem 1983. The relevant passage appears there in the second half of the tenth chapter. ↑

9. Several examples are brought here that I will skip for the sake of brevity. I will only note that his assumption that there is another explanation is only at the analytic level. There is no doubt that it is more reasonable that someone arranged the stones (and this is essentially the physico-theological proof in its "philosophical" direction). To be sure, the conclusion that someone arranged this inscription does not arise analytically from observing it, and in fact this is the basis for most objections (including the Kantian one). In Taylor, the assumption that it was arranged by chance is only a methodological assumption, whose purpose is to sharpen his variation, which is presented immediately below. ↑

10. Skepticism here means lack of trust in cognition (and perhaps also in thought, since our thought trusts the eyes), not skepticism regarding the existence of God. The latter is of course a special case of the former, but we will get to that later. ↑

11. For the sake of simplicity, I refer here to the opposite of skepticism as rationalism. I mean trust in cognition and rational thought. Later in the notebook I will emphasize this more, namely that belief in God is a condition for rational thought. For now this terminology can be adopted merely for the sake of simplicity. ↑

12. Rationalism here means trust in the sensory faculties (that is, in rational and scientific thought; see below). ↑

13. For a similar consideration, see Ludwig Wittgenstein, Philosophical Investigations, translated by Edna Ullmann-Margalit, Magnes, Jerusalem 1995, sections 143–245, on the issue of following a rule (Following a rule). Wittgenstein shows there, in the same mathematical way, that there are countless possible ways to continue any given series of numbers, and each of them will have its own mathematical logic. There is no simple or natural continuation, in any objective sense, to the given series. My argument here is an adaptation of that famous argument. ↑

14. This is still not abduction, since the graph is not really a theory but a general law. When we formulate a theory that explains the second law, that is, the direct relation between force and acceleration, then we have performed an abduction, since we have moved from the cases to the theory. See above in the first part, chapter 2. ↑

15. One might have said that it belongs to grammar, but that is not so. Grammar is the linguistic structure of the sentence, whereas our concern here is with the nature of the sentence’s contents, what the sentence and its grammar are meant to express. ↑

16. Samuel Hugo Bergmann, Introduction to Epistemology, Magnes, Jerusalem 1976. ↑

17. See on this, and on these new critiques, at much greater length in Gadi Taub’s book The Slouching Rebellion. Taub sharply criticizes this critique, and below I will argue that he is mistaken in this. ↑

18. Except for the origin itself, which in polar coordinates is actually a line. We will not go into that here. ↑

19. Although Kant himself did not think so. In his view these are synthetic a priori propositions. I think he meant their application in our world/space, but in the Platonic world they are analytic propositions. ↑

20. By the way, the relation between logic and computer science is more complex, and it is not clear whether it belongs to category A or B. ↑

21. This sentence is not entirely accurate. After the "death of God," in Nietzsche’s terminology, skepticism really did begin to spread in the world. True, it related mainly to abstract cognitions and not to trust in the senses, and therefore it seems that this phenomenon refutes only our variation on Taylor’s proof. The argument from the reliability of the senses remained intact. The argument from epistemology may be somewhat affected. ↑

22. In Jewish law a woman can be betrothed by means of benefit. For example, in the case of "Be betrothed to me on condition that I speak on your behalf to the authorities," or if she says to him, "Dance before me" (the woman becomes betrothed to him through the enjoyment of watching his dance. The enjoyment has monetary value, and this is the "money" of betrothal in this case). ↑

23. There is also an example from Jewish law of a situation of dual motivation, whose details we will not enter into here. See Mishnah Zevahim 13a, "for the sake of the Passover offering and for the sake of peace offerings," and parallels. ↑

24. In the context of Jewish law there is room to connect this to the issue of coercion and consent (a person who willingly performs an act that he is compelled to perform). See a brief discussion of this in the Talmudic Encyclopedia entry "Coercion (Necessity)," section 10. ↑

25. For a similar discussion in Jewish law, see Arukh HaShulchan Orah Hayyim sec. 308:15 (and see also his note there in subsection 68) on handling on the Sabbath an implement whose normal use is for a permitted task, "for no need at all." ↑

26. Immanuel Kant, Groundwork for the Metaphysics of Morals, Magnes, 1933, pp. 77-78. ↑

27. John Rawls, A Theory of Justice, p. 12. ↑

28. See on this in Hugo Bergmann’s book The Philosophy of Immanuel Kant, Magnes, Jerusalem 1980, pp. 102-3. Hereafter: Bergmann. ↑

29. The translation is taken from Bergmann there, p. 103. ↑

30. See on this in my book The Sciences of Freedom, in the third chapter. ↑

31. See on this in my article The Categorical Imperative in Jewish Law, Tzohar 31, 2008, and in the sources cited there. ↑

32. Theoretically, one could raise the claim that a person receives services from the state and that tax is the payment for them. Whoever does not pay his share steals the services he receives. It is doubtful whether this claim holds up from a consequentialist perspective, but in any case our concern here is only with the illustration, so we will not go into it further. ↑

33. The parallel between the cases is not complete. We saw that when I decide to evade tax, this does not harm my fellow citizens. Only if all of us evade tax will there be real harm to all of us. Still, when I examine myself against society as a whole, the situation resembles that of the prisoner’s dilemma. ↑

34. See on this in Nadav Shnerb’s article, Reflections on Idolatry, Akdamot 19 (2007) 47-64 ‬. ↑

35. There Maimonides defines worship out of love as doing the truth because it is truth and not for the sake of any benefit whatsoever (including reward in the world to come). This is essentially what is defined here as "acceptance of God." This is certainly not the love being discussed here (which is a psychological interest). Maimonides has several concepts of love, and this is not the place to elaborate on that. ↑

36. In the book Essays on the Foundations of Judaism, Yoram Hazony and Yosef Yitzhak Lifshitz (eds.), Shalem, Jerusalem 2004. ↑

37. See more on this in my article, The Gates of Conversion: On Violence and Good Intentions, Akdamot 22. ↑

38. In Tzohar 25, Spring 2006. ↑

39. See the two versions in Maimonides’ Laws of Kings, end of chapter 8, and in my above-mentioned article. ↑

40. See, for example, in his book This World, Yedioth Books and Beit, 1990. And likewise in an article from it that also appears in Shdemot issue 114, 1990, and on the BINA website, under the title "A Jew is anyone who looks in the mirror of history and sees a Jew," 1.4.1990. ↑

41. Published in the essay collection See Thus and Renew, The Free Jew and His Heritage, edited by Yehoshua Resh, Sifriyat Poalim, 1987, pp. 225-233. ↑

42. See chapter 3 of my book The Sciences of Freedom, and throughout the book Man Is as Grass. There I contrast a Taoist conception of morality (natural morality) with Kant’s conception (morality of subordination to command). ↑

43. Extreme logical positivists would probably disagree with this. ↑

44. For the sake of simplicity, I am ignoring here the difficulty of defining and assessing kindness. ↑

45. For a brilliant discussion of this question, see chapter 1 of C. S. Lewis’s book (yes, yes, the one from Narnia), The Abolition of Man, translated by Lahad Lazar, Shalem, Jerusalem 2005. See also chapter 16 of my book Truth and Uncertainty. ↑

46. See Tomer Persico’s article, Six Tablets of the Covenant – Jonathan Haidt on Different Shades of Morality, on his blog The God Loop, dated 29.2.2016. The article is a critical review of Haidt’s book: Jonathan Haidt, The Righteous Mind: Why Good People are Divided by Politics and Religion, Vintage, New York, 2012 ↑