Notebook 2 — The Cosmological Argument

With God’s help

The Cosmological Argument – A Systematic Analysis

Michael Abraham

Contents

Chapter 1: The Cosmological Argument among the Proofs for the Existence of God

Chapter 2: The Cosmological Argument

Chapter 3: What Is Wrong with Infinite Regress?

Chapter 4: Converging Infinities

Chapter 5: A Preliminary Examination of the Assumption of Causality

Chapter 6: On an Eternal Universe, Causes, and Reasons

Chapter 7: Between a Whole and Its Parts

Chapter 8: A General Look at the Structure and Significance of the Cosmological Argument

1. The Cosmological Argument among the Proofs for the Existence of God

Types of proofs for the existence of God^[1]

Kant, in his great book Critique of Pure Reason, divided the proofs for the existence of God into three kinds: the ontological argument, the cosmological argument, and the physico-theological argument. An ontological argument is one based on a purely logical line of reasoning, without assuming any factual premise. The next two types include arguments based on reasoning that rests on some factual assumptions.

Beyond these three types of argument, there are additional ways of arriving at faith. Some see it as a simple intuition that requires no proof, something like an axiom. Others arrive at God on the basis of the moral argument (which is also presented by Kant, in another of his books). Others arrive there through tradition, which transmits to us the information about God’s revelation to our forefathers or to some previous generation. Later we will note that each such argument presupposes a different definition of the concept of God.

In our discussion of the ontological argument, we noted the logical difference between the various arguments. The ontological argument is a purely logical argument, that is, a logical argument based on conceptual analysis. True, we saw there that the argument rests on assumptions, but they are not factual in character. Most of the criticism directed at that argument focused on this logical character. The cosmological argument (as well as the physico-theological one) does assume a factual premise, and on that basis builds a logical argument that leads to the factual conclusion that God exists.

As we saw there, there are two ways to attack such an argument: either to challenge the basic premise, or to challenge the validity of the argument itself (that is, whether the conclusion truly follows from the premises). In any case, unlike the ontological argument, which aspired to be a purely logical proof, a logical structure like that of the cosmological argument does not claim the crown of certainty. The premise at its base is factual, and as such it is open to challenge.

For this reason, the debate here will not be between rationalists and empiricists. Once one starts from a fact, there is no principled obstacle to deriving another fact from it. Even an empiricist can agree to such a structure. Still, it is important to understand that even within the empiricist picture there are moves of thought that go beyond observations. Scientific generalization is a procedure that takes us from particular observations to a general law, a step that is plainly not empirical.

I should note that at least one of the factual premises here is trivial: that something exists. It is hard to see anyone disputing that. Another premise is the principle of causality, which is admittedly not purely factual, but again it is hard to see anyone disputing it. So this is an argument of no small force, even if it does not have the certainty of a purely logical argument.

Historical survey

The cosmological argument was first presented by Thomas Aquinas, who relied on the writings of Aristotle, where he found the concept of a first cause that itself has no cause outside it. Avicenna, the well-known Muslim philosopher, proposed a somewhat different formulation based on the distinction between entities whose existence is contingent and entities whose existence is necessary (we discussed this in the notebook on the ontological argument). If we move from the Middle Ages to the eighteenth century, we encounter the German philosopher Leibniz, who, instead of grounding the cosmological argument in the principle of causality, chose to ground it in what he called the principle of sufficient reason.

Standing over against the cosmological argument is always the Aristotelian option of an eternal universe. At every stage we must examine whether what exists may not have always been here, since if the world is indeed eternal then it was never created, and therefore perhaps there is no need to posit the existence of a cause, or agent, that created it.

In the twentieth century the discussion of this argument entered the sphere of science. First, בעקבות the discovery of the Big Bang theory, William Lane Craig proposed an updated version of the argument, based on the fact that physics rules out the assumption of the world’s eternity. Once it is known that the world was created, we return again to the question of who or what created it. At a later stage quantum theory also entered the discussion, since it turns out that, contrary to what the cosmological argument assumes, there is a possibility of the spontaneous appearance of particles from the vacuum (without a cause).

We will discuss all these components of the debate as we proceed.

1. The Cosmological Argument

Introduction

The most popular formulation of the cosmological argument cannot withstand even simple objections. Still, because it is so widespread, we will begin with it, and from the objections to it we will later propose a revised version.

The cosmological argument: an initial formulation

The causal formulation of this argument is constructed as follows:

Premise A: Everything that exists has a cause for its existence.

Premise B: Things exist (the universe exists).

Conclusion: There is a cause for their existence.

We call this cause God.

Premise A is a premise about reality (about relations between things in reality). Premise B is straightforwardly factual, though, as noted, rather trivial (unless we are dealing with skeptics). Few would dispute that something exists, or that the universe exists. It is important to understand that the cosmological argument assumes that something exists, and it does not much matter what that something is. Therefore, one can also take as the starting point of the argument the assumption that I exist (following Descartes’ cogito), and derive the existence of God as the cause of my existence. Even someone who does not accept the validity of the cogito argument usually does not doubt that he himself exists. Therefore this premise, even if it is not philosophically certain or proven, is a good starting point for any argument.

Another important note. We already mentioned in the notebook on the ontological argument that any argument proving the existence of God must begin with a definition of the concept of God. In the case of the cosmological argument, we are speaking of God as the cause of reality. This is unlike the God of the ontological argument, who is defined as the perfect being (or the being than which no more perfect being can be conceived).

First and obvious objection: what is the cause of God’s existence?

This formulation is exposed to several simple attacks, and we will encounter them below. But first we must refine the argument and bring it to its optimal form. To that end, we begin with the primary and obvious objection that usually arises upon hearing this argument. Even if one accepts the assumption that everything must have a cause, once the argument proves the existence of God (who is the cause of what exists), the question arises: what is the cause of His existence? After all, the premise is that everything must have a cause, so why should God be exempt from it? And if He is not exempt, then the conclusion does not really resolve the difficulty raised by the premises.

To sharpen the meaning of this objection, let us try to carry this line of thought further and see that this objection cannot stand on its own. For the sake of the discussion, let us accept the objection’s premise that God’s existence too requires a cause, and call it God1. Now a similar objection will arise requiring the assumption that there is also a God2, and then God3, and so on. Each is the cause of the other. We receive an infinite chain of entities, each link in which is the cause of the next link. What we called God is the penultimate cause, and the final being is the thing whose existence we assumed (our world, ourselves, and so on). That is the last link in the chain of causes.

Is such an explanation acceptable? This is what philosophy calls an “infinite regress,” and it is generally considered a fallacy. Philosophers assume that an explanation resting on an infinite chain of causes or successive explanations is not acceptable. In the next chapter we will try to explain why this is indeed a fallacy, but before that it is important to clarify the significance for our purposes of the claim that this is indeed a fallacy.

If an explanation by infinite regress is indeed fallacious, then an explanatory chain cannot be infinite. From this it follows necessarily that the chain we described above must stop at some point. The place where the chain of causes stops is a link with no prior cause for its existence. It is the initial beginning. But now we must notice that the very existence of such a thing contradicts the assumption that every thing must have a cause for its existence. We have reached the conclusion that there exists something with no prior cause, and בכך premise A of the cosmological argument presented above is negated.

If so, the objector with whom we are dealing here is in fact implicitly proposing that we give up premise A of the argument, the premise that states that everything must have a cause. But if that is so, what is the point of asking questions about the cause of God’s existence? He could have challenged premise A directly and argued that it is not true that every thing’s existence requires a cause. One can perhaps see the form of his argument as a reductio ad absurdum proving that the assumption that everything must have a cause is false (since it gives rise to a contradiction or absurdity). In any event, in the final analysis this objection attacks premise A.

The cosmological argument: a revised formulation

Indeed, this objection is very persuasive. Premise A leads us to infinite regress, that is, to a fallacy (in the next chapter we will explain why this is a fallacy). To assume it is to introduce into the discussion with our own hands the absurdity of infinite regress (for if everything has a cause, then necessarily we arrive at the conclusion that the chain of causes must be infinite). Therefore we now propose a revised formulation, which is both more plausible and also answers the objection presented above (it does not assume that everything must have a cause):

Premise A: Everything of which we have experience must have a cause (or ground).

Premise B: There are things of this kind (the universe, ourselves, or any other object).

Conclusion: There must be a cause for the existence of these things. We will call it X1.

True, this is not yet the end of the road. For now, following our objector, we ask: is X1 of the kind of things that fall within our experience? If so, then it too must have a cause, which we denote X2. If not, then we stop here. To be sure, even if it is not of the type of objects about which we have experience, it may still have a cause, and we again denote it X2. If it has no cause, we stop here and conclude that X1 is an uncaused object, and we call it God. If we have not yet reached an uncaused object (the X1 we found has a cause), we continue the process and ask the same question about X2: is it of the type of things in our experience? If so, it must have a ground, which we denote X3. If not, we stop here. And so we continue until we arrive at a link that has no ground (which necessarily is not of the type of things in our experience). This ground does not satisfy premise A, but it also need not satisfy it, since premise A deals only with things within our experience. Therefore the chain stops here. The final link we reach will be called God.

Existence claim

There is only one point we must examine before congratulating ourselves: must there in fact be such an object? Who guarantees that this process will stop? Could it not be that we continue forever with objects that have causes, ad infinitum? Here infinite regress returns to us, this time in a positive role: if infinite regress is indeed a fallacy, then the chain cannot be infinite. Necessarily, at some stage this chain will arrive at an object that is its own cause (that has no cause), and that object we call God. We have proven the existence of God by way of negation (reductio ad absurdum): without positing such an initial link, we fall into a fallacy.

If so, the objection that was raised against the initial formulation of the argument is itself the revised argument that leads to the proof that God exists. We threw God out the door and got Him back through the window. We adopted the implicit assumption of that objection, that not everything must have a ground (only things within our experience), and precisely this is what led us to a proof of God’s existence. God is an object not subject to the conclusions we drew from experience, since we have no experience of objects like Him (He is not of the type of objects we know and have experience of), and therefore precisely He can be the first link in our causal chain.

If so, it is precisely the fallacy of infinite regress with which the initial formulation of the argument was charged that builds the fuller formulation. We must now examine this fallacy, and in fact see why it is a fallacy at all.

1. What Is Wrong with Infinite Regress?

Introduction

The revised formulation of the cosmological argument is based on the assumption that an infinite chain of explanations is fallacious. Such a chain is not an acceptable explanatory option. In philosophy it is customary to think that infinite regress is a fallacy, and in this chapter I will try to explain why this is so.

“Turtles all the way down”: is an infinite chain an explanation?

There is a well-known story (probably originating with the American philosopher William James) about a Greek physicist who gave a lecture on his cosmological theory, according to which the world stands on the back of a giant turtle. One of the listeners raised her hand and asked a question: what does the turtle stand on? The physicist did not lose his composure and answered: “On the back of another turtle.” The woman persisted and asked: “And what does the second turtle stand on?” He replied: “On a third turtle.” When the woman continued asking what the next turtle stood on, the physicist answered impatiently: “Madam, don’t you understand? It’s turtles all the way down.”

This story illustrates the problematic nature of an infinite chain of explanations. One can ask what “all the way down” means. What is this “down”? There is no down; in fact it just keeps continuing without end. The assumption that there is a “down” itself says that the chain begins somewhere and does not continue to infinity. But then, of course, the question will arise: what does the first turtle, the one that is there “down below,” itself stand on? Extending the chain as though there were infinitely many turtles is a fiction. The physicist who presents this explanatory chain as if it keeps descending farther and farther is not really offering an explanation; he is evading the giving of an explanation. He presents the false appearance that there is a “down,” and thereby exempts himself from answering the difficulty that still remains: if there is a turtle that is lowest down, what does it itself stand on? And if there is not, then what explanation are you actually offering us?

In fact, what the physicist offered as an explanation of the world’s location is the following explanation: there is an explanation of what the world stands on. He did not actually offer the explanation; he only claimed that there is one. To actually present the explanation he would have had to traverse the entire chain and present it in full, which of course cannot be done. If you were in the place of the woman, would you accept such an explanation to your question of what the world stands on? Would you accept the answer “I have an explanation” without its actually being presented? But that is what this physicist did. Alternatively, think about the question: which came first, the egg or the chicken? Suppose someone answered you that there is an infinite egg-chicken-egg-chicken chain […]. Is that a sufficient explanation?

Another well-known example is the fallacy known as “the homunculus fallacy.” Think about the attempt to explain how a visual image is deciphered within a human being. Would you accept an explanation of the following kind: there is a little person inside us (= homunculus) who sees on our behalf? Obviously not, because the question would now simply shift and revolve around that little person—how does he see?—and then we would need yet another tiny person inside him. Let us present this as a conversation in which A tries to explain to B how we see, of course without resorting to the concept of a homunculus:

A : I see an image.

B: How do you see it?

A: Light waves pass through the retina and create an image inside the eye.

B: Which the homunculus reads?

A: No, the image from the retina is transferred to the visual cortex in the brain, and there it is scanned.

B: And the homunculus reads the scan?

And so on.

What is the point of this dialogue? A scientific explanation of the process of vision is being proposed here, but each time an explanation is reached, an attempt is made to clarify whether we have now gotten rid of the need to resort to a homunculus—that is, whether a replacement explanation has in fact been offered here. It turns out that at no stage has this happened. It is self-evident that such a chain is not a defective explanation; it is not an explanation at all.

So too, the infinite chain of turtles is not a failed explanation. It does not offer an explanation at all. It is really saying that indeed there is no “down”; it just keeps going. Each turtle explains the one above it, and so on to infinity. But the explanation in full has not been presented; at most there is merely the claim that it exists. But a hypothetical claim that an explanation exists is not itself an explanation.

I should note that there are infinite regresses that may be acceptable. That is when one actually offers a description of all the links in the chain, even if only inductively. If, for example, we were to offer a description of the whole series by means of some formula, then there would be here a way of presenting an infinite chain, and perhaps one could accept it. Thus, for example, in the paradox of Achilles and the tortoise (which will be brought in the next chapter), or in Hilbert’s hotel (which will be brought later here), one can see the picture as if it contains a presentation, even if in implicit form, of the whole chain. But in the case of the turtles, the chicken and the egg, or the homunculus, we are dealing with chains that do not present an explanation at all, but at most claim that an explanation exists, if that. I should note that mathematical intuitionism (see below) does not accept even the admissibility of these chains.

The Kantian explanation

Kant, in his Critique of Pure Reason, in the chapter dealing with the nullity of the possibility of a cosmological proof,^[2] raises the following objection against the cosmological argument (the second dialectical pretension):

The principle of inferring, from the impossibility of an infinite series of causes given one above another in the world of sense, to a first cause—a thing for which the principles governing the use of reason do not authorize us even within experience, much less authorize us to extend this principle beyond experience (for there this chain cannot be prolonged at all).

Kant argues that the assumption that infinite regress is impossible is valid only with respect to the world given to us in experience, and that we must not extend this beyond it.

As we shall see below, the problematic nature of an infinite series of causes is not learned from experience (it cannot be learned from experience, since in any case we cannot follow an infinite causal chain; therefore, even if such a chain existed, it is no wonder that we have not encountered it until now. That teaches us nothing about its impossibility), nor does it concern only things within experience. We have already seen, and will further see later in the chapter, that the problem is fundamentally logical and connected to the nature of the concept of infinity and to the caution with which it must be handled.

But beyond all this, even if Kant were right that infinite regress is in principle possible outside the world of experience, still, as we saw above, no explanation has really been presented here; it has only been claimed that there is one. Moreover, even if the regress did amount to an explanation, it would at most be the proposal of an implausible alternative in order to reject the cosmological argument. We have already seen that this argument does not aspire to certainty but to plausibility. Therefore, the proposal that the chain of causes is finite even outside our experience is obviously preferable. Throughout his discussion there, Kant understands that the aim of the cosmological argument, like that of the ontological one, is to infer with certainty the existence of God, and therefore he offers these objections. But, as stated, that may perhaps be true with respect to the ontological argument (see our notebook there), but it is certainly not the right way to understand the aim of the cosmological argument (and the physico-theological one as well). See more on this below in the summary at the end of the last chapter.

What is infinity?

As stated, the fallacy in infinite regress is bound up with the concepts of infinity. Let us first clarify somewhat the nature of this vague concept. At the beginning of the widely read book by the Dutch-American historian and writer Hendrik Willem van Loon, The Story of Mankind,^[3] the following story appears:

Far away in the north, in a land called Svitjod, there stands a rock a hundred parasangs high and a hundred parasangs wide. Once every thousand years a little bird comes to sharpen its beak on this rock. And when the rock has thus been worn away, one day of eternity will have come to an end.

This description tries to give us some sense of eternity, that is, infinite time. Beyond the understandable amazement this passage arouses, does it succeed? What in all this comes close to describing infinity? Only the last word in the passage. The height of the rock, the frequency with which the bird arrives, and the processes of erosion contribute nothing to the understanding of infinity. At most, this brings us to understand that we are dealing with something large, perhaps very large. But very large is a very poor metaphor for infinity. As we shall see later in the chapter, the very large—even a billion billions of billions of years—is exactly like one second in comparison to eternity. When we try to approach an understanding of eternity, there is no essential difference between it and one second. No matter how much we magnify the description, we have not come a hair’s breadth closer. Therefore the only element in this passage that gives a sense of eternity is merely the fact that all this vast magnitude is only one moment of eternity. And how many such moments are there? Infinitely many. That is of course equally true even if we were to describe the moment of eternity in terms of eating a cup of yogurt. Here too we would need infinitely many such moments in order to construct eternity. The enormous span of time required to erode the rock added nothing for us, except perhaps to our feeling before eternity, but not to its definition itself. Infinity is completely indifferent to size.

One can offer the following analogy. To understand what a three-dimensional object is, let us try to use a two-dimensional object. If we enlarge the two-dimensional object more and more, will we thereby come closer to understanding what three dimensions are? It does not seem so. Three-dimensionality is an entirely different kind of reality and of objects, and it cannot be constructed from the lower kind by processes of enlargement. True, there is some relation connected to size between two and three dimensions. In some sense, two dimensions are less than three, or are contained within three. But the relation is not quantitative in the simple sense. One cannot construct the three-dimensional from the two-dimensional, however large the latter may be. So too, when we enlarge יותר and more the span of time we are considering, we do not really come closer to understanding what an infinite span is. In fact, we are treading water, even though one cannot deny that we experience some illusion of understanding.

At this point the question naturally arises: does such a thing as eternity exist at all? Can it be defined? Apparently not in any simple way, certainly not by way of the very large. In moving to the infinite we are not merely continuing to enlarge and enlarge, but in fact leaping into another conceptual world, if any. It may be that we are leaping into the vacuum—that is, talking about something undefined and perhaps nonexistent. If, as we have seen, the process of approaching it does not bring us any closer to defining and understanding it, the question naturally arises whether such a thing exists at all. Is there really somewhere “down there” something toward which we are trying to approach in this way?

Intuitionism

In the philosophy of mathematics there is an approach known as intuitionism. According to this approach, mathematics is nothing more than a description of constructions built in the human mind. Therefore, anything that has not actually been constructed there is not admissible in intuitionist mathematics. Intuitionists are very suspicious of infinities, since these were never built in our minds. At most we try to approach them (with or without success), but infinity has never existed as a concrete concept actually constructed in our minds. True, we have a symbol for it (∞), but this is no more than a fiction (sometimes useful, and usually confusing) behind which there is nothing. They even raise questions about proofs by mathematical induction. Such proofs are built on showing that if a proposition is true for n=k, then it is necessarily true also for n=k+1. One also shows that it is true for n=1, and from this it follows that it is true for every n whatsoever. Extreme intuitionists hold that such a proof is not admissible, since we have not actually constructed all the infinitely many steps in question (for n=1,2,3…).

In the end, most intuitionists do accept proofs by induction, but for that purpose they distinguish between concrete and potential infinity. Potential infinity is a mathematical mechanism that refers to infinity only implicitly—for example, when one says that after every number there comes another one. There is no explicit talk here of there being infinitely many objects and of referring to this totality in its entirety as something existing. We only say that after every number there is another one, or that there is no number that does not have a successor. Infinity, by contrast, is concrete when one refers to a set of infinitely many objects as an existing whole, or to _∞ as a number and not as some potential limit (see below). An especially radical approach within intuitionism, finitism, does not accept even reference to potential infinity.

If one adopts this distinction, then talk of an infinite chain of explanations is meaningless, and certainly inadmissible. Such a chain of explanations is a concrete reference to infinity, and therefore inadmissible. For it is not enough for us to say that after every link there is another link, since by that we have only said that there is one. But we have not offered a full explanation for the existence of the universe. Such a full explanation would have to say in positive terms that there are infinitely many links, but that is not legitimate within the intuitionist picture.

Later in the chapter we will refine the distinction between concrete and potential infinity, so that the rejection of infinite regresses will not depend specifically on an intuitionist worldview.

Hilbert’s hotel

Ancient philosophy used the concept of infinity in various philosophical discussions, and at times it even served there as a designation of God Himself. Down to our own day, in philosophy, and even more so in theology, people tend to use the term infinity rather recklessly, as though it had a well-defined meaning, whereas for quite some time it has been well known that this is not the case.

When modern mathematics developed, many mathematicians tried to introduce this concept into the number system (as they did with 0), and it turned out to be difficult to do, if not impossible. The assumption that there is such a concrete number leads to paradoxes, or at least to various oddities, unless one offers it a very rigid mathematical definition, and usually also a rather artificial one (not what we mean in everyday language when we say infinity). The natural conclusion is that this concept is generally defined as a potential rather than concrete concept, that is, as some abstract limit that does not really exist in the ordinary sense the way every finite concrete number does. The problems of concrete infinity can be described by means of what is called “Hilbert’s hotel” (see the entry under this title in Wikipedia), and I will briefly describe some of them here.

The hotel example was used by the famous mathematician David Hilbert to illustrate the problematic character and the surprises hidden in the concept of infinity, and in particular our inability to think about it intuitively and to build arguments and inferences drawn from the world of finite numbers. We are dealing with a hotel that has infinitely many rooms, each of which is numbered by a natural number: …1,2,3,4. The story begins when all the rooms in the hotel are occupied, one guest in each. Now another person arrives and asks the hotel owner for a room. The owner very much wants to oblige him, so he does not say that there is no vacant room, but instead performs the following operation: he asks every guest in whatever room he occupies (whose number is n) to move to the room to his right (numbered with the succeeding number: n+1). Thus the occupant of room 1 moves to room 2, that of 2 moves to 3, and so on. In room number 1, which has been vacated, he lodges the new guest, and all is well. Of course, this process can be carried out because the number of rooms in the hotel is infinite. To see this more precisely, let us number the guests according to their original room numbers, and now try to think whether there is any guest who has no room. Any guest you point to, we can immediately say where he is staying. None of them has been left outside. So the process is well defined.

Now the neighboring hotel, which also contains infinitely many rooms, suddenly bursts into flames. Its owner asks the owner of our hotel to house the guests who have been left without a roof over their heads. He, in his good-heartedness, immediately agrees, and instructs all the miserable guests (who had not yet even had time to recover from the previous move and fall asleep) to move to another room. The guest from room 1 will move to room 2, the one from 2 will move to 4, from room 3 to 6, and from room n to the room numbered 2n. The original guests now occupy the even-numbered rooms, and infinitely many odd-numbered rooms have been vacated in which the guests from the burned hotel can be lodged. The guest from room n in the burned hotel will be housed in room 2n-1 in the host hotel (the guest from room 1 in the burned hotel moves to room 1 in the host hotel; the guest from room 2 moves to room 3 in the host hotel, and so on). And again, you will not be able to point to any guest from either hotel who has no room, and therefore this process too is well defined.

One can of course continue this further. Now infinitely many buses arrive (they too are numbered, each with a different natural number), and all their passengers want to stay in our thriving hotel. There is, of course, no problem. One could repeat the process we carried out infinitely many times, but there is a way that is even more elegant. The hotel owner asks his guests for patience and consideration, and once again instructs every one of them who is staying in room n to move to room 2n. The experienced guests do this easily (they are already familiar with the procedure). Now all the odd-numbered rooms have been vacated. The owner turns to the passengers of bus 1 and tells them to take all the rooms that are powers of 3 (the smallest prime number available for this purpose). Passenger 1 goes to room 3, passenger 2 to room 9, passenger 3 to room 27, and so on (passenger n to room 3^n). All these powers are odd, so all these rooms are indeed vacant. He houses the passengers of bus number 2 in rooms whose numbers are powers of 5 (the next prime number). The passengers of bus 3 are housed in powers of 7. According to a well-known theorem in mathematics, there are infinitely many prime numbers, and all of them (except 2) are odd. Moreover, because they are prime, their powers never intersect one another, and therefore even after we have housed all the passengers of the previous buses, the rooms designated for the passengers of the next bus are all vacant. In fact, even after this process is finished (?!) there will still remain infinitely many vacant rooms (those that are not even and are also not powers of a prime number. For example, rooms 15 or 63, with a breathtaking view of the lake, are still vacant. Hurry and sign up).

If we return for a moment to the rock in the land of Svitjod from the beginning of the chapter, we can now see that even infinity goes into infinity infinitely many times. Therefore the very large is a poor metaphor from which to construct infinity. There is no real difference between it and the tiny. Adding one person to the hotel is similar to adding infinitely many buses with infinitely many passengers. It is a very similar process. We can bring infinitely many passengers into the hotel in powers of the prime number 1001. The first passenger will enter room 1001, the second room number about a million, then a billion, and so on. After we have passed a billion rooms we have housed only three guests. We still have infinitely many others left. But, surprisingly, they will all fit. We still have infinitely many such rooms for all the infinitely many passengers in the infinitely many remaining buses that still need to be housed. The rate at which the numbers increase when dealing with a very large prime number does not really matter. It behaves exactly like the powers of the prime number 3. The same number of rooms belongs to the series of powers of 1001 as to the series of powers of 3, and likewise to the series of powers of a prime number with a thousand digits or a billion digits. The very large is no better an approximation to infinity than the very tiny. Infinity is completely indifferent to the difference between them.

What is the meaning of all this?

Everything we have said so far is true only of a hotel with infinitely many rooms. In a hotel with a finite number of rooms, however large it may be, if it is full we can never put more guests into it. The same is true in the opposite direction: in every hotel with a finite number of rooms, after you remove enough guests it will be empty. In a hotel with an infinite number of rooms you can remove as many guests as you like and it will still be full (or can be represented as full). In any case, the same number of guests—infinite—still remains in it as there was at the beginning. This means that things that seem self-evident to us about finite numbers are not necessarily true about infinity. What is very easy to say about some number cannot necessarily be said about infinity.

I once saw a beautiful everyday-language definition of the concept of infinity.^[4] It is basically another way of saying “as many as you like.” If we have a container with 1000 tomatoes, then after you take enough tomatoes from it, it will be emptied. Even if it contains a million tomatoes, one can take from it a certain number and no more. But from a container that contains infinitely many tomatoes one can take as many tomatoes as one wants. There is no number of tomatoes that one could not get from it. When we say that the container contains infinitely many tomatoes, what we have really said, in other words, is that it contains as many tomatoes as you like. So in what sense is infinity a number? In fact, there is something here that is not a number. Saying that something is infinite is only a negative statement: it is not any number we know. That of course only tells us what it is not, but is there also something positive to say about it? Usually not. Therefore mathematicians and philosophers tend to relate to infinity as a potential rather than concrete concept. It speaks of something that perhaps does not really exist, and it is defined only by negation. Thus an explanation built in the form of an infinite chain of links, each explaining the next, is really telling us that there is no explanation here. It is not an explanation but an escape from explanation. Put differently, one may say that explaining by means of infinite regress is like saying “I have an explanation” without giving it. But so long as you have not given your explanation, you cannot expect us to regard you as someone who is offering an alternative explanation.

This is similar to the well-known story about Hershele, who entered a bakery and asked for doughnuts. After he received them, he changed his mind, returned them, and asked instead for rolls. He sat down and ate the rolls, and then left without paying. The baker chased after him and demanded the money owed him, but Hershele could not understand what he was talking about: “What do you want me to pay for?” he asked. The baker answered, “For the rolls you ate.” “But I gave you the doughnuts in exchange for them,” Hershele argued. The baker became angry and shouted, “Then pay me for the doughnuts.” But Hershele still did not understand: “And why should I pay for something I did not eat?! הרי I returned the doughnuts to you.” This is evasion in a chain (an infinite one?…), but we all understand that there is no real explanation or justification here for not paying.

Additional examples of the tricks of infinity

Now think of an infinite hotel with no corridors and no spaces other than the rooms themselves. There is a door connecting one room to the next. In addition, one cannot enter a room until it has been vacated by the previous occupant. Now the hotel owner tries to house in his hotel the additional guest who has arrived. How does he do it? It is easy to see that in such a hotel there is no way to define the process. One would have to begin from the last room on the far right and clear it rightward. Then clear the one next after it (the one to its left) into the room that has been vacated, and so on. But there is no room that is farthest to the right, and therefore we have no starting point. This is in fact the “down” of the chain of turtles. The rightmost room is a mere abstraction, but it does not really exist. There is no room whose number is ∞. The symbol ∞ is only a notation that tells us that the number of rooms is not described by any number known to us.

Of course, if it were possible to clear the rooms to the left, the hotel owner could borrow one room from the neighboring hotel and solve the problem. He vacates the guest in room 1 into the borrowed room, then the guest from room 2 moves into room 1, and so on. But then the clearing process never ends, and the additional guest will never be able to enter (if he enters one of the rooms, then necessarily one of the original guests will remain in the borrowed room and it will not be possible to return him). The clearing process we described above is possible only if beside every room there is a corridor, and all the guests can leave simultaneously into the corridors beside them, and then enter their target rooms.

The process I described here is equivalent to the process of moving along some infinite axis, whether of space or time. Suppose we are at the origin of the axes (x=0) and begin walking to the right at some given rate, say speed 1, meaning that we advance one unit of space for every unit of time. This process is well defined, and at any given time I can tell you where we will be. Along this route we cover the entire positive part of the x-axis, since for every x you ask about I can tell you at what moment we will be there (or pass through it). But now think of a spatial axis that is infinite to the left. A person begins at its extreme left end (∞-) and advances rightward at a given rate (say, one unit of space per unit of time). Now I ask you: when will he be at the point x=-347? There is no answer to that. This process is not defined.^[5] It is not defined because it assumes that there is a “down” from which one starts. But infinity (or ∞-) is not a concrete point but a potential one. We can speak about progressing toward it, because then the reference is potential, but not about setting out from it, because that is already a concrete reference (as though such a thing existed and one could speak about it positively).

An infinite chain of explanations begins from the first explanation and builds the rest upon it. Going in the opposite direction—that is, starting from the explained thing (our world) and descending the explanatory chain—is a process that does not assume the existence of a first explanation, that is, the existence of some “down.” But such a chain can be regarded as an alternative explanation only if it presents a picture that begins from a first explanation and rises upward to the explained thing. Otherwise the “down” exists only potentially and not concretely, and in fact does not exist. In reality, you have not offered an explanation here; you have only claimed that somewhere such an explanation exists. As stated, the meaning of this is that there is not really an explanation here. The explanation must be something concrete that carries the rest of the chain of turtles on its back. If there is no concrete turtle down there, the explanation of the chain of turtles says nothing. In other words: there must be someone or something that created the universe. It is impossible to suffice with the claim that one can simply continue forever down the chain of explanations, so long as one does not assume that there is there “down below” some real thing that is the cause of everything. But descending an infinite chain is like walking to the right on the x-axis from the origin, and that is a picture that does not assume the existence of a right-hand end to that axis. Walking rightward toward the origin does indeed assume the existence of an end (the origin itself), but as stated the process is not defined (because it has no starting point).

And yet something positive about infinity

From the picture described so far, it seems that infinity does not really say anything. It is a concept that merely negates certain properties but has no properties of its own. Seemingly, when we said infinity we really said nothing. This is basically intuitionism. But now we will see that this too is not precise, and here we will already go beyond intuitionism. We will see that infinity does have positive content in a certain sense, and later we will see why this is important for our discussion of the cosmological argument as well.

To illustrate this, let us look for a moment at the concept of the limit of a sequence. Usually we describe a sequence of numbers in such a way that at each place n in the sequence there is a number described in terms of n. For example, a sequence like 0, 1/2, 2/3, 3/4, … comes closer and closer to 1. What does that mean? 1 itself is not a member of the sequence, since at no place n do we get it. 1 is called the limit of the sequence, that is, the point toward which the sequence “tends,” or “converges.” The sequence is a progression toward 1 in a way that is continually moving from potentiality to actuality. It is never completed, and 1 is never actually present. 1 is present in the sequence potentially but not concretely.

By contrast, think now about the following oscillating sequence: 1,-1,1,-1,1,-1…. What is the limit of this sequence? Even without entering into precise definitions of the limit of a sequence, it is clear that this sequence has no limit. It does not tend anywhere; that is, it has no direction at all. The meaning is that in fact there is nothing there at the end that would allow us to view the sequence as a potential approach toward it, or in different language, there is no “down” in the sense of the sequence of turtles.

Let us now move to a third example, the sequence of natural numbers 1,2,3,4,5…n…. What is its limit? In this case the limit is infinity (denoted ∞). Again, ∞ is not a number or a member of the sequence. The sequence tends toward it potentially. But one cannot say that this state of affairs resembles that of the oscillating sequence. Here there is a limit, even if it is not exactly a number and not a member of the sequence itself. When we said that the sequence of natural numbers has an infinite limit, we did not say that it has no limit. It has a limit, but not a limit in the same sense as the limit of the first sequence we described. It is not a number. We do have something to say about it, although we do not know how to describe it positively. What we can say about it is that it is greater than every number we can think of (and therefore it is not itself a number). About the limit of the oscillating sequence we cannot say even that, since there there is no limit at all, not even in this abstract sense. By contrast, the sequence of natural numbers does have a limit in some sense, except that the limit is not a number and is not included in the sequence itself except potentially. We can only say what it is not (it is not any number we know), in the manner of Maimonides’ doctrine of negative attributes regarding God. We say of ∞ that it is not finite, but not that it is infinite in some positive sense.

Above we saw that an infinite chain of explanations is a kind of evasion, as in the chain of turtles. Does saying that some sequence has an infinite limit amount to saying nothing? Here we have seen that it does not. It says something, but chiefly something negative. If we apply this to the chain of turtles, when we propose an infinite explanatory chain we are only saying that there is an explanation, but it is not any of the explanations that can actually be presented. Again, on the philosophical plane this is evasion. In fact, no explanation has been presented here. After all, the cosmological argument also says that there is an explanation, so in what way does this alternative disagree with it? It does not offer another explanation, but only claims that there is one. But on that there is agreement in any case. For that there was no need at all to entangle ourselves in infinite regress.

Another example

Let us take another example. Consider the figure below:

The length of the horizontal side is a and the length of the vertical side is b. We divide each of these lengths into n equal parts, and thus construct n steps, each of which has height b/n and width a/n. The larger n is, the more steps there are, and of course the height and width of each of them are smaller. What happens if we take the number of steps to infinity? Seemingly we obtain a right triangle whose legs have lengths a and b. What will the length of the hypotenuse be? According to the Pythagorean theorem it will be √(a²+b²).

Now let us ask what the length of the path is along all the steps from the lower right end to the upper left end. It turns out that this length does not depend on n. For every given number of steps n, we of course obtain a path of length a+b. This is easy to see if we look at the two projections of the path. In the horizontal projection we have traversed a total length of a. In the vertical projection we have traversed a total length of b. Therefore the total length of the path when crawling along all the steps is a+b. Notice that this length does not depend on the number n, that is, on the number of steps. Now let us ask: what will the limit be when we take the number of steps to infinity? Since the result for the length of the path does not depend on n, the limit is also a+b. So the limit when the number of steps is infinite (and each small step shrinks to zero) differs from the length of the hypotenuse in the triangle described above. This is an example of the fact that the limit of an infinite process is not always what our eyes would expect.

Speaking frankly about concrete infinity

Cantor does not stop his discussion here.^[6] He now asks whether there is some number of guests that would challenge the owner of our determined hotel. According to Cantor, it turns out that the answer is yes. Think now of an infinite set of guests, each of whom has an identity number containing infinitely many (countable) digits. Moreover, in our set of guests not only does every guest have a number, but every number has a guest (whose identity number it is). Cantor argues that this set would indeed challenge our hotel owner, that is, he would not be able to find it room in his hotel.

The proof is by way of negation (this is the method called Cantor’s diagonal argument). Let us assume that we succeeded in housing all the members of this set in the hotel. Now each of them has a room with a natural number. And now I will show that I can find a number such that the guest with this number is not staying in any room in the hotel. I go to room 1 and ask the guest staying there what the first digit of his identity number is. When he answers 9, I write down for myself some different digit, say 2. Then I move to the second room and ask the guest staying there what the second digit in his identity number is. He answers 4, and I immediately write down a different digit in the second place, say 3. In the third room there is a guest whose third digit is 1, and I immediately write down 9. At that point I have written the number 239. I continue passing through all the rooms, and each time I write in the nth place a digit different from the nth digit in the identity number of the guest staying in room n. A brief glance shows that the number that will be written down by me at the end differs from all the identity numbers of the guests staying in the hotel (at least in the digit corresponding to their room number). But we assumed that every identity number has a guest, meaning that there is at least one guest who did not succeed in being placed in a room in the hotel, contrary to our assumption that all of them are housed there. If so, that assumption collapses, since it leads to a contradiction. It is impossible to house all the members of this set in the rooms of our hotel.

One can look at this in terms of correspondences between sets. For sets that have the same number of elements, one can find a correspondence between their elements such that for every element in set A there will be one corresponding element in set B, and vice versa. In such a case we say that the two sets have the same cardinality, that is, the same number of elements. What we tried to do above was to create a correspondence between two infinite sets: A—the set of members with identity numbers containing infinitely many digits, and B—the set of natural numbers (the rooms in the hotel). To house every member of set A in a different room with a natural number is in fact to find such a correspondence. What Cantor proved is that there is no such correspondence (the assumption that there is one leads to a contradiction). Cantor concluded from this that there is a hierarchy of sizes of infinities, that is, not all of them are the same size (cardinality). The infinity that describes the number of members in set A (those with identity numbers containing infinitely many digits) is larger than the infinity that describes the natural numbers, that is, the cardinality of B. Therefore it is impossible to create a correspondence between them. In fact, Cantor showed that there is a hierarchy of infinitely many such infinities, each of which is greater than its predecessor.

But in doing so, Cantor said something positive about infinite numbers. The intuitionists criticized him for treating infinity as a concrete concept and not as a potential one. It seems that Cantor did indeed say something positive about the concept of infinity, and this indicates that there is no obstacle to saying that there is an infinite thing (or that such a thing can be defined). But that does not mean that this thing is a number, or that it has properties like ordinary numbers. If above we saw that infinity is not devoid of content but only abstract and vague, and that it is important to define carefully what one is talking about, here we see that it does have content. Concrete infinity may perhaps exist (contrary to the intuitionist position), but usually there is no way to describe it coherently in positive terms. True, I am not sufficiently expert in this subject, but my sense is that Cantor is not necessarily speaking about concrete infinity. One can see his hierarchy as a scale of potential measures. His infinities are potential rather than concrete concepts, and it is still possible to rank them in the way he proposes. But that is already a question for experts greater than I am.

Evaluating hypotheses

Before we continue and clarify further the problematic nature of infinite regress, we must ask ourselves where we stand at present. Even if the infinite explanation were possible and well defined, one must now set beside it the option that there is such a thing as “down below,” that is, that there is a first cause at a finite point in the chain, a turtle that does not require another turtle to stand on. If indeed we have two alternatives—either there is or there is not a primary turtle—then the cosmological argument is not necessary. The conclusion that there is a first cause no longer follows necessarily from the premises, because there is an alternative. But even so, we can still ask which of these two explanations is preferable. If the explanation in terms of God is preferable, then the cosmological argument still has significant force. It may not be necessary, but it makes the existence of God more probable than His nonexistence.

Even if an infinite chain of explanations is a real possibility, the very fact that it is a vague and unclear concept, and that it troubles us and looks like an evasion, has significance in the discussion. Intuitively it is reasonable to prefer the option of a first cause (that there is such a thing as “down below”), and therefore the cosmological argument has already done part of the work. The burden of proof shifts to the objectors.

Summary

We have seen that the concept of concrete infinity is controversial, and there is great doubt whether it has any meaning at all. It is important to understand that this is a dispute over whether the concept is well defined, or whether it contains contradictions, or at least is empty of content. But even if we adopt the view that concrete infinity is well defined, there still remains the question whether it is realized in our world, that is, whether it exists (not everything that is defined also exists). Moreover, even if we decide that such an infinity exists (for God too is a kind of infinite entity; see also below), still, as we have seen, an infinite chain of explanations is not an explanation (not even a failed one) but an evasion of giving an explanation, or a mere contentment with saying “I have an explanation” without presenting it (see the examples of the turtles or the egg and the chicken). A chain of infinitely many explanations says nothing, except that there are in the chain “as many links as you like.” But, as stated, such a statement does not really offer an explanation. This is probably the reason that in philosophy infinite regress is commonly regarded as a fallacy. Therefore the claim that God exists, even if one sees it as a claim about the existence of a concrete infinite entity, is still preferable to an explanation by means of infinite regress.

But even if such a chain did amount to an explanation, we still saw above that such an explanation is inferior to an ordinary explanation, since it uses a vague concept that admits of various interpretations and is highly doubtful to exist in the world in actuality (even if, for the sake of the present discussion, we assume it is well defined). Therefore it seems that the burden of proof shifts to the objectors.

1. Converging Infinities

Introduction

In the previous chapter we saw why infinite regress is a fallacy. The appeal to the concept of infinity was not sufficiently careful. If we now return to the revised cosmological argument presented in Chapter 2, then we now have a valid argument:

Premise A: Everything of which we have experience must have a cause (or ground).

Premise B: There are things of this kind (the universe, ourselves, or any other object).

Conclusion: There must be a cause for the existence of these things. We call it X1.

We saw that the cause X1 itself may be of a type that also has a cause, or it may be its own cause. Therefore one may continue the argument onward to additional causes, one above another. But because infinite regress is not an option, the conclusion is that somewhere there must necessarily be a first link in the chain that is its own cause. That cause is the God whose existence the cosmological argument proves. Here there is no longer room for the objection to the initial formulation that wondered who God’s own cause is. In this chapter we will deal with a refinement of the previous objection and with its significance, and explain why it too does not undermine the argument.

The refined objection

At first glance, it seems that God as a first cause absorbs into Himself the infinity from which we tried to escape. First, theological definitions of Him as omnipotent and infinite in many respects are exposed to the same difficulty of concrete infinity. If we do not accept the existence of concrete infinity but only of potential infinity, then the existence of God too must be rejected. One can answer this on two different levels:

First, here one can speak in potential rather than concrete language. God is a being greater than anything known to us. We say nothing positive about Him, but only provide a description of Him by way of negation. True, the claim that God Himself exists is a positive claim, and it is asserted of an infinite being, but we have already seen above that one cannot determine that infinite beings do not exist. What can be said is that a coherent positive description of them is probably impossible, or at least requires a sharp definition (as Cantor did when he built his hierarchy). So long as we have not offered a definition or a positive description of Him, there is no obstacle to speaking of Him as existing, and to describing Him as infinite in a potential meaning and language. He exists, and all the descriptions attributed to Him are only in a potential sense. He is not infinite in the positive sense, but greater than everything known and familiar to us. This is unlike an infinite chain of explanations, which, as we saw, implicitly contains a positive reference to an infinite number of links in the chain.

Second, this difficulty is not relevant to the cosmological argument but perhaps to certain religious traditions. The cosmological argument claims nothing beyond what is contained in it: it proves the existence of a first cause. It does not claim that this cause is infinite or not infinite, and says nothing about it beyond its being the first cause of the universe. No more than that. Therefore this argument has no need of the various theological traditions and the claims about God’s infinity in any sense whatsoever. Accordingly, criticisms based on His being infinite are not relevant to this argument, but at most to the various religious or philosophical traditions.

True, even if we ignore the theological traditions and focus only on the being whose existence is proven by the cosmological argument, still, in the picture described here we implicitly assume that God has existed for an infinite amount of time, since no other cause preceded Him. But here once again there is hidden a concrete infinity (the time axis). True, we do not need it within the argument itself. After all, that was not the explanation we offered as the cause of the universe. There we only showed that there must be such a cause, without entering into the question of what its nature is. The infinity along the time axis is at most a result of the explanation. If God is the first cause, then there was nothing before Him, and therefore He apparently exists for an infinite duration. Therefore here it seems legitimate to say that God exists for an infinite time in the potential sense, namely, that there was no time at which God did not exist. We are not claiming here that He existed for an infinite span of time in the positive sense.

Put differently, one can say the following. Before we enter the question of God’s age (the duration of His existence), we must first determine the duration of the time axis itself. How old is our universe? As we have seen, here one cannot speak of an infinite age, since such a claim assumes that we have already advanced from the first age until now through an infinite amount of time. This is a backward glance along the time axis, and as we saw in the previous chapter it is not well defined (it assumes the existence of a “down” at the time point t=-∞). Therefore one can simply say that the time axis is at most infinite in the potential sense, that is, one can at most give only a negative description of it—for example, that its length in years is greater than every number known to us. We can now also say that God exists for an infinite time in this potential sense. We are saying nothing about infinity in the positive (concrete) sense, but only that there was no time at which God did not exist. If we have failed here with concrete infinity, that failure lies in the description of the time axis itself, independently of the definition of God and of the cosmological argument. Therefore the problem of the infinity of the time axis is a general philosophical problem that does not touch our discussion. Once the atheists solve it and define the time axis properly, it will be possible to place God upon the time axis thus defined. The problem of the infinity of the time axis is in no way connected to the cosmological argument.

One can add here the fact that follows from the Big Bang theory in physics, according to which the time axis is indeed not infinite. It was created about 15 billion years ago. We will return to this point later.

The convergence of an infinite series

The Greek philosopher Zeno of Elea challenged the existence of motion in the world, and even denied its existence. To ground his position, he presented a series of paradoxes that challenge the conception that there is motion, or more precisely the very concept of motion. The best known among them is the paradox of Achilles and the tortoise. Achilles, the fastest of human runners, competes with the slow tortoise, whose speed, for the sake of simplicity, we assume to be half that of Achilles: Achilles runs 1 meter per second, and the tortoise runs 1/2 meter per second. In his generosity, Achilles gives the tortoise an initial head start of 1/2 meter. If we analyze the race, it seems that Achilles never catches the tortoise. When Achilles reaches the tortoise’s starting point, 1/2 second has passed, and in that time the tortoise has already advanced another 1/4 meter. When Achilles reaches that point, another 1/4 second has passed and the tortoise has already moved another 1/8 meter, and so on. Thus even after infinitely many steps Achilles does not catch the tortoise, but only comes closer and closer to it.

This paradox is based on the assumption that an infinite series cannot add up to a finite sum. But today we know that this is not so. To understand this, let us return to the previous chapter where we described an infinite sequence. There we dealt with its nth term, and with the limit of the sequence, which is the number toward which the sequence tends as n grows larger and larger toward infinity. In mathematics one also speaks of an infinite series, that is, of calculating the sum of all the terms in such an infinite series. For example, one may ask what the sum of the following infinite series is: 1/2 + 1/4 + 1/8 + 1/16 + … . To define this sum, we define a sequence of partial sums. The first term in the sequence of partial sums is simply the first term in the series, namely 1/2. The second term is the sum of the first two terms in the series, namely 1/2 + 1/4 = 3/4. The third is the sum of the first three terms, 1/2 + 1/4 + 1/8 = 7/8. The fourth term is the next sum: 1/2 + 1/4 + 1/8 + 1/16 = 15/16, and so on.

When we want to calculate the sum of all the terms of this series, what we have to do is compute the limit of the sequence of partial sums (that is, the sum of the first n terms in the original series, as n grows to infinity). The sequence of partial sums tends toward some number, and that number is defined to be the sum of the original infinite series. In this way the question of the sum of an infinite series—which is itself not defined (because it assumes summing over the whole concrete infinity of the terms)—is translated into a well-defined question about the limit of a sequence of numbers.

So what is the sum of all the terms of the series? A simple glance shows that the sum never reaches 1. The explanation for this is very simple. We saw that the first term in the sequence of partial sums is 1/2. The distance between it and 1 is of course 1/2. Now we add to the first sum another 1/4, which is exactly half of the distance remaining to 1. We obtain the next sum, which is 3/4. The distance between this sum and 1 is 1/4. The next term added to the sum is 1/8, which is of course exactly half of that distance. Thus every partial sum advances toward 1 in such a way that it covers half the distance left by the previous sum and leaves half of what remained before. In this way we approach 1, but of course never actually reach it. It is clear from this that the sum of the entire series tends to 1, that is, the limit of the sequence of partial sums is 1.

This can also be seen by direct calculation. The nth term of the sequence of partial sums is the sum of a geometric series with n terms. Therefore in the sequence of partial sums, the first term is 1/2, the second is 3/4, the third is 7/8, and so on. More generally, the nth term of the sequence is: 1-(1/2)^n. As n goes to infinity one may ignore the fraction (every exponent makes it smaller. This is precisely the distance of the sum from 1, which, as stated, keeps getting smaller), and what remains is 1. This is the limit of the sequence of partial sums, and in fact it is defined to be the sum of the series. Of course, for every finite number of terms we do not reach this sum, but it is defined to be the sum of the entire series.

We have obtained here a rather surprising result. One can add infinitely many numbers together, and the result still will not exceed some finite number. This is exactly the solution to Zeno’s paradox about Achilles and the tortoise. If you examine what distance Achilles covers after infinitely many steps of the kind we described, you will discover that he covers exactly a distance of one meter (in the first step he covers 1/2 meter, in the second 1/4 meter, and so on. We have already seen that the sum of this series tends to 1). If so, the description consisting of infinitely many steps describes the first meter of the race, but it does so by decomposing that meter into infinitely many smaller and smaller segments. The time that elapses in light of these infinitely many steps is of course one second, since Achilles runs at a speed of 1 meter per second, and therefore he covers one meter in one second. If you sum the times of the various segments, you will find that this is indeed the time it takes Achilles to traverse these infinitely many steps. So Zeno was offering a description of the first second of the race, or the first meter of the race, and indeed Achilles catches the tortoise after one second and after he has run one meter (and the tortoise one meter). He does not catch the tortoise during the course of the first meter, and in that sense the description is entirely correct. Only there is no paradox in that.

Back to the cosmological argument

Why is this relevant to our issue? Because it turns out that the sum of infinitely many magnitudes can converge to a finite magnitude. First, let us ask whether this phenomenon can give meaning to an explanation of the type of infinite regress. Seemingly one could say that this explanation merely decomposes the one explanation into infinitely many segments, but in truth there is here one overall explanation that serves as an alternative to the explanation that hangs on God.

But this is of course not correct, because these infinitely many links are not a mathematical sequence, and therefore there is no meaning of convergence here. The overall explanation is not the sum of the links but their conjunction (a philosophical conjunction, not a sum in the mathematical sense). Moreover, there is no decrease in the size of the links as the chain advances, and therefore there is no place to speak of a convergent infinite sum. For such a series to converge, the original sequence of terms being summed must get smaller all the time. Therefore there is no meaning to speaking of convergence of a sum of explanations, at least so long as no clear definition of such a thing has been offered to us.

An alternative formulation

According to the assumption that entities like our universe must have a cause, whether one accepts the existence of God or not, there ought to be something that is the cause of our universe. Therefore, even if we adopt the proposal of an infinite chain of explanations, we can define the infinitely many lower stages in the chain as one object, and call it God. All the turtles all the way down are nothing but one large turtle. As an analogy, one may relate to this as to the sum of an infinite series that gives us one single factor.

If one looks at this infinite chain of explanations, then this infinite object is what stands at the basis of the existence of the universe, and therefore it is our candidate to be God. In this way we have actually proved the existence of an infinite object that is the cause of everything that exists in reality, and this is God. Again, it is enough for us that it be infinite only in a potential sense, since we are not assuming here anything positive about its infinity: everything beneath the first turtle is one big turtle (which can perhaps be described as the sum of infinitely many little turtles that become smaller and smaller, but that is not really important, as we saw with Achilles). Our chain is finite, and at its base stands a being that is infinite in the potential sense.

Later we will see that some have proposed an even simpler solution: simply to include our own world itself in this definition, and to identify the universe itself with God. This is essentially Spinoza’s pantheism, which will be discussed later.

1. A Preliminary Examination of the Assumption of Causality

Introduction

At the basis of the cosmological argument lies the assumption that everything (within our experience) must have a cause, or ground. In this chapter we will examine that assumption, its meaning, and its scope.

Objections to the principle of causality

The assumption that everything within our experience must have a ground that brought it into being is a version of the principle of causality. True, the principle of causality usually deals with processes and events and states that everything that happens has a cause, whereas here it is translated into objects or entities, each of which must have a ground (something that created it or is responsible for its existence).

The cosmological argument is often attacked by means of a series of common objections connected to this assumption: how do we really know that everything has a cause or ground? And even if it does, is that necessary? Is it not possible that there are exceptions to this rule? Is this principle necessarily applicable even to the existence of the universe as a whole?

First and foremost, it is important to emphasize that the cosmological argument does not pretend to prove the existence of God with certainty. This is not an ontological argument based only on conceptual and logical analysis (see our notebook on the ontological argument), but an argument based on factual and other assumptions, and therefore by definition it is not necessary and is not supposed to be. What we are looking for here is plausibility, not certainty. The purpose of the cosmological argument is to show that the existence of God is a plausible and reasonable conclusion called for by ordinary rational thought. A claim about lack of necessity is not a relevant objection. From here on we will deal with what follows from rational thought.

The source of the principle of causality

Some attribute the principle of causality to experience. Up to now we have seen that things happen because of causes, and therefore we assume that this is so with respect to every occurrence, in the past or in the future. But David Hume, and Kant following him, already showed that this principle cannot be learned from experience. We have no way of knowing that event A is the cause of B, because what we see is only the temporal precedence of A over B, and also a logical relation between them (which usually takes the form: if A then B). But the causal connection contains an additional element: physical bringing-about.^[7] This element is not learned from experience, and therefore David Hume, as an empiricist, regarded it as a kind of illusion. But Kant determined that it is a basic assumption of reason, that is, of rational thought. In Chapter 18 of my book Emet Ve-lo Yatziv and in the second appendix to my book Elohim Mesachek Be-Kubiyot, I presented a strong argument in favor of the Kantian conception. There I showed that the Humean picture does not reflect the ordinary way of rational thinking, and in particular it also fails to explain the results of science.

If so, anyone who tries to undermine the premise of the cosmological argument by rejecting the principle of causality, or by treating it as a fiction or as a form of our thinking rather than as a principle that describes reality itself, will have to depart from ordinary rational thought. The assumption that something occurred without a cause is implausible, and usually anyone who proposes such a thing will be regarded as irrational. For some reason, in discussions surrounding the cosmological argument, the position that rejects the principle of causality has become rather popular. If we have succeeded in showing that rational thought leads to belief in God, or that giving up that belief means giving up rational thought, that is enough for us.

Kant, in his Critique of Pure Reason, in that same chapter dealing with the nullity of the possibility of a cosmological proof, raises the following objection against the cosmological argument (the first dialectical pretension):

The transcendental principle of inferring from the contingent to a cause—a principle that has meaning only in the world of sense, and beyond it has not even meaning… and the principle of causality has no meaning whatever, and has no distinguishing mark for its use except in the world of sense; whereas here it was supposed to serve in venturing beyond the world of sense.

He argues that the principle of causality applies only to things in sensory experience, and therefore one must not apply it to things beyond that (such as causes of the universe, or God).

How does this fit with his own view that the principle of causality is not derived from experience but precedes it? One should note that he is not dealing with the source of the principle of causality, but with the domain of its application. Its source precedes experience, but it applies only to sensory data. Once we understand this, the weakness of this argument becomes clear. After all, the cosmological argument applies the principle of causality to things within experience. The product of the argument speaks about things beyond experience. On the contrary, as we saw in Chapter 2, the Kantian objection itself is the basis of the revised argument. Because all things within experience require a cause, and because we reject infinite regress, we are compelled to conclude that there must be something outside experience to which the principle of causality does not apply. This is precisely the necessity of inferring the existence of a first cause.

Between cause and ground: occurrences and objects

The principle of causality deals with events and occurrences. It states that every occurrence must have a cause. We must now ask two questions:

1. Is what is true לגבי events also true with respect to objects? Whence, if at all, do we derive the principle that every object must have a ground responsible for its existence? Is there a connection between this principle and the principle of causality?
2. What is the nature of that cause? Are we speaking of a being, a mechanism, or perhaps a law, or something else entirely?

1. Events and objects

We saw above that the source of the principle of causality is not empirical, but rather an assumption of pure reason (rational thought). By contrast, at first glance it seems that the source of the principle that every object has a ground is empirical. We learn it from experience.

But on closer inspection it seems that one can ground this principle in the principle of causality. The coming-into-being of the thing is a process or occurrence, and according to the principle of causality such an occurrence should have a cause. In fact, we assume that the objects around us are not necessary beings, nor are they their own cause (see our notebook on the ontological argument), and therefore they must necessarily have come into being. Hence there must be a cause for their coming-into-being, that is, a cause of the fact that they exist. If so, whoever accepts the principle of causality should also accept the corresponding principle regarding the existence of objects or entities.

2. The nature of the cause

What is that cause that stands at the basis of occurrences or at the basis of the existence of objects? The cosmological argument argues in favor of the existence of some being that is the cause of the universe. Hidden here is the assumption that the cause of the existence of the universe is a being and not something else.

The laws of nature relate occurrences to physical mechanisms, that is, to laws, fields, forces, and the like. At first glance it seems that the cause of every occurrence is another occurrence, and that there need not necessarily be some object in the background. Therefore one could propose that the causes of the existence of the universe are laws of nature or something similar, and accordingly there is no necessity to infer from the cosmological argument the existence of some entity. Even if we accept the assumption that the existence of our universe requires a cause or ground, that cause can be a law of nature or an occurrence, and not necessarily an object. Moreover, even if it is an object, it is not necessarily personal, that is, possessed of personality. It may also be some inanimate substance.

Let us look for a moment at two examples of causality in physics. According to Newton’s second law, force is the cause of acceleration. In the accepted picture throughout physics, sources of charge (charges) are causes that generate force (and this in turn generates acceleration). The first example (the causal relation between force and acceleration) seemingly links an event (the action of a force) with another physical event (motion with acceleration). But the second example (the connection between sources of charge and force) already links objects with an occurrence. If so, even when we look at the force that causes acceleration, that force has sources that are objects (the charges).

If we now return to the coming-into-being of the universe, this can indeed be the result of a physical process, but at the end of the causal chain there always stands an object. Some being generates the process that gives rise to the second process. This is precisely what the cosmological argument teaches: that there exists some object that is the primary source or cause of everything that exists here. Whether and to what extent this object is personal is another question. In any case, the cosmological argument does not enter into its various characterizations. It only states that there must be such a being that is the cause of the world.

Even if we assume that the laws of nature are the primary causes of the existence of the universe, laws merely describe something. A law itself is not a being, but describes beings. For example, the law of gravitation describes the relation between masses and the acceleration produced under their influence. What causes motion is not the law of gravitation but the force of gravitation. The law of gravitation only describes the action of the force of gravitation. If so, even when we say that the laws of nature caused something (such as the existence of the universe), by doing so we are treating them as beings. From the standpoint of the cosmological argument, they themselves can be the primary being, or the first cause. Or perhaps they are a being acted upon by another being, but at the end of the chain there exists a first cause.

If the laws of nature are not beings but mechanisms, we have seen that there must be some being at the basis of their existence, for we have already seen that a process is always brought about by an object, even if this is done through another process. Either way, at the beginning of this chain there is some being, and everything exists by its power. It is the cause of everything.

Objection from the possibility of spontaneous coming-into-being: from Anaximander to quantum theory

The assumption of causality at the basis of the cosmological argument in effect rules out the spontaneous coming-into-being of entities. But in quantum theory we find spontaneous creation of particles out of the vacuum, and this places a question mark over the assumption at the basis of the argument. Even if the principle of causality is an assumption of reason, seemingly we see that factually it is not correct.

In quantum theory, it is indeed believed that there is a possibility of spontaneous creation of particles, but this creation has to satisfy several important conditions, foremost among them the non-violation of the conservation laws. When a particle with electric charge e is created, the total charge in the universe changes. But the law of conservation of charge does not permit such a change, and indeed it turns out that spontaneous creation always preserves the total charge in the universe. If a particle with charge e is created, an antiparticle whose charge is –e must necessarily be created together with it, so that the total charge in the universe does not change. If the created particle also has mass m, then, so that the law of conservation of mass is not violated, an antiparticle whose mass is negative, -m, is created together with it, so that the total mass in the universe is also preserved. The law of conservation of energy is likewise not violated in such spontaneous creations.

Amazingly, this modern argument was preceded by an argument by the Greek philosopher Anaximander, a student of Thales of Miletus, who likewise proposed a solution that allows spontaneous creation without violating the conservation laws.^[8] In the only original fragment of his thought that has come down to us, he writes as follows:^[9]

The unlimited is the beginning and foundation of all that exists. It is neither water nor any other of the things called elements, for it has another, unlimited nature, and from it came the heavens and all the worlds within them. From the place from which being comes to all beings, to that same place destruction also goes, according to necessity. For they give one another ransom and recompense for their injustice according to the order of time.

To contemporary ears, these words sound like an ancient cosmogony that has long since become obsolete, but on second look one can see here an anticipation of modern scientific principles. He makes two claims here: 1. The world was created by a process of producing various opposites: cold and heat, liquid and solid, and the like. The creation of opposites ensures that the conservation laws are not violated (they ‘give one another ransom and recompense’). 2. These opposites were preceded by a prime matter (=the unlimited) that does not possess the characteristics of the matter familiar to us. The splitting of the prime matter is what created these opposites.

The first claim looks exactly like the modern description from quantum theory of spontaneous creation subject to the conservation laws. But the second claim seems unclear. Why did he need at all the assumption that a prime matter preceded this coming-to-be? Unsurprisingly, there seems to be no parallel to this claim in quantum theory.

Is this really spontaneous creation?

A further look at the picture presented here shows that it is difficult to treat it as describing spontaneous creation. If a particle is indeed created out of nothing without any supervision or anything that generates and governs it, how does it manage to preserve the conservation laws? Who sees to it that another antiparticle will always be created together with it to balance it out (to give ransom and recompense for its injustice)? After all, if before this creation there really was a complete vacuum, then there was nothing there, and there was no thing or person to supervise the process and take care of all this. Even so, there is something there that preserves the framework of these spontaneous occurrences. Without entering into the question of what that something is, it is clear that the laws of quantum theory and the laws of physics in general are there. As we have seen, laws always describe something in reality itself. Therefore the existence of laws indicates that there was something in reality itself that supervised and governed this "spontaneous" process. In other words, this is not really spontaneous creation. Quantum theory admittedly does not know how to describe what that cause is that generated and governed this creation, but it is clear that there is always something of that sort there. The quantum character of reality is the cause of this creation, meaning that it does not really occur in a vacuum. This creation takes place in a reality in which there are laws and processes that direct it and control it.

As I showed in my above-mentioned article in Tzohar, modern science is blind to this point, and it seems that דווקא the Greek Anaximander noticed it. As stated, what troubles modern physics is the conservation laws. When it constructs a model that describes physical processes, it always makes sure that those laws are not violated. But still, something else in this process seems problematic. Even if when such a pair of particles is created no conservation law is violated, two new beings have still been created here, and they have been created out of nothing. קודם the universe was empty, and now it is populated. There is admittedly no law in physics that forbids this, since the conservation laws deal only with the preservation of physical properties (such as mass and charge), yet there is still something troubling here. This can be defined as the violation of another ‘conservation law,’ namely the law of conservation of being. This law does not deal with the characteristics (charges) of matter, but with its very existence, or its very being. Two entities have been created here out of nothing, and in effect the law of conservation of being has been violated. In other words, just as the conservation laws must hold, so too the creation of something from nothing cannot occur (even if no conservation law is thereby violated). If our world had been created in parallel with another anti-world, so that all the conservation laws would be satisfied and the physicists would not be troubled, such a creation would still be problematic on the philosophical level. As stated, this implausibility is "transparent" from the standpoint of physics. Physics does not notice it, because it deals only with characteristics (properties, charges), not with the things themselves. But philosophy is broader than physics, and to see physics as the whole picture is a mistake. Anaximander, as a philosopher, was alert to this difficulty, and it seems that his second claim is trying to answer this problem. In this sense, he proposed something more sophisticated than the proposal of modern physics, because his proposal solves the philosophical problem as well and not only the physical one.

As we have seen, he establishes in his words an additional principle, according to which from all eternity there has existed in the world a prime element devoid of properties (and in modern terminology: devoid of charges). It was not physical matter in the sense familiar to us, since matter in the form familiar to us today emerged from it. The matter familiar to us has properties, that is, various charges. The only thing that can be said about prime matter is that it exists. The creation of opposites out of prime matter preserves the totality of all properties (=charges) in the world, that is, it satisfies physics, but also the law of conservation of being, that is, it satisfies philosophy as well. Therefore only Anaximander’s two claims together offer a real solution to the problem of creation ex nihilo.

In this context, Nahmanides’ words in his commentary on Song of Songs (3:9) are interesting. He explains that according to Plato, creation ex nihilo is impossible, and therefore one must posit the existence of prime matter before creation.^[10] On the other hand, in his commentary on Genesis (1:8) he apparently contradicts these words and writes that the world was created ex nihilo.^[11] It may be that Nahmanides means to argue that the initial prime matter was indeed created ex nihilo, but that, in keeping with Plato’s view, the matter familiar to us today was created out of prime matter, and this because of the law of conservation of being. Prime matter is separated into various opposites, and thus the reality familiar to us today was created. In the process of formation (after creation), the laws of nature and philosophy are no longer violated, and therefore at this stage creation must be explained in Platonic terms.^[12]

From another, though very similar, angle, one may say that even on the plane of forms (charges, qualities, or attributes) another ‘conservation law’ is broken, since the concept charge and the concept mass are created here, although they did not exist קודם לכן. Admittedly, the quantity of charge or mass did not change in the process of creation, and therefore the physical conservation laws were preserved, but these concepts and qualities themselves did not exist at the previous stage. So something has still been broken here, even if not on the scientific plane.

To answer the problem of the conservation of qualities, we must add to Anaximander’s unlimited and undefined matter potential properties, that is, qualities such as charge or mass. This is still prime matter, since we cannot say that prime matter had some particular level of charge, or that it had mass in some particular amount, for otherwise it would not be prime matter. These came into being only after the split, and then the primeness was removed. But those qualities in themselves, that is, the concepts mass and charge themselves, were already latent within it beforehand.^[13]

In my article I pointed out that this question too is "transparent" to the scientific angle or mode of observation. Science does not ask itself about the very concepts it uses. It uses them as self-evident, since they constitute its language and its conception of reality. Scientifically, questions about them have no meaning, because science operates within them, and the questions it asks are asked within this conceptual framework. From a scientific standpoint they were not created at all, because these are not entities. What exists is some specific mass or charge, not the concepts of mass or charge themselves.

To summarize, what physics calls spontaneous creation is not really spontaneous. The vacuum from which the particle pair is created is not a genuine vacuum. It contains prime matter (devoid of properties), and it contains laws that supervise and govern this "spontaneous" process. And from this it follows that there is probably also something or someone standing behind this creation (the creator, or the lawgiver, of the laws). The cause of this pair uses the laws of nature to knead the prime matter and quarry from it two kinds of matter that offset one another. It is what sees to it that the conservation laws are not violated (laws that it too enacted).

The scope of the principle of causality

Some challenge the cosmological argument with the claim that the principle of causality should not be applied to the universe as a whole. Causality is a phenomenon within the world, and there is no justification for assuming that the existence of the universe as a whole also requires a cause. In any case, such a conclusion does not necessarily follow from the principle of causality.

Admittedly, rational thought usually assumes that what is found to be true in one place will probably be true in every place and at every time until proven otherwise. For example, the law of gravity as measured on the surface of the earth is assumed by us to behave similarly in space and in the various stars within it. The same is true of the rest of the laws of nature. The assumption is that the fundamental laws are always true, unless there is good reason to assume that certain circumstances are different. If so, it seems reasonable to assume that if we adopt the principle of causality in every context of our daily lives, we should adopt it in every other context as well, at least so long as the contrary has not been proven.

But when discussing the existence of the universe as a whole, this seems like a situation that raises a genuine doubt about the principle of causality. Perhaps this can be formulated more sharply as follows: can the principle of causality itself also be subjected to the principle of causality? That is, can we ask what the cause is for the existence of the principle of causality itself? Here the answer is seemingly negative, since before the principle of causality itself exists there is no necessity to assume the existence of a cause for everything. Only from the moment such a principle exists is it correct to assume that everything must have a cause.

As we saw above, the principle of causality itself is the product of an a priori assumption of reason, and not the result of experience. Therefore, apparently, there is no need to limit it only to entities in our experience, and it would be right to apply it also to the universe as a whole. But this argument is problematic. True, the principle of causality does not arise from experience, but it applies to experience. When we see a branch placed in fire being burned, this in itself does not prove that the fire is the cause of the burning. As Hume and Kant showed, that assumption is a product of our reason. But this product speaks about causal relations that are observed by us in the world. In light of this assumption, we understand that the branch is indeed burned because of the fire. Therefore, even if the source of the assumption of causality itself is not experience, there is room for the claim that it should be applied only to things in our experience. Let us recall that this was also the reason that in chapter 2 we had to refine the cosmological argument and apply the assumption of causality only to entities of the type given to us in experience.

If so, we must ask ourselves whether it is right to apply this assumption to the universe as a whole. Is there justification for the claim that the existence of the universe requires a ground, just like the existence of every object within it. This challenge can be formulated from two angles: 1. Perhaps the universe as a whole is eternal (it has always existed), and therefore there is no need to assume that something caused its existence? It does not require a ground or cause. 2. Perhaps the universe as a whole is not subject to the principle of causality, since this principle is relevant only to events and objects within the universe, but not to the universe itself? These questions will be discussed in the following chapters.

1. On an eternal universe, causes, and reasons

Introduction

Ever since the cosmological argument has existed, the Aristotelian possibility of an eternal universe has stood מול it. Even if we accept the assumption that everything that exists must have a ground or a cause, this applies to objects that were created at some stage. But what about objects that have existed from all eternity? Here, seemingly, there is no room to assume the existence of a ground or cause. In the previous chapter we saw that the principle that determines that there must be a ground for the existence of an object is learned from applying the principle of causality to the process by which those objects came into being. But objects that were never created did not undergo a process of coming into being, and therefore with respect to them there is seemingly no need to assume a ground for their existence.

Reversing the direction

What is attacked by this challenge is the assumption that everything in our experience (including the universe) must have a ground for its existence. But the other side of the coin is that the cosmological argument addresses whoever adopts its assumptions. And one who adopts this assumption probably assumes implicitly that the things in our experience, and in particular the universe, are things that were created in time or at some stage, and therefore must have a ground for their existence. What is the justification for such an assumption? We will offer here several such justifications, one scientific and two philosophical.

First philosophical rejection: actual infinity again

First, the proposal that our universe is eternal returns us to the discussion of actual infinity. In chapters 3-4 we discussed what can and cannot be said about infinity. We saw there that concrete references to infinity are problematic, and that at most one can speak of infinity in potential terms. Does speaking of an eternal universe amount to an actual or a potential reference?

Simply put, when the claim is made that our universe is eternal, this is actual and not potential infinity. The reason is that this claim is intended to negate the need for a first cause. What exists always does not require a cause. But here we must assume that the universe exists for an infinite time; it is not enough for us that it exists for as long a time as we wish (‘however long we like’). In terms of the chain of turtles, there is embedded here the assumption that there is some turtle ‘below,’ and one is not satisfied only with a potential reference to successive stages.

One may now ask why, when the cosmological argument concludes that God is the first cause of the universe, it is not exposed to this difficulty. After all, there too we claim that God is eternal, and seemingly here too we are speaking of an actual and not a potential reference to His infinity. We already dealt with this question throughout chapter 4, and there we explained that the claim of eternity with respect to Him is דווקא a potential use of the concept of infinity. How is this different from the claim about the eternity of the universe?

With regard to God, the assumption that He exists for an infinite time does not come to negate the need for a cause. He does not require a cause because the principle of causality does not apply to Him. On the contrary, we did not assume there at all that God is eternal. The conclusion that He is eternal was a result of the conclusion of the cosmological argument that He does not require a cause (He is the first link in a chain that by its very nature and type does not require a cause). One can now ask how long He has existed, if before Him there was nothing? To this we answered that He fills the time axis, and with respect to the time axis one can speak in potential terms. Beyond that, the infinity of the time axis is an assumption not related to the cosmological argument. By contrast, the assumption that the universe is eternal, or infinite, is brought precisely in order to reject the need for a cause of its existence. That is the body of the argument. As stated, the assumption of the refined cosmological argument was that the universe is of the kind of things that do require a cause, and therefore there only a claim about its eternity can serve as a basis for denying the need for a cause of its existence. Therefore, when we speak about the eternity of the universe, we do indeed need actual and not potential infinity. By contrast, the conclusion of the cosmological argument with respect to God does not directly assume His eternity, and a potential statement suffices for us, as we explained.

Scientific rejection: the Big Bang

Even if we ignore the question of actual infinity, two possibilities stand before us: either the universe was created at some stage or it was not. In Aristotle’s time both possibilities existed, and if one does not assume the existence of God it seems there is no escape but to assume that the universe is eternal (and therefore does not require a cause). But in the twentieth century this question seems already to have received a scientific answer. In the 1920s a new solution to Einstein’s field equations was proposed by Friedman and Lemaître, from which Big Bang theory was derived (ironically, its name was given to it by its greatest opponent, the astronomer Fred Hoyle). This theory assumes that the universe was created about 14 billion years ago, in the form known as an explosion, that is, a point of concentrated matter (a singular point) begins to expand, and thus space, time, and the universe within them were created. It should be noted that during the twentieth century several fairly solid scientific findings accumulated in support of this theory. The first of them is the redshift effect discovered by the astronomer Edwin Hubble in 1929, which indicates that the galaxies are moving away from one another at a speed proportional to their distance. So too the background radiation of the Big Bang, discovered by Penzias and Wilson in 1965, for which they won the Nobel Prize in Physics. This theory and these findings indicate that our universe was created a finite time ago (as stated, about 14 billion years ago), and before that it did not exist. In contemporary physics there is almost a full consensus that the world was indeed created at some point in time, and that it is not eternal. If so, the Aristotelian option of an eternal universe has been scientifically ruled out.

There are still to this day various attempts to speak of prior phases that existed before our world, and these also include theories about oscillating universes that perish and are rebuilt alternately, which leaves open the possibility of an eternal reality (even if our specific universe is not eternal). But these are preliminary attempts that are not backed by real empirical findings, and therefore if we must choose which of the options that science currently allows is more plausible, it seems that the formation of the universe at a certain time is the more plausible option. This is of course strengthened in light of the philosophical argument from the previous section, which rules out talk of actual infinity.

There are also those who argue that according to Big Bang theory time and space too were created with the creation of the universe. If so, it is true that the universe has a finite age (and not an infinite one), but before it there was no time at all. Does such a state render the need for a cause unnecessary? Very doubtful. Rational logic says that if something was created, it has a reason/cause. If the time axis did not exist then, then the relation between the cause and the universe that it created cannot be described temporally, but that does not mean that the principle of causality is not relevant to such a process.

Second philosophical rejection: the principle of sufficient reason

Even if we were prepared to speak about an eternal universe without being troubled by actual infinity, and even if we ignored the findings of physics that indicate that the world is created and not eternal, we would still have to examine what that means. It turns out that even in such a case the cosmological argument remains intact.

To understand this, we must define here another principle, which is very similar to the principle of causality but not identical to it. The eighteenth-century German philosopher Gottfried Wilhelm Leibniz, who formulated it, called it the principle of sufficient reason (incidentally, Leibniz himself already pointed out that this principle applies both to facts and to entities). His claim is that everything that exists must have a sufficient reason that explains it. This sounds similar to the principle of causality, but this is only a partial similarity. One implication of the difference is the question of temporal direction. The principle of causality requires a cause that appears before the effect. By contrast, the principle of sufficient reason deals with reasons and not causes, and therefore it can also make do with a reason that appears after the thing it explains (or grounds). For example, a person can say: I made a phone call in order to set a meeting tomorrow with my friend. This is an explanation of an action he performed, but it roots it in a future event and not in an event from the past. This is what is called a teleological explanation, and it is sufficient from the standpoint of the principle of sufficient reason but not from the standpoint of the principle of causality.^[14]

But the main implication for our purposes of the difference between these two principles is with respect to eternal things, that is, entities that were never created. As we have seen, the principle of causality is not relevant to eternal objects, since they were never created and therefore there is no question as to what their cause is (who created them). But the principle of sufficient reason determines that even such entities require a reason.

The American philosopher Richard Taylor, in his book Metaphysics, gives the following example. Suppose we are walking in a forest and discover a large glass sphere with colorful, intricate, and beautiful drawings inside it. We wonder who created this sphere, and who brought it דווקא to this place. Would we accept the answer that it has existed forever and has always lain here? And suppose a heavenly voice came out of the sky and told us that indeed this sphere has existed from all eternity and has always been lying here (as remembered, our current assumption is that our world is eternal). Would that be a sufficient explanation? We would still ask ourselves why there is דווקא such a sphere here and not another one. And why דווקא here? That is, even though the sphere is eternal, we would still seek a reason for it.

Let us perhaps take another example: the laws of nature of our world. Let us assume for the sake of discussion that the laws of nature are eternal. From all eternity these were the laws of nature, and not others. Incidentally, here we do not even need the assumption that the world is eternal, because the laws of nature could also have existed before the universe (they were here before it and also governed the way it was created, developed, and has conducted itself until today). These laws of nature are complex and unique. Does the fact that they have been here in this form from all eternity answer all the questions? Is there no room left for the question of why the laws are דווקא such and not others? After all, the laws could have been a little different, or very different. Why are they these and not others? This is a legitimate question, even if the laws are indeed eternal.

Here one sees that the present discussion leads us to the realm of the physico-theological proof, which proves the existence of God from the complexity, the fit, or the design that we see in our universe. And indeed, in the next booklet, which will discuss the physico-theological argument, we will make further use of it. But here we are dealing with the cosmological proof, which is based solely on the assumption that something exists, without entering into its properties (such as complexity, fit, design, and the like). Even so, after the illustration of the principle of sufficient reason with complex things, like the glass sphere or the laws of nature, perhaps we can also apply it to the very existence of the universe, regardless of its properties. Even if the universe had existed from all eternity, there would still be room for the question of why it is here, and why it is as it is. Even if no cause is needed, a reason is still required.

There is room to deliberate whether this move is really justified. With respect to complex things there is a sense that a reason really is required for their existence as such, even if they have been here, and so, from all eternity. But with respect to the very existence of some thing, apart from its properties, it is not clear whether a reason really is required. This is definitely a weak point of this argument. Perhaps we should return here to the philosophical rejection that ties eternity to actual infinity. The feeling that even the existence of an eternal thing requires a reason perhaps stems from the fact that the claim that it is eternal refers to it concretely as infinite, whereas we can at most speak of its infinity in a potential sense. But if there is no actual infinity here, we have not solved the question of the reason or cause. Therefore, even if this being is eternal, our feeling is that a reason is required for its existence as such.

Cosmological argument on the axis of cause and on the axis of reason

If indeed even the existence of an infinite (eternal) universe requires a reason, what can that reason really be? Here the cosmological argument returns and proposes that God is the reason for the existence of the universe. Now He is not the cause of the universe but its reason. He did not create the universe, because according to our current assumption it has been here from all eternity, but God is the one who sees to it that the universe exists and that it is as it is. In a certain sense, even if the universe is eternal, the conclusion is still that the universe and God have existed side by side from all eternity, and God is the one who saw to it and sees to it that the universe should exist, and that it should be as it is.

The relation between God and the universe is not a relation of cause but of reason. In kabbalistic terms one can say that God is presented here not as the creator of the world (as in the regular cosmological argument) but as its emanator, that is, the one who serves as the foundation of the world’s existence and character. Emanation is a process that occurs between God and the universe at every single moment, whereas causation or a cause acts on the thing only when it is created.

One can of course now return and ask, as we did in the discussion of the causal formulation of the cosmological argument, what the reason is for God Himself. After all, if everything requires a reason, then God too is not exempt from this. And of course at the next stage we will again say that God is not of the type of things that require a reason, for otherwise we would fall into an infinite regress. On that basis we will reformulate the refined cosmological argument, which demands reasons only from objects in our experience, and so on. The entire course of the discussion can repeat itself with respect to the new formulation of the argument.

And so the cosmological argument presented here can go through the whole process that we carried out with the causal argument, except for one difference: the causal chain and the infinite regress now take place on the axis of reason and not on the causal axis (or the axis of time). This is a cosmological argument based on reason and not on cause. The principle of sufficient reason replaces in it the assumption of the principle of causality that grounds the cosmological argument in its usual formulation.

1. Between a whole and its parts

Introduction

In the previous chapter we examined the challenge that is based on the claim that even if we adopt the assumption of causality according to which every object has a cause, the universe as a whole is not subject to it because it is eternal. In the present chapter we will continue to examine this possibility (that the universe is not subject to the principle of causality and therefore does not require a ground for its existence), but this time from another angle. The principle of causality applies to every entity that exists in the world of our experience. But does it also apply to the universe as a whole? If the universe is the totality of all the particulars within it, is it necessary to assume that the whole is subject to the principle of causality to which each of the particulars is subject?

Relations between an individual and the collective that contains it

In principle, two basic models can be proposed for the relation between an individual and the collective that contains it:

1. The quantitative model. The collective is nothing more than the collection of particulars that compose it, and the difference between the individual and the collective is only quantitative.
2. The essential model. The collective is an entity that exists in its own right, beyond the collection of particulars that compose it.

In the context of human ideologies, many see this distinction as the difference between fascism and individualism. Fascism sees the collective (the nation, or the people) as the basic entity, and the individuals are organs within the general organism, and therefore their role is to serve it. Individualism, by contrast, conceives reality in the opposite way. In its view, the individual is the entity that really exists, and a collective is at most a useful fiction. There are of course intermediate conceptions that see the nation as something important, but are still not willing to subordinate the individual entirely to the collective (the nation). On the metaphysical plane, these conceptions actually reflect the second model, since they accept the nation as an existing and meaningful entity. At the same time, however, they do not give up the existence of the individuals. For these approaches there are two kinds of entities, individual and collective. Therefore it is also clear that even if someone’s metaphysics advocates an essential conception of the collective, it does not follow that he advocates a fascist ideology, of course.^[15]

There is no dispute that we use collective definitions. The dispute is whether these definitions are grounded in ontology (=the theory of being, a branch of metaphysics), or whether they are nothing more than useful fictions. On the legal plane, one customarily defines a body such as a company as a corporation, and this has implications for the responsibility of the company’s owners and employees for various actions of the company. To what extent are they held responsible for wrongs committed by a company, and can they be sued by virtue of the results of its activity (in this context people speak of the corporate veil, which separates the corporation from the people who compose it or are included in it). Does defining certain companies as corporations require a different metaphysics? Certainly not. Many see this as a useful fiction for various legal purposes, nothing more.

On the cultural plane too, various collectives, such as a nation or a community, are defined as relevant factors. This has a psychological benefit for creating identity and identification of people with the society in which they live. Does this necessarily reflect a metaphysical conception according to which a nation or community are entities that exist beyond the private individuals included in them? Here too the answer is not necessarily positive. Again, all of these can be seen as useful fictions and not as a metaphysical determination. For example, on the plane of international relations it is almost impossible to manage without collective definitions. It is not reasonable for international discourse to be conducted between individuals (so, for example, at the UN there would be representatives for every citizen in the world). Therefore, in order to streamline this discourse, intermediary circles of identity are defined, through which individuals can express themselves. Citizens will elect representatives on their behalf, and these will represent the entire collective in international discourse.

Halakhic examples

Let us perhaps give an example of this.^[16] In the IDF there was an order that unloading a weapon after guard duty be done only by an officer, and he had to use a flashlight to check whether the chamber was empty. Rabbi Mordechai Eliyahu was asked by an officer in the IDF whether on Shabbat he was allowed to operate a flashlight in order to inspect the chambers of his soldiers’ weapons. He answered that certainly yes. If we ask ourselves what the real chance is that someone will be harmed if the weapon is checked without a flashlight, the chance is minuscule. No decisor in the world would permit desecrating Shabbat in order to avoid such a remote danger. Therefore, if some officer had asked me the same question, I would have answered him that the matter is of course forbidden. But Rabbi Eliyahu took into account that his answer would become known to many officers, and once it is a response to many, it is clear that the matter should be permitted. Why? Some would see in this a different consideration when it is a question of an individual as opposed to a public question. I have seen a source brought for this from the Talmud (Shabbat 42a and parallels), where the rule is stated that one extinguishes a metal ember in the public domain, despite the prohibition against extinguishing on Shabbat. In the private domain this is of course not permitted (because the danger to life is not very high and does not justify desecrating Shabbat). Again we see that the treatment of the public is different from the treatment of the individual, and risks concerning the public are given extra weight.

Does the essential model of public versus individual find expression here? Not necessarily. We must take into account that when an instruction goes out to all IDF officers not to operate a flashlight when unloading weapons on Shabbat, then even if the chance of injury to life is tiny, it must be multiplied by the number of officers who receive the instruction. Thus the chance of injury to life rises because of the number of people involved. The same applies to a metal ember in the public domain, where admittedly the chance that it will harm any given person is small, but because many people pass there, the chance is in fact much greater and already justifies desecrating Shabbat. These rulings therefore reflect at most the quantitative model, and it is not correct to derive from them an essential model, that is, to see the public as something essentially different from the particulars. It is entirely possible that this is merely a quantitative difference.

On the other hand, there are halakhic examples from which an essential conception of collectives emerges.^[17] For example, it was ruled as halakhah in the Responsa of the Rosh (section 5), and also brought as halakhah in the Shulchan Aruch (Yoreh De’ah 228:35), that the oath of parents does not bind the children. A person can impose an oath only on himself. A community, on the other hand, can impose a ban (a ban functions like an oath or a vow), and this will apply even to future generations. Moreover, there are conceptions that see a Jew’s obligation in the commandments as an oath that we swore at Mount Sinai (‘already sworn from Mount Sinai,’ see Nazir 4a and parallels)^[18], and from this it follows that parents can indeed place their descendants under oath.^[19] The simple explanation of this is that the addressee of the oath is not the individual who stood at Mount Sinai, or the citizen who was a member of the community when the ban was adopted. The addressee is the collective, and even if all the particulars that composed it at that time died or were replaced, the collective (community or people), that is, those who compose it now, is still bound by virtue of that oath or ban.

A similar phenomenon is seen in the law of a communal sacrifice whose owners have died. Tosafot, s.v. ‘sacrifices,’ Me’ilah 9b, writes as follows:

Communal sacrifices belong to the collective—that is, even if that generation of the communal burnt offering has died, the collective remains, for ‘one generation goes and another generation comes’ (Ecclesiastes 1).

Tosafot learns from the verse at the beginning of Ecclesiastes that a collective does not die. At most, the individual particulars that compose it are replaced. Therefore, when a collective sets aside a sacrifice and all the particulars in that collective die, the sacrifice is not considered a sacrifice whose owners have died. The owner is the collective and not the private people who compose it.

These examples are very difficult to explain through the quantitative model. Here it seems clearly that halakhah sees the public as an entity that exists in its own right and not merely as a collection of particulars. To complete the picture, I will only note that the halakhic conception apparently advocates a two-hats model: each of us is an individual and also an organ within the collective. Neither of them is absorbed into the other nor subordinated to it.^[20]

The living body as an organism

The clearest example of an essential conception of a collective is a biological organism. Every body is composed of cells, every cell of molecules, and these are composed of atoms, and those too are composed of subatomic particles at various levels. One may ask whether for us a living body is nothing more than a collection of cells (which of course is arranged in some particular way). To the same extent, is a cell nothing more than a collection of molecules (arranged in some way) and no more? Most of us see the human being as an organic entity and do not think that what exists is only subatomic particles. In the opinion of most people, human beings, mice, or lice are not merely useful definitions, that is, useful fictions and nothing more. The organic collection of the cells or molecules is conceived by us as an existing entity, and it has existence beyond the collection of cells.

In philosophy, the example usually brought in this context is the ship of Theseus. It entered dry dock for repairs after the storm, and several parts were replaced. After another storm, more parts were replaced, and in the end there is not a single part in the ship from among the original ones that were there when it was built. Is it still Theseus’s ship? On the legal plane (to whom the ship belongs), the answer is of course yes. The present ship still belongs to Theseus. It is clear that this does not necessarily require a different metaphysics. But what shall we say about a living body when all of its cells have been replaced (this happens to each of us several times over the course of our lives): is it still the same person? Most of us would say yes. Is this only a useful fiction, or is our metaphysics collectivist? It seems to me that many of us would say that it is indeed the same person, and not only as a useful fiction. It is likely that if an experiment were proposed to us in which our entire biological structure would be destroyed and then reconstructed precisely, we would not agree to it, neither to be destroyed nor to be among the destroyers. Our intuition tells us that such a whole is not merely a simple collection of its components (what we above called the quantitative model). The meaning of this is that even if a ship is nothing more than a collection of parts, in a human being as a whole there is something beyond the collection of cells that compose him. And what about a people, a community, all of humanity, or a herd of zebras? Here opinions seem divided.

The universe as a whole: another challenge to the cosmological argument

Our universe too is a kind of whole. With respect to it as well one can ask whether this is no more than a useful fiction, or whether the universe is something beyond the collection of particulars (inanimate particles, plants, human beings, and animals) that compose it. The significance of this for our discussion is that if the universe is conceived as an essential whole, that is, as something beyond the collection of its parts, then the question can arise whether the universe itself is subject to the principle of causality, or to the principle of sufficient reason. Even if every entity in the universe requires a reason, a ground, or a cause, it is still possible that the universe as a whole does not require this. This is a possible challenge to the cosmological argument that proves the existence of God by virtue of the requirement that the universe have a cause. If there is no necessity for the universe as a whole to have a cause, there is no proof here of the existence of God as the cause of the universe.

Back to the particulars

First, we must return once more to the particulars, that is, to the individual entities in the universe. If we focus on one of them, then it belongs to the entities that must have a cause. We now ask what its cause is, and begin the process of the cosmological argument with respect to it. In the end, we will have to reach a link in the chain that is its own cause (or does not require a cause). Once we reach the final stage, our challenge claims that there are two possibilities (and not only one, as follows from the cosmological argument): a. that link is the universe itself. b. that link is God. The existence of possibility a makes it possible not to accept b.

But how can one speak of the universe as the cause of one of the particulars that compose it (or in fact of each one of those particulars)? Is there in the universe something beyond the totality of the particulars? Is the universe some additional thing, or is it nothing more than the collection of particulars? Not for nothing does this picture remind us of Spinoza’s conception called pantheism, which identifies God with the universe (the totality of being). This totality is the God who created the universe. There is in fact an identification here between the two possibilities presented above.

But this identification is problematic. Again we must decide whether the universe as a whole is some additional thing beyond the collection of particulars. If not, then pantheism is nothing but atheism in disguise. When the pantheist speaks about God, he is really referring to the material universe of which the atheist speaks, only calling it by another name. This is not belief in God but a semantic trick.

And if what the pantheist means is to say that in the universe as a whole there is something beyond the collection of the individual particulars that compose it, then this "something extra" is itself God, and its existence is proved by the ontological argument. So what is new about pantheism? What does it add to our discussion, or to philosophical discourse in general? The same is true with respect to the challenge to the cosmological argument: if the universe is nothing but the collection of its components, then of course it cannot be the cause of any of them (certainly not of all of them). And if there is something else in it, then the two possibilities presented above are in fact identical. Both tell us that there is something extra that is self-caused, and it is the cause of all the other entities that exist, and more generally we will say that it is the cause of the universe.

To summarize, let us put it this way. Viewing the universe as a quantitative rather than an essential whole eliminates possibility a above (there is no option of another entity). Whereas viewing it as an essential whole identifies these two possibilities, and once again we are left with the conclusion that there exists a first cause of the universe, and that is what we call God.

From another angle, what this alternative proposes is in fact a picture of an infinite causal cycle in which every individual entity in the universe is caused by a cause that is itself another individual entity in the universe, and thus the universe as a whole exists forever. The particulars that populate it do indeed change, but it exists always (something like what we saw above in the halakhic examples concerning the oath at Mount Sinai and a community ban). But if the universe as a whole is not something additional to the individual entities, it certainly cannot appear in that chain. So in fact we are left with Aristotle’s conception of eternity that was discussed in the previous chapter. We have arrived here at a chain of infinite regress of causes or grounds, and as stated this is precisely the first challenge we dealt with at the beginning of the booklet. In chapters 3-4 above we already saw that this is actually a fallacy. It is not an explanation but an evasion of providing an explanation. And if the universe as a whole is something extra beyond the collection of particulars that compose it (the essential model), then that something is the first cause, that is, it is God. In the next section we will spell this out further.

On vitalism and the existence of souls

We have already seen that an organic body is the clearest example of an essential model for a collective entity. A person is not merely a collection of cells but something beyond them. Why indeed is this so? Why is this collection of cells perceived by us as something additional, beyond the collection of cells itself? It is hard to see any justification for this if one does not accept that at the basis of the organic structure there exists an entity that organizes it (organize, in both senses). Some call it spirit, and others soul, but there has to be something else there so that the collection of cells will not be merely a quantitative increase but a different essence.

The meaning of this is that at the base of the essential model there stands an ontic addition. If we look at a group of entities and see in them something essentially different, then there is necessarily something extra there beyond the collection of those individual entities. Without that, how can the whole be seen as something existent? Without this addition, the quantitative model according to which the collective is nothing more than a useful fiction is clearly what is called for.

In the biology of the last generation, such talk is considered almost like profanity. This is the much-maligned vitalism, which maintains that biology cannot be built on a material basis alone (only chemistry and physics), but that there has to be something else there (spirit). Contemporary biology rejects this conception with disgust. Seemingly, then, we are assuming here an outdated scientific conception according to which at the basis of the living, material organism there is another, non-material substance.

I will make several remarks about this. First, this "scientific" claim, and really this meta-scientific one, is more ideology than science. No one today has a full explanation of the phenomena of life, and even the definition of the concept of life is quite elusive and disputed. What exactly distinguishes a living body from an inanimate one? Biology tries to reduce everything to physics and chemistry (through biology), but in the meantime there is no complete picture there. There are stages along the way from chemistry and physics to biology and life, but it cannot be said that we have reached a full understanding and ruled out the need for an additional element. As of now, no one can say that he possesses a full explanation of the phenomena of life without resorting to anything beyond physics and chemistry. Biological explanations are of course satisfactory, but so long as we have not fully reduced them to physics and chemistry, there is no systematic way to claim that at the basis of biology there is nothing but matter (that is, nothing but physics and chemistry). This is, at best, begging the question.

It seems to me that the more correct way to understand the meta-biological position that rejects vitalism is on the methodological plane and not on the ontic plane. We are not dealing with what exists and what does not exist, but only with the question of how science ought to proceed. The claim against vitalism is not that it is false but that it is not useful in the scientific sphere. Adding another undefined element will not improve our science. The assumption that there is spirit or soul does not help us in any way to understand life and biology. Scientific explanations require rigid quantitative laws that give us predictions and can therefore be subjected to empirical testing, and we have no such laws for spirits and souls. In this the biologists are probably right. Therefore there is no point in dragging concepts like spirit or soul into biological scientific research. It does not help us at all, but only obscures and blurs. But there is not even a shred of an argument here against the philosophical intuition that says that if this whole is an organism and not merely a quantitative collection of cells or molecules, there must be another entity of a different kind at its base. This is of course not a claim that stands open to refutation, but philosophy need not be like that. Indeed, we have no scientific tools for dealing with this claim, but that does not mean that it does not exist. We have no scientific tools for dealing with many other phenomena in the world and in the human being, and it would still be unreasonable to deny their existence. Therefore one can accept the materialist approach on the methodological and scientific plane, and still be a dualist on the philosophical plane. I will mention here the discussion of Anaximander’s model that was conducted above in chapter 5. There too we saw that there are domains that science does not address and also need not address. The fact that science is not troubled by the law of conservation of being does not mean that philosophy is not supposed to be troubled by it. Science is not the whole picture. The same applies to the question of vitalism. Science is not supposed to deal with this question, since it does not fall into the category of a scientific question, and introducing an additional substance probably has also not been found useful on the scientific plane.

In fact, there is another question that is not accessible to scientific examination, and that is the question of the existence of God. There too there are claims that the existence of God is not a scientific claim, that it is of no use to our science and is not open to empirical examination. There too the answer is that all of this is true, but the fact that something is not relevant to scientific discussion says nothing about its existence or truth. At most, it calls for caution in defining the concepts and examining the philosophical arguments, since we do not possess the scientific-empirical tools to test them. We will return to this point near the end of the booklet.

Back to the distinction between cause as causation and cause as emanation

If so, our conclusion is that if one raises the alternative of the universe as a whole, it can be based only on the essential conception. As we saw in the example of the living organism, this means that at the base of the collective there must stand another entity that organizes it. We also said that even if such an entity underlies the organicity of the universe (the essential model), the cosmological argument in fact identifies it itself as God and proves its existence.

What is the relation between such an entity and the collection of particulars? Is it their cause? Reflecting on the example of the living body shows that this is not the precise relation between the two substances (matter and spirit). There is no causation here in the sense of before and after, cause and effect, agent and generated thing, or cause and caused. The relation is synchronic, that is, it exists at every moment. The soul or spirit animates the organism and turns it into an organism. They did not ‘turn’ it into one, but ‘turn’ it into one. They are what makes the organism essential and not mere quantity.

This is what we above called emanation, or reason, and not cause. Spirit is not the cause of matter but what turns it into an organism. Therefore the God who is disclosed by the cosmological argument in this formulation is a God on the axis of emanation and not on the axis of causes. God is the emanator of the universe and not its cause. He is what turns it into an organism.

To conclude, let us note that in a certain sense we have arrived here through the back door at the physico-theological proof, which proves the existence of God from the complexity of the universe or from the fit between its parts. The physico-theological argument states that there must be some factor that sees to this fit or that assembled this complexity. Admittedly, here the perspective is one of emanation and not of cause (He did not necessarily assemble the universe, but rather stands at the basis of its organicity).

Emergence^[21]

Before I summarize, we must touch on another aspect. In the dispute between materialists (those who believe in the existence of matter alone) and dualists (those who believe in the existence of two substances: matter and spirit), the claim about mental phenomena constantly arises. After all, a person experiences emotions and sensations, desires, thoughts, and a host of other phenomena that we do not usually attribute to inanimate objects, that is, to something made of matter alone. Chief among all of these stands free will, whose existence actually contradicts the laws of physics. Dualists argue that these phenomena prove that there is also a non-material element in human beings (spirit). What do the materialists answer to this?

As for free choice, many of them deny its existence. But the rest of the mental phenomena certainly exist in us. The prevalent materialist approach with respect to these phenomena attributes them to what is called emergence (emergence, rising out). The claim is that when many entities join together and form a collective entity, phenomena or characteristics appear (emerge) that do not exist on the individual plane. One of the first to raise this claim was the American philosopher John Searle, in his book Minds, Brains and Science.^[22] Searle gives an example that illustrates the phenomenon of emergence. Water is a collection of H₂O molecules. Clearly a single molecule is not liquid, and yet the whole cluster is a liquid. States of matter in general (solid, liquid, or gas) characterize only clusters of particles (atoms or molecules), and not single particles. So here we have it: some phenomenon can emerge on the collective plane even though it has no existence at all on the individual micro plane. Thus, Searle argues, the mental phenomena (including free will) emerge on the plane of a complete human organism, even though it is nothing more than a material whole, and certainly no molecule of matter is endowed with free will.

The meaning of the claim of emergence is that the appearance of various characteristics on the collective plane does not require the assumption that there exists another substance. In our terminology, the quantitative model alone can also explain the renewed collective phenomena. There is no need for this purpose to move to an essential model on the ontic plane (that is, to assume the existence of something beyond the individual particulars). This of course stands in opposition to our claim above, according to which the appearance of the phenomenon of life on the collective plane indicates that there is in the organism something beyond individual units of matter.

This claim is very interesting, but as I showed in my book it has no scientific basis. Many have already pointed out that states of matter are phenomena that can be called weak emergence. The macro characteristic (the state of matter) can be explained by means of properties of the micro level. It is true that one cannot attribute a state of matter (such as liquidity) to a single molecule, but the electric field around it is what causes the phenomenon of liquidity (taking into account thermodynamic circumstances and conditions, such as temperature, volume, and pressure). Therefore, the phenomenon of liquidity, like states of matter in general, can indeed be reduced to properties of the individual entities (the molecules). This explanation and mechanism are well known to every physicist. If so, it is clear that there is no need to assume the existence of an additional element in order to explain a state of matter. But the emergence of mentality out of a material whole is something much stronger. Here not only do we have no explanation for this in terms of the properties of the individual entities (molecules, nerve cells, and the like), but we do not even have a language that could give us hope of finding such an explanation. We simply say that a given neural state X (a material-physical state) is expressed in a psychic phenomenon Y. But unlike the example of liquidity, here we have no description of the mechanism that leads from this to that.

Committed materialists continue and argue that this is indeed a different phenomenon, and they call it strong emergence. This is a phenomenon at the macro level that cannot be reduced to the micro. And yet their claim is that this phenomenon emerges from the very quantitative accumulation of the individual entities (and from the particular form of that accumulation; it is not only quantity, of course), and therefore there is still no need to assume the existence of an additional substance.

Despite how widespread it is, this is an extremely speculative claim. Any scientific example we might bring of a process of emergence will by definition be an example of weak emergence. For if there is a collective phenomenon that cannot be reduced to the properties of the individual entities, how do we know that what we have here is really emergence (arising by virtue of quantity), and not the essential model (that there is in the collective something beyond the collection of individuals). A scientific example is based on a mechanism that science has recognized. But if science recognizes it, then necessarily this is a mechanism in which we understand the process of emergence, and therefore it is weak emergence. Talk of strong emergence is nothing but evasion. Materialists are basically claiming that they have another explanation, but without presenting it. This is certainly not a scientific claim, and certainly there is nothing in it to alter our philosophical intuitions, according to which new phenomena point to the existence of an additional element. It is no accident that this discussion recalls the brief discussion of vitalism that we conducted above.

If so, it seems that the philosophical intuition that says that for some whole to count as an organism there must be in it an additional element beyond the collection of particulars, something that organizes them, remains in force. And if so, the conclusions of our discussion in this chapter also remain valid.

Summary

Viewing the universe as a whole was presented as a possible challenge to the cosmological argument. If indeed the universe as a whole does not belong to the kind of entities that require a cause, then seemingly the cosmological argument collapses.

We have seen that this is not so. If we are dealing with a quantitative whole, then through the back door we have returned to the fallacy of infinite regress. There is nothing here beyond the collection of individual particulars, and the original argument remains intact. And if it is an essential whole, then at most we have proved the existence of God as an emanator (a cause on the axis of emanation and not on the temporal-causal axis). Either way, at the beginning of the chain of grounds (whether causal or emanational) there must stand a link that has no prior ground that brings it about.

1. A general look at the structure and meaning of the cosmological argument

Introduction

Up to this point we have seen the cosmological argument in several versions: an argument on the causal axis and on the axis of emanation (or reason). The argument assumes that entities of the type familiar to us were created at some point in time (they are not eternal), and that they were not created by themselves. It further assumes that something that was created has a ground that created it. From this one can derive the existence of a first ground for everything that exists.

At the very beginning of our discussion we pointed out that this argument has a different character from ontological arguments (which we dealt with in the previous booklet). An ontological argument is based on purely conceptual analysis, or at most (as we saw there) also on additional basic assumptions that are not factual. Kant too defined it this way in his famous classification of the proofs for the existence of God into three categories. A cosmological argument, by contrast, is also based on a factual assumption whose source is observation. Beyond that there may also be conceptual analysis and non-factual basic assumptions. But as Kant determined, its distinctiveness lies in the fact that among its assumptions there are also facts.^[23] If so, what we have here is in fact a move that looks scientific. Science too draws conclusions from observations of reality. One can view the scientific process as a transition from given factual claims to conclusions. In many cases this involves a generalization of the cases we observed into a general law of nature. In other cases we may perform an analogy between what we have seen and what we expect to see under similar circumstances. In still other cases we infer the existence of a cause from observing some occurrence or other. All these are inferences that are based on factual assumptions and derive from them various conclusions. This is exactly what the cosmological argument does as well. It observes the (trivial) fact that something exists, and uses the principle of causality to derive from it a conclusion (that there exists something else that is the ground of what I observed to exist).

In this chapter we will try to discuss the nature of this logical move from a bird’s-eye view. We will ask whether it reminds us of scientific inferences. Is the claim that there is a God a scientific claim? If not, what is the difference between it and a scientific claim? Is it a plausible claim, or perhaps a certain one? We will try to clarify and assess the question of how reliable it is in comparison with the reliability of scientific claims.

On the nature and reliability of scientific inference

In the booklet on the ontological proof, we pointed out that there are three kinds of logical inference: a. Deduction—from the universal to the particular. This is a necessary inference, that is, its conclusion follows necessarily from its assumptions. As I showed there, the conclusion is embedded in some way in the assumptions, and therefore it adds nothing beyond them. b. Analogy—from particular to particular or from one universal to a parallel universal. This is a non-necessary inference, because it takes a speculative step and adds something beyond the information embedded in the assumptions. c. Induction—from the particular to the universal. This too is a somewhat speculative inference, since here too there is a novelty beyond what is embedded in the assumptions.

Scientific inference is always one of the latter two, that is, an inference that adds information beyond the direct observations we observed. When we speak about a cause for something that happened, a generalization of a collection of phenomena and the formulation of a general law, or any other inference, we are making a speculative move. At its end we have more information than we had at its beginning (than what arose from the observations themselves). What justifies such a step? Why do we trust our scientific conclusions? In my book Truth and Instability (see throughout the fifth part, and especially in chapter 18), I argued that the foundation of this trust lies in our faculty called intuition, which is a kind of non-sensory cognition. This is the ability to discern the ideas or general notions beyond the facts we observed. In appendix B of my book The Science of Freedom, and also in my article on Ockham’s razor (Badad 25, 2012), I presented a statistical argument that supports this thesis. In brief, the very success of science testifies that we possess such a faculty. If the generalization were a shot in the dark, then almost none of the predictions of scientific generalizations that we made would be confirmed in laboratory experiment. The very fact that a considerable percentage of our generalizations work means that this faculty is not merely something subjective, but rather an ability to grasp something in reality itself. Scientific generalization or inference is also based on this faculty.

There is another characteristic of scientific law, and that is the ability to subject it to empirical testing. Popper already pointed out that a scientific theory or law cannot be proved, but at most refuted. For example, if we are offered a theory that all ravens are black, proving it is impossible. However many black ravens we may see, we can never know whether we have observed all the ravens in the world or not. Therefore, a generalization about all ravens is always something with a measure of speculation in it. But a single raven that is not black is enough to refute this theory. Popper therefore proposes a minimalist but more realistic definition of the scientific status of a theory: the possibility of subjecting it to an empirical refutation test. According to Popper, a theory is scientific if one can propose an experiment whose results would refute it. If it is indeed refuted, then it is a scientific theory that has been refuted, and if not, then it is a scientific theory that has not been refuted (and some propose seeing it as a theory that has been confirmed). But a theory that cannot be subjected at all to a refutation test is not scientific.

Many see falsifiability as a criterion that replaces deduction. After all, scientific inference is speculative by its very nature. Unlike logic and mathematics, whose conclusions follow necessarily from the assumptions (they are based on deduction), here there is always the possibility of error. What, then, distinguishes it from uncontrolled speculation? Most of us do not regard science as a collection of wild speculations. Usually science serves as a counterexample to speculative and unfounded thinking. Many would say that being subjected to refutation tests is the substitute for deductive certainty. The willingness to take the risk of subjecting the theory to an empirical refutation test is what gives it its strength. This strength is of course not absolute, since we are still dealing with generalizations and non-deductive logical steps, but this is the maximum power one can expect beyond deductive inferences.

Ultimately, our trust in scientific results is supposed to be limited. On the one hand, laws are based on generalizations and analogies, that is, on non-absolute inferences. On the other hand, they are subjected to empirical refutation tests, and those that survive these tests are regarded as confirmed (though not certain. They may still be refuted in future experiments). Some see this picture as undermining the validity of science. If it is not absolute, then one should have no trust in it at all. In my book Truth and Instability there, I argued that this conclusion is rash and unreasonable. It is true that science and its laws are not absolute and certain, but neither are they arbitrary and wholly doubtful. They possess a fairly high degree of reliability (its strength corresponding to the measure of direct and indirect empirical confirmations the theory has received), and that is all one can expect from a scientific theory.

Belief in God as a scientific claim

In light of what we have described so far, is the claim that there is a God a scientific one? Clearly it cannot be subjected to a refutation test. I am not familiar with, and cannot think of, any experiment whose results might refute the claim about the existence of God. For this reason, many see faith as something dubious and speculative. It does not have the empirical support possessed by the laws of science. Some go one step further and even define faith as a feeling or emotion, and not as a factual claim about the world. In the booklet on the ontological proof I pointed out that this is a mistake. It is a factual claim about the world, even if it cannot be subjected to a refutation test: either there is a first cause that has no cause outside itself, or there is not. There is only one possible answer here. The cosmological argument claims that the positive answer is the correct one, but atheists too agree that there is only one correct answer, that is, that we are dealing with a factual claim (a false one, in their view).

If so, the claim that God exists is a factual claim, but it is based on a non-deductive inference (from the fact that something exists to the conclusion that it has a cause), and therefore it is not certain. Admittedly, if we append to the argument the necessary assumptions—the factual assumption that something exists (the universe, or I myself), the meta-factual assumption that everything in our experience must have a cause, and the logical-philosophical claim that infinite regress is a fallacy—we obtain a valid argument. But of course one can dispute any of its assumptions, and therefore there is no necessity to accept its conclusions. It is not a certain conclusion.

But as we have seen, these assumptions are very reasonable, and in fact an inseparable part of rational thought. Therefore, although there is no certainty in the conclusion of the cosmological argument, one can say that it is a rational and logical conclusion, and in fact more plausible than its opposite. The transition from the assumption that something exists to the conclusion that there exists another being that is the cause of its existence is an inference of the scientific type. It is a speculation (in the sense that it is not a deduction), but it is based on the basic assumptions accepted in rational thought. As I explained at the beginning of this booklet, in arguments of this kind we can expect at most this kind of reliability. This kind of inference is not essentially different from the inference regarding the law of gravity. There too we went from specific observations to the general law, on the basis of reasonable and accepted basic assumptions. Admittedly, there the conclusion can be subjected to an empirical refutation test, and we have indeed subjected it more than once to such tests, but even before it stood the test we gave it credibility because we have a basic trust in our faculty called intuition. We do not treat mere speculations as claims worth investing in and examining empirically. Our trust in intuition is what stands at the basis of treating such a claim as scientific.

The fact that the predictions of claims that are accepted in this way repeatedly stand up to empirical tests gives justification to our trust in our intuition. And from this it follows that if those same intuitive tools give us conclusions that cannot be subjected to a refutation test, we still have justification for placing considerable trust in them. This is of course when we are dealing with claims that by their very nature cannot be subjected to empirical testing (that is, where there is no evasion in their formulation whose purpose is to prevent empirical examination, that is, to turn the claim into something unfalsifiable). This brings us back once again to the discussion of Anaximander’s hypothesis in chapter 5 and of vitalism in chapter 7. There too we saw that philosophical claims need not stand a refutation test but a plausibility test. We also saw there that the fact that science does not deal with this kind of claim does not mean that it is incorrect, but only that it lies outside its domain and in fact outside the relevance of scientific tools.

Summary

To summarize, belief in God is not a scientific claim, but it is also not supposed to be one. It belongs to the realm of philosophy, and therefore the inability to subject it to a refutation test is not an argument against it. If from the set of observations in which we saw bodies with mass fall toward the earth we arrived at the law of gravity, then in a fairly similar way we arrive from the observation that something exists (a universe) at the conclusion that there must be something else that is its cause. The procedure of moving from the facts to the theoretical conclusion is similar to the scientific procedure. Admittedly, it is true that the conclusion of the cosmological argument does not stand up to an empirical refutation test.

If so, the cosmological argument grounds the thesis concerning the existence of God in a way similar to the way in which we arrive at scientific generalizations. Therefore it seems that one can place reasonable trust in it even without its standing up to refutation tests.

However, as we have already noted, Kant throughout his discussion assumes that the purpose of the argument is to prove the existence of God with certainty, as he writes there in the fifth chapter:

[…] Yet to go so far as to say: such a being necessarily exists—this is no longer the modest expression of a permissible hypothesis, but the bold pretension of an apodictic proof; for what we seek to cognize as absolutely necessary, our cognition of it must itself involve absolute necessity.

His objections there attack again and again the necessity and certainty of this proof, but again we must return and emphasize that this is not an argument that leads to certainty, nor does it pretend to be one. The nature of scientific inference on a factual basis is that doubt always accompanies it. And yet, even in the scientific context, we do not give up our (non-absolute) trust in the laws of nature that we have discovered; our claim is that the same is true regarding the conclusion of the cosmological argument. It is admittedly not certain, but it is definitely reasonable and acceptable.

1. See on this the second chapter of my book God Plays Dice. ↑

2. The second part of volume 1, second division, second book, third section, fifth chapter. ↑

3. Amichai, Tel Aviv 1963, translated by Shmuel Schnitzer. ↑

4. In Gadi Alexandrovich’s article, ‘No End to Weirdness: On Hilbert’s Crazy Hotel,’ YNET Science, 7.11.2011. See also on his blog, Not Exact, in the article: ‘Hilbert’s Hotel, or—Why There Are Different Sizes of Infinity,’ dated 8.11.2010. ↑

5. Perhaps this distinction is connected to the halakhic distinction between the concern ‘perhaps he died’ and the concern ‘perhaps he will die.’ The Gemara in Gittin 28b determines that we are not concerned about ‘perhaps he died,’ but we are concerned about ‘perhaps he will die.’ We are concerned about death when we look along the time axis forward, but not backward. This is an asymmetry that arises from the definition of the process. At some point in the future, the person will certainly die, since we have an infinite distance to traverse. Therefore we are concerned about ‘perhaps he will die.’ But when we look backward, a finite stretch of time has passed, so why should we fear that the person died precisely during this stretch of time? Here, of course, the stretch behind us is finite, and there is no place to elaborate here. ↑

6. This form of presentation too is taken from the above-mentioned articles of Alexandrovich. ↑

7. See on this at length in my book The Science of Freedom, chapter 5. ↑

8. See an analysis of his argument in my book That Which Is and That Which Is Not, fourth gate, second chapter, and also in my article, ‘Wisdom, Understanding, and Knowledge (On the Dialectic of Torah Study and Academic Research),’ Tzohar 35, 2009. ↑

9. The translation is taken from Samuel Sambursky’s book Physical Thought in Its Formation, Bialik Institute, Jerusalem 1953, p. 62 (and in one sentence also in Sambursky’s own introduction on p. 30). See also the Hebrew Encyclopedia under the entry ‘Anaximander.’ ↑

10. We should note that the midrash in Pirkei de-Rabbi Eliezer, on which Nahmanides relies, is cited in the Guide for the Perplexed (II:26) as the most wondrous and astonishing midrash (!) that he encountered in the words of the Sages. The reason is that it stands in opposition to the belief in creation ex nihilo. ↑

11. There he interprets the above-mentioned midrash from Pirkei de-Rabbi Eliezer allegorically. ↑

12. And indeed, in his sermon The Torah of the Lord Is Perfect (Writings of Nahmanides, Mossad Harav Kook edition, p. 156), Nahmanides writes: the thing the Greeks called… hyle—and its meaning is matter. And it is a generative power on which the elements depend… According to the sages of Israel, the hyle was created: ‘In the beginning God created’ the hyle of the heavens and the hyle of the earth… and this is the agreement of all the sages. From this point on He created nothing, but only brought forth being from being. And likewise in his commentary on the Torah: ‘Formlessness and void’… the Holy One, blessed be He, created, brought forth out of nothingness, a very subtle element that has no substance, but it is a generative power, ready to receive form. The first matter is called by the Greeks hyle, and in the holy tongue it is called formlessness, and the form, and the form clothed in this matter, in the holy tongue—void. ↑

13. It is very easy to identify prime matter with the kabbalistic Infinite Light. This is a light that has no end, since it is not limited. It has no properties, since properties are limitations (a property of something means that it is such and not such). And behold, the author of the book Leshem Shevo Ve-Ahlamah (see, for example, the book The Explanations, Discourses on Circles and Straightness, branch 2, section 7, section 9, and elsewhere), proves by force of such a consideration and others the claim that hidden sefirot were latent in the Infinite Light. The sefirot in Kabbalah are the various properties (the ideas, in Platonic terminology; and for us—the mass and charge themselves, as distinct from concrete masses and charges). In the Infinite Light the properties were in a completely prime state, that is, they were not yet even properties; only their concepts were hidden within it, similar to what we saw here. ↑

14. Admittedly, in chapter 6 of my book The Science of Freedom I showed that this teleological explanation can be translated into a causal explanation (I argued there that the uniqueness of human will lies in the fact that it turns the goal into a cause). Here I shortened things because our concern is only with the illustration. ↑

15. On the principled level, the reverse is also not necessary. A person may see the collective as nothing more than a useful fiction (and not an entity), and still place the nation above the particulars that compose it. But a correlation certainly exists. Just look at fascist discourse, which in many cases revels in romantic conceptions of the spirit of the nation and the like. Since here I am only illustrating the metaphysical conceptions as such and not analyzing the issue of fascism, I allow myself not to enter into such refinements. ↑

16. See on this the article by my student Hanan Ariel, ‘Public Transportation—A Halakhic and Moral Obligation,’ Tzohar 15 (2003), pp. 15–22. ↑

17. See several examples and sources brought in note 15 in my book Two Wagons and a Balloon. ↑

18. Strangely enough, most of the medieval authorities did not understand the Gemara this way, but this is not the place for it. ↑

19. See on this the book Kli Chemdah, parashat Nitzavim, section 2. ↑

20. See on this my article, ‘The Problem of the Relationship Between the Individual and the Collective and the "Defensive Shield" Dilemma,’ Tzohar 14. ↑

21. For a detailed discussion of this topic, see my book The Science of Freedom, chapter 13. ↑

22. Am Oved, 1984. ↑

23. Admittedly, he argues there that this is an illusion, and that in fact the cosmological argument too is nothing but an ontological argument in disguise. In my opinion he is mistaken about this. ↑