The Voice of Prophecy, Lesson 33

[Rabbi Michael Abraham] This is Section 2, Paragraph 11, right? We’re in Section 2, Paragraph 11, in Talmud Eser HaSefirot. Actually, we finished with some opening remark that was meant to close off some topic in preparation for what comes next. It says—let me just read the paragraph: “Nature, or the higher cause, insofar as it is asked about among what is known, I only compare it with the known action, the order of the world, and this is always according to human analogy in arranging divine actions.” And here he explains what this prophetic measure is that he talked about above. He says that it is basically according to human analogy. We mentioned a bit what is unique about analogy; I’ll just go over it a little more, because it came up at the end. What distinguishes analogy, in practice—one of the things that distinguishes it—is that when we compare one thing to another, there is some requirement of a relation of relevance between the feature of similarity and the thing being inferred. Meaning, if we take an example—I don’t know—if this table has a writing surface, and this is also a table, and I infer that this table also has a writing surface, then that is not a deductive inference. It comes by way of resemblance, analogy. Since they resemble each other in this respect, I infer that just as this one has a writing surface, that one also has a writing surface. But I can’t, for example, infer from that that this one is to my right, this one is to my left, therefore this one is also to my right. Why not? How do I decide which features I can infer as existing on the basis of the resemblance, and which features I cannot infer as existing on the basis of the resemblance? I need some notion of the relevance of the properties that I am comparing, relative to the properties that define the resemblance. If these two things are similar in something, there are things in which they are not similar, and things in which they are. That part in which they are similar gives me the power to infer other properties in which they are also similar—but not all of them, only some of them. Which ones? Only the ones that have some relation of relevance to the properties of resemblance. For example, location has nothing to do with the fact that both of them are tables. Why not? Because being a table is not a relevant property for inferring location. In other words, location is not a function of whether this object is a table or not a table. Therefore, the fact that these two things are tables does not mean that they will also resemble each other in where they are located. That changes nothing. By contrast, it is very relevant to the question whether they have a surface or do not have a surface—a writing surface. If this one has a surface, then presumably that one also has a surface. So analogy really requires some understanding that is not the result of the analogical reasoning, but a presupposition of it—some understanding of the connection between the parameters by which the things are similar and the parameters that I want to infer. How do I know about that connection? We spoke about Socrates and mortality and Jacob our forefather—Jacob our forefather is a human being, therefore he too is mortal. I think that was the example we gave last time. So here too it’s the same thing. We said that being mortal has to be connected somehow to being human. Otherwise I can’t infer from the fact that both are human beings that both are mortal. Mortal in the sense of beings that have to die. So I need somehow to come equipped in advance with this information—that dying, or being mortal, and being human are probably two related parameters. And from the fact that the two people are similar in this parameter, that both are human, they will probably also be similar in that parameter, that they are mortal. Now of course, if I already know the fact that every human being is mortal, then this is not analogy, right? It’s just deduction. Since all human beings are mortal, then I do not learn that Jacob our forefather is also mortal from his similarity to Socrates, but rather: he is a human being, and I know that all human beings are mortal, so in particular he too, as a human being, is mortal. That is to say, when I make an analogical inference, I do not know with certainty some essential connection between being human and being mortal. If I knew that, it would not be analogy; it would be deduction. So what then? Apparently I sense, or assume, that there is some connection between the teaching property and the learned property, and that is what this analogy is based on. In other words, I need some way to sense the relation of relevance—the fact that there is a relation of relevance between being human and being mortal. If that relation were given to me, then of course what I just did would not be analogy at all; it would just be deduction, and I would not need Socrates in the picture. If I do need Socrates, then in fact I do not know with certainty about the relation between being human and being mortal. Maybe I can get some hypothesis about it, a hypothesis strengthened by the fact that I see this connection in Socrates. So I say: well, if it is true in Socrates, then apparently there is something to this connection, so I infer that it is true regarding Jacob our forefather as well. So let’s move now to Paragraph 12.

[Speaker B] Where it says “nature, the higher cause”—does it say there that it changes the order of the world?

[Rabbi Michael Abraham] Here he compares it with the known action, the order of the world. The point there, against that, is that this is still a remnant of referring to negative attributes. Nature, the higher cause, the Holy One, blessed be He—speaking about Him by way of analogy with the order of the world, with the things I know around me—I can conjecture things said about Him. Even though obviously I cannot infer the matter by necessary inference, because He has a different nature. But that still doesn’t mean that I can say nothing about Him. This is basically an opening to his proposal for why I can nevertheless know something about divinity. Above, he calls it by allusion “the prophetic hint,” or alternatively, what he calls here “human analogy.” We’ll come back to that later. “Every investigator”—that’s in Paragraph 12. “Every investigator seeks something that has not fallen under the sight of the eye and has not been grasped by the senses, and he tries to establish it by way of bringing proofs from the intelligible. For if that were possible, there would be no need for sight, nor for inquiry, nor for deriving one thing from another. But we needed inquiry to reveal it to us, and proof—or sight—to clarify it for us, because it was neither visible nor perceptible.” As Rav Saadia Gaon says in Emunot Ve-Deot, at the beginning of the Gate of Knowledge. And likewise Rabbi Shlomo Ibn Gabirol in Mekor Chayim,

[Speaker C] We already mentioned that book here, right? A book originally written in Arabic in the 11th century, which the entire Christian world thought

[Rabbi Michael Abraham] was written by a

[Speaker C] Christian philosopher named Avicebron.

[Rabbi Michael Abraham] And only at the end of the 19th century did they discover that Rabbi Shlomo Ibn Gabirol wrote it. “What is self-evident does not require proofs for its knowledge, and what is not self-evident must be known through proofs.” And by making the effort to preserve the laws of logic—that is, the rules of rational give-and-take—we will reach certain conclusions. First of all, that opening paragraph is actually very important in many contexts. Today there is a certain rule accepted—at least in this century—in the philosophy of science, which says that a scientific theory cannot be proven, only falsified. That is the criterion for the status of a theory as a scientific theory. Karl Popper introduced this idea—Karl Popper, a philosopher of science in the middle of this century. And since then it has more or less ruled until today. Even those who claim not to agree with that direction are basically formulating the same thing in a somewhat more sophisticated way. A scientific theory cannot be proven. Why? Seemingly, science is empirical study—that’s how it is usually understood. An empirical way, meaning what comes from experience. I look at the world and infer certain conclusions about its nature. Not metaphysical speculation—that’s not what the Greeks used to do, arriving at all kinds of scientific truths through some kind of speculation, sitting in a room without bothering to look at the world. There was no awareness at all that one also had to test these statements in the world. And that’s how they arrived at all the… statements of Newton that… not Newton, Aristotle—that stones, for example, fall according to their weight, and their speed is proportional to their weight. Now, you don’t have to be such a great scientist. Just take two stones up high and see that it isn’t true. Go up some tall tower and throw two stones, one large and one smaller, and you’ll see that they fall together, Aristotle. More or less together—air resistance may interfere a little—but certainly you’ll see that it isn’t proportional to weight. But there was no awareness that one had to test statements about the world. If something emerged through philosophy, through metaphysical analysis—because science was, of course, a branch of metaphysics—then you didn’t need to test it in the world; there was no such awareness. Modern science differs from the science of old—what used to be called science—precisely at this point: it feels more committed to reality. But that doesn’t mean that from here on everything is simply a matter of looking at reality and we have empirical proofs for every scientific theory. We haven’t gotten there, and probably never will, I have to say. Scientific theories cannot be proven just by observation. There is always still a speculative element, an element of human metaphysical speculation. Why? So for example, the example—I think this is the example Popper gives, and everyone after him at least sticks with it—is that all ravens are black. A scientific theory that says all ravens are black. How can it be proven? How does one, as a scientist, go about testing such a theory? One tries to observe ravens, right? But I have no way to prove it. All I can do is see one raven and see that it is black. Observe another and see that it too is black. Observe another and see that it too is black. But who told you that the next raven, the one you haven’t seen, will also be black? That you cannot know, right? There is some process of induction here. But you cannot infer the law from your observations in a necessary way. Your observations—even assuming I do not intend to be a skeptic or an idealist, and for me what is seen counts as proof, okay? Fine. But of course even at that level of sensory proof, that too is not available for scientific theories. Because in the end there is always speculation. I saw three, four, ten black ravens; I infer that all ravens in the world are black. That is a completely speculative inference. Seemingly, we haven’t advanced very far since Aristotle. Who told you that the next raven will also be black? And alternatively, what distinguishes scientific work from mere speculative thinking or anything else? We said we can’t prove. We also can’t derive it from observations. So Popper proposed the criterion that scientific thought—and this is exactly the point where modern scientific thought differs from Aristotle’s thought—is that the theory… what is called a scientific theory? It is a theory that can be falsified. Not verified—falsified. That is the constitutive criterion of a scientific theory. What does that mean? If I find one white raven, then I have refuted the theory that all ravens are black, right? Meaning, I am indeed in some relation to reality, but reality cannot build the theory; it can only destroy it. A theory that is not scientific is a theory that deals with—or makes claims about—things that cannot be empirically tested at all, yes? Meaning, I certainly cannot prove them, but I also cannot refute them. Meaning, I also don’t bother trying, and I also can’t. If there is no fact that would unambiguously refute the theory—I don’t know—the theory that there is or isn’t a God, that is not a scientific theory. It is not a scientific theory because there is no unambiguous empirical datum that can tell me or refute the theory. Certainly not prove it, as we said—there is no theory that can be empirically proven. But this theory cannot even be refuted. Therefore it is not defined within the domain of science. A scientific theory is not just another name for a true theory, yes?

[Speaker C] It’s

[Rabbi Michael Abraham] a very specific kind of theory, one that is committed to observations. And it is committed to observations in a negative way, not in a positive way. Meaning, it always has to test itself in the world to see whether it has been refuted. But proving the theory is never possible. So what does science do? It keeps subjecting the theory to another test, to see whether in fact it will be refuted by that experiment. That is the meaning of scientific experiments. You do an experiment in order to see whether the theory will be refuted, not whether the theory will be confirmed. Because the fact that you saw the theory work in the lab doesn’t mean it will work next time too. Maybe that was because of some other factor, because there was electricity here, because there was something here—various things you can’t know, yes? So you can’t take one particular case and infer: this theory is true, it always works. But one thing is clear: if it doesn’t work, then clearly this theory is not correct. If once an object does not fall toward the earth, then you know that it is not correct to say that all objects fall toward the earth. Okay? Now seemingly one might come and say: what do you mean, what is the problem with proving the theory that all ravens are black? Let’s gather all the ravens, look at them one after another, and see that they are black. There you go. Let’s check whether ravens are black or not. Or let’s gather all the objects, check whether they all currently fall toward the earth, and in that way confirm the theory. Here the answer is of course twofold. Why is that the answer to this challenge? First, you would need infinitely many observations. That would obviously be very hard to do—gather infinitely many objects, especially if we are talking about the past and the future. But even statements about the present—there one might think perhaps this can be done. If I gather all the objects that ever were and ever will be that fall toward the earth, those I can never gather into one courtyard, yes? But maybe at least if I make certain statements about the law that currently prevails, maybe that is

[Speaker C] provable?

[Rabbi Michael Abraham] And I think there is a more central point here. After I gather all the ravens and see that they are all black, or I gather all the objects and see that they all fall toward the earth, then the theory that says all ravens are black is no longer a scientific theory. It is simply a summary of a set of empirical facts that I observed. A concise description of all the facts I observed in all of them. But that is not a scientific theory. Its whole purpose is to try to describe things you did not see. A database is not a scientific theory. A database is just a collection of all the scientific facts that I saw, and I entered them into a computer or a book or a notebook or whatever. I have a database. A database is not a scientific theory. A scientific theory is an attempt to say things about things I have not seen. In light of what I did see, to try to infer what will happen in cases I have not seen. If I merely summarize backward, but I have already seen all the relevant cases, then I have removed that matter from the domain of science. Because it has moved into the domain of a database, but it no longer belongs to the realm of scientific theory. Therefore this is actually essential, not merely technical—it’s not just because there are infinitely many objects, so I can’t test them all and see that they all instantiate the property I’m talking about. The point is more essential. If I could collect them all, it would no longer belong to the domain handled by science. Then I’ve already seen everything and that’s that. I summarized the results of my research by saying that all the objects I saw fall. What have I said? I have merely summarized the set of things I saw. Whenever I say “scientific theory,” I am always making a general statement. It is some statement that will also include events or objects I did not observe. And I want to say something about them too, in light of things I saw in certain cases. In other words, speculation or induction is at the foundation of science. It’s not some unfortunate accident that we work with induction or speculation. It has to be that way. Meaning, without that it’s just… to collect all the individual events I observed and formulate them in one inclusive sentence—that is the art of formulation, not the art of science, yes? That I formulate, instead of formulating infinitely many facts, I formulate it in one sentence: all objects fall toward the earth. There is no scientific law here; this is just a summary of all the observations I gave. When I say this is a scientific law, I mean something more than that. I mean that all objects must fall toward the earth. There is something essential here: even the objects I have not seen will have to fall toward the earth. That is not merely a summary of observations. It is some statement about the nature of the world. And a statement about the nature of the world is always something that cannot be inferred from observations alone. There is always some speculative metaphysical element here. I move from several things that I saw to some more general claim. So that is really the first paragraph he is talking about: “Every investigator seeks something that has not fallen under the sight of the eye and has not been grasped by the senses. But he tries to establish it through bringing proofs from the intelligible. For if this were possible”—possible in what sense? by seeing, or through the senses, and so on—“there would be no need for proof or inquiry or deriving one thing from another.” Why would we need all human thought if everything were attainable by the senses? Then there is no room for speculation or science or anything else, and certainly not philosophy, yes? It is not a matter for thought and proofs from the intelligible, because I have already seen it. We demonstrated this first with science, but it is true everywhere. Also in philosophy, of course, these are not claims that simply gather the set of data I observed until now; rather, they are claims that offer some interpretation of what I observed, and that interpretation will also have implications for things I have not yet observed. Okay? So every investigator—that is what he is saying here—deals with, or tries to deal with that. Now the question is: so how is this actually done? How do we, if I haven’t seen it, then how do I really know that it is true? Okay—after all, I say the following: I have seen a thousand objects up to now, and all of them are indeed firmly attached to the earth, and if they rise a little above it they fall back down. So up to now everything I have seen does in fact fall toward the earth and does not just manage to rise. The question is how I can infer from this that it is true of all objects, at least objects with mass. How can I derive such a thing? I saw only a collection of objects for which that was the property. So who says that any other object I have not yet seen will also have that property? How can I know that? Notice that this very much resembles the problem we discussed before, the problem of analogy. I saw a thousand objects, all of them falling toward the earth. Now I infer: all objects—and I added in parentheses, objects with mass—all of them, I know, surely, clearly, will fall toward the earth. Why? Because the scientific theory I inferred in light of those observations said that being possessed of mass means—or not means, but is always bound up with—falling toward the earth and not managing to take off, yes? So if that is the case, then of course from now on, every object with mass, even if I have not seen it, I will infer that it falls toward the earth. So once again, the point I’m making now is: how do I know that relation of relevance between having mass and falling toward the earth? Because there are objects—say, an electromagnetic field, that too maybe one could call an object, and in fact that is also true—it does not fall toward the earth even when it passes through here. Why? Because it has no mass. In other words, I already know a specific statement about those things: not every object in the world falls toward the earth, only an object with mass. How do I know that specifically their having mass is what causes them to fall toward the earth? I saw a thousand objects. I could have thought of other things they have in common besides having mass. How do I know that specifically their having mass is what caused them to fall toward the earth? This is once again a question of relevance, as we saw with analogy. How do I know that this particular property is the relevant one to my conclusion, which deals with falling toward the earth? Induction and analogy are cousins, as we’ll soon see. So let’s move to Paragraph 13. Here he really starts discussing how this is done. How do we infer these conclusions about things we haven’t yet seen? As he said in the previous paragraph, every investigator wants to say things about things he hasn’t seen, so how can he really do that? He says: “proofs from the intelligible.” How does that work? Now he tries to analyze it. So in Paragraph 13 he says this: “The proof, the logical demonstration, comes to establish and compel a matter already at issue, but it does not discover it unless it had already arisen in our mind. The discovery of truth, its existence and finding, is by means of an inference that raises it to the mind, when one compares one thing to another through analogical inference.” Here we have the basic statement that opens the door to the answer. He says: the proof, logical analytic thought—what we called in Maimonides—that is a kind of thought that cannot discover new things. Logic cannot discover things I did not already know. Yes? How is a logical argument structured? A logical argument is structured like this: all human beings are mortal, Socrates is a human being, therefore Socrates is mortal. Yes? It appears in the next paragraph; Maimonides will bring it there as an example everyone knows. In any case, how is such a logical argument really structured? Seemingly, if I know that all human beings are mortal, then I already knew that Socrates is mortal too, right? Already at the stage of the premise. I have two premises that I know: all human beings are mortal—that is the first premise; this is called the major premise of the inference. And the minor premise is that Socrates is a human being. Fine? Those are two things that I know. The conclusion I arrive at through the logical inference says that Socrates too is mortal. This of course follows necessarily from the two premises. But why does it follow necessarily from the two premises? It follows necessarily from the two premises because it is already there in their content. There is nothing here that is any more than what was already in the premises—if anything, less. It is something that was already hidden within the premises. If I know that all human beings are mortal and I know that Socrates is a human being, then in particular—even before I made this argument—I already knew that Socrates too is mortal. Because all human beings are mortal—I already knew that beforehand. And I knew that Socrates is a human being. So in particular I knew that Socrates is mortal, right? So the logical conclusion—everything it can do is reveal to me something I had already entertained, something I already knew. It cannot add something that at the stage of the premises I did not know. On the contrary, that is the whole essence of logic. The whole essence of logic is that it does not discover new things; it only clarifies better for me things I already know. And therefore logical reasoning is considered necessary reasoning, something indisputable, absolute truth. Why? Precisely because it says nothing; that is why it is absolute truth. It merely clarifies for me something that I knew even before the logical reasoning. It just sharpens it for me more, or draws my attention to that point—that Socrates is mortal—even though I also knew it implicitly beforehand. Logical reasoning only sharpens things I knew before, that’s all. Which means that logical reasoning cannot discover new things for me. So how do new things become known? If that’s the case, then how do they? Earlier we opened the previous paragraph. The previous paragraph said that all investigators want to discover things that go beyond what they knew before, beyond the facts they observed before, right? I want to discover things beyond the things I knew previously. So in the first two lines of this paragraph we see that logic cannot do that job. Logic cannot discover things for me that I did not know before. It can clarify well the things I already know, but it cannot discover things I did not know before. That’s the first two lines. The next lines are the answer. “The discovery of truth, its existence and its finding, is by means of an inference that raises it to the mind.” What does “raises it to the mind” mean? Brings it to us, to our knowledge, yes? Not just reveals something that was already there. It raises the thing to the mind “when one compares one thing to another through analogical inference”—that is analogy. So analogy is the form that can teach us new truths that we did not know before. Logical thought, necessary thought, mathematical thought—it can never add information we did not know beforehand. And the statement

[Speaker C] that all people are mortal—that isn’t a statement that just comes, as it were, from within the concept of all people.

[Rabbi Michael Abraham] Okay, we’ll get to that in a moment. It’s a bit more—this is what we talked about in the previous series. This is basically Hume’s challenge to induction. Okay? The next section talks about that. In any case, here we distinguish between—let’s even call it—three forms of thinking. He talks about two, because two of the three here are roughly the same thing. There are three forms of thinking: deduction, induction, and analogy. Okay? Deduction is thinking from the general to the particular. That’s logical, necessary thinking. If I know something about all X’s, then in a particular case I can draw a conclusion about one of those X’s, right? That’s thinking from the general to the particular, and it’s necessary thinking, by mathematical, logical force. That’s what is called deduction, a logical proof, as he writes below. After that there is induction. That is thinking from the particular to the general—sorry. I know particular facts, and from them I derive some general conclusion or law. I know that several objects fell to the earth, and then I conclude that all objects fall to the earth. That is induction, generalizing from the particular to the general. And there is analogy, which is moving from one particular to another particular. I know a certain fact about one particular case, and I infer that same fact in a second particular case through some similarity between the two cases. That is analogy.

Now in practice, these three are really three that are two. Because analogy and induction are cousins. Superficially, I might have said there is a hierarchy among these three forms of thought. Deduction is the strongest. It is necessary, absolute. Induction and analogy are not necessary. The question is whether there is some relation between them—which is stronger and which is weaker. At first glance it would seem that analogy is stronger than induction. Stronger than induction not in an essential sense, but maybe in a quantitative sense. Since analogy claims less, it plays it safer. Let’s draw a conclusion only about one object. I saw one object, so I draw a conclusion about one more object. Right, it’s not deduction, it’s not necessary, but there is no extraordinary boldness here. Maybe I’m right, maybe I’m wrong, but still it isn’t claiming anything overly strong, so it is more likely to be true. I’m taking fewer risks, and therefore it is more likely to be correct—the rule of profit according to risk.

In induction I saw one or two or three particulars, and I draw some sweeping conclusion about all particulars, or all particulars of a certain type. That already involves a kind of wild speculation. In other words, there is a much greater chance that I’m saying something false, because maybe it’s true of one particular, maybe it’s true of two, but who says it’s true of all particulars? Okay? So I would say that if there is some hierarchy here, it would be deduction, then analogy, and then induction, in terms of the power of the arguments, the strength of the arguments. But actually, when you come to it—and still, it’s true that the logical argument is only deduction, and the others are really the kinds of arguments that can add truths for me, the power he spoke about earlier.

The truth is that this argument, this relationship, is not correct, it does not exist—the relationship between the last two elements, between induction and analogy. Why doesn’t it exist? Because let’s think for a moment about how an analogy is structured. Analogy, as we said—how is it structured, yes, analogy. So I say the following: since Socrates is a human being and he is mortal, then Yaakov too, since he is a human being, is also mortal. So apparently that’s from one particular to another; I haven’t made any far-reaching speculations. But what is really hidden in the background here? What is hidden in the background is: how did I infer this? I inferred it because I inferred, as we said before, the relevance between being human and being mortal. Right? So in fact I did infer a general law, that every human being is mortal. True, I didn’t say it explicitly, but instead jumped straight to the particular conclusion that Yaakov is mortal. But in truth some generalization is hidden here behind it. Because the claim of relevance, what we called it earlier, is actually always a general claim. When I speak about a relation of relevance between the feature of similarity and the feature I am inferring, that relevance is a general dependence. Being human is always relevant to being mortal. There is induction in the background here, right? Therefore analogy actually relies implicitly on induction. So it cannot be stronger than induction. If part of its inferential process includes an inductive stage, it cannot have greater force than induction, right? The strength of a chain is the strength of its weakest link. Okay?

So it comes out that it isn’t—on the contrary—that it is weaker. Right, although if you think about it as I’m saying now, then that’s not really correct either. Because it’s enough to find one human being who is not mortal. True, you haven’t refuted the conclusion, but you have refuted the argument leading to the conclusion; you have refuted the relevance of mortality to humanity. So in fact, if that really is the line of thought behind analogy—and by the way, this can be discussed a lot, it’s not certain that every analogy is built this way—but at least many analogies certainly are built this way, namely that they are really hidden inductions. Only I don’t formulate the inductive conclusion as a general sentence, but instead discuss a specific item directly.

And then what comes out here? What comes out is: how is analogy built? Analogy is really built through the following logical process: I take a particular fact—Socrates is human and mortal. I assume a general conclusion, or infer one, it doesn’t matter, by induction: a general conclusion that every human being is mortal. And from that general statement, by deduction from the general to the particular, I infer that Yaakov too is mortal. Right? So what is analogy really? It is simply a shortcut for a pair of processes—an induction followed by a deduction. Right? An induction that moves from the particular to the general, and after that a deduction that comes back from that generality to another particular. Okay? So it is just linking together two of the logical processes we talked about earlier into a chain, and that is what is called analogy. Okay?

On the other hand, it is also clear that if you examine what induction is, induction too rests on analogy. Not only does analogy rest on induction, induction rests on analogy too. Why? Because how do I really infer from the fact that Socrates is a human being who is mortal that all human beings are mortal? Because I make an analogy between Socrates and every other human being. I say: obviously, his humanity is what causes him to be mortal, so so-and-so, who is a human being, will also be mortal, and that other person, who is a human being, will also be mortal; therefore all human beings are mortal. I construct the induction through some understanding of relevance, through something actually very similar to analogy. Therefore, in some sense, the motivation for why you move from one thing to another—when I see two things, two human beings of a similar character, I don’t know exactly why they are similar, I sense that there is something similar here, and therefore I infer that if this one, in such a situation, would hit so-and-so, then that one, in such a situation, would also hit so-and-so. Here, if I don’t know whether I can explicitly formulate some transition through a general law when I make that inference, it is some connection of similarity between two particulars. It’s true that one can always formulate it as: all people with a trait

[Speaker C] like that—but it

[Rabbi Michael Abraham] didn’t pass through some general statement, certainly not consciously, though subconsciously maybe yes. That’s a question. I don’t know; I once wrestled with it. Try to think of clearer examples of that. But in any case, one thing is clear: there are two families here. Induction and analogy are one family, and deduction is another family. If we call them, basically, by terms from Immanuel Kant’s thought, let’s call them analytic thinking and synthetic thinking. Analytic thinking—deduction is analytic thinking. Analytic thinking means dissecting thought. Analysis is dissection. I analyze what I already know, and that’s how I reach a conclusion, and that is logical analytic thinking, right? Synthetic thinking is thinking that makes a synthesis between the knowledge I have now and other knowledge that I do not have now. That is synthetic thinking. Synthetic thinking can be composed of processes of analogy and induction. Deduction is not a synthetic kind of thought; it is something standing above that. It only comes to establish and compel things that I already know, or to sharpen things that I already know. It cannot add information that I do not know. It cannot make a synthesis with new information. It can analyze what I already know and extract some detail from it, or focus attention on some detail—that Socrates too belongs there. If I think carefully about what I already know, then I will understand that I already know that Socrates is mortal. Okay? That is analytic thinking versus synthetic thinking.

And in fact we can summarize the relation between analytic thinking and synthetic thinking and say that analytic thinking is thinking that cannot teach me anything new. The analytic, mathematical form of thought cannot teach me anything new. And precisely because of that, it is necessary. It is necessary because it actually claims nothing new; that is why it is necessary. If you are only clarifying what I already know, then it is necessarily true that if I know that, then I know that. That goes together; it is obvious. It is necessary, but it is necessary specifically because it has said nothing new. And that is the balloon joke. Do you know it? About the people who were in a hot-air balloon and were in a bit of trouble, and they drifted somewhere and didn’t know where they were, and they saw a person below and asked him, “Where are we?” He looked up at them from below and said, “You are inside a hot-air balloon.” So one of the people in the balloon said to the other, “That must be a mathematician.” He said, “Why a mathematician?” So he said, “Because first, what he says is necessarily true, and second, it doesn’t help us at all.” And that’s the common joke about mathematicians. But what I want to say—at least about mathematicians—is that these are not just two unrelated characteristics. They are two characteristics that have a necessary connection between them. It’s not by chance that it doesn’t help us at all and that it is necessarily true. Everything that is necessarily true is so precisely because it doesn’t help us at all. After all, he took no risk at all in saying that you are in a balloon, because that is obvious; it is a fact. Therefore it is obviously true, and therefore it also obviously does not help us at all. Whenever you want to gain something, you have to take a risk. It’s well known, a well-known rule in economics, right? Return is according to risk. Profit comes according to risk. The graph of profit versus loss—actually the slope of that graph is basically the risk, in the economic definition of risk. When you take a strong risk, then a small investment gives a large profit, right?

[Speaker C] So the slope of the graph is steep; that return will be large.

[Rabbi Michael Abraham] Right? Look at the graph: I invest a hundred shekels, I can earn a hundred shekels. I invest two hundred shekels, I can earn two hundred shekels—beyond some basic level. That’s the idea that money makes money. The more money you invest, the more you earn—not just getting back the same money plus return; you earn more. Right? But the question is how much more. That question—how much more—is what is defined in economics as a parameter called the slope of the graph of profit versus investment. That is basically what is proportional to risk. Right? So here too, it’s the same thing; in thought too it’s the same thing. The more daring you are, the more you can gain things that are more far-reaching, more substantive—you say things that are true in a more general way, about much more, things that contain much more content. But of course that is also more questionable, because it is much farther from what you already know. The farther you are from what you already know, the more powerful the statement is, but also the more difficult it is to justify. Right? Therefore deduction, which basically says nothing, has no risk, and therefore also no gain. Right? It involves no risk; it only clarifies things I already know. So it is necessarily true, no doubt. And analogy and induction, as we saw earlier—there may be a difference in risk between them. Here I take a risk only in a statement about one object; here I say it about all of them. Maybe that’s not the same, maybe it is the same, as we discussed earlier. But here there is already some risk. I am making a speculative statement in a certain sense, beyond what I already knew. Therefore it can also turn out to be wrong; it is no longer necessary. Okay?

So let’s read what is written there now. Let’s read section 14, where these things are basically written, and afterward we’ll sharpen one more point that comes up there. “The exemplary, general logical inference called the syllogism, the foundation of ancient Greek logic that ruled throughout the Middle Ages, is built from two premises. The first is major, general; the second is minor, particular; and a conclusion.” “Conclusion” is already the third thing, yes? Two premises and a conclusion. The two premises are one major and the other minor, particular, and then a conclusion. “But the exemplary inference does not innovate anything; rather it analyzes, confirms, and compels what is already known.” Which is exactly what we explained now. That was already said in the previous paragraph, maybe a bit more implicitly. “As in the example in Milot Ha-Higayon: every human is living, every living being feels, therefore every human feels. For the conclusion is included in the premise. Every living being feels, so a human being also feels.” The famous example: all human beings die—that is, they are mortal, as we said earlier. Socrates is a human being, therefore Socrates dies. For already in the premise “all human beings die” it is included that Socrates also dies. Right? Therefore this inference innovates nothing; it only analyzes, confirms, and compels what is already known.

“However, the inference that does innovate something not previously known is analogical inference, inference by resemblance, comparison, called analogy.” Analogy is the way to reach things I do not know. That is exactly how one goes beyond mathematics. Mathematics cannot give me any information I did not know before; it can only help me analyze what I already know—mathematics or deduction. Analogy is the way—science, in fact, is in a certain sense the antithesis of mathematics. It is the possibility of reaching things I do not know, of trying to broaden the horizons of my knowledge, not only analyze them. Therefore one needs analogy there. That is what we saw earlier: a scientific process is always an analogical process, really an inductive one. It is not a process based on deduction. “Also the inferential search that rises from particulars to the general, called induction, whose value is great in modern logic and the modern sciences, is founded on analogy, comparison.” We talked about that earlier—that at the foundation of induction there is some analogy. Earlier we also saw that the reverse is true too, that at the foundation of analogy there is induction. And therefore there is really no hierarchy between them, and he also does not distinguish between them. In other words, from his perspective analogy and induction are two forms of thought that are one, what in our terms we would call synthetic thought, thought that can make a synthesis with new knowledge. Deductive thought is analytic thought, thought that only analyzes what I already know.

Therefore, the logic of the interpretive principles by which the Torah is expounded—here this is actually the introduction to what is about to come now—the claim is that the interpretive principles by which the Torah is expounded are simply an alternative logic, analogical logic, not deductive logic. And therefore it can teach us things that we did not know at all in the first place. An a fortiori inference is like that too, and we will talk about that later. Okay, let’s just finish the discussion of the three forms of thinking, and then we’ll begin the discussion here that starts in the next sections.

“Modern logic” or “the modern sciences” that he speaks about here, about a line before the end—we mentioned Francis Bacon, the inductive logic of Francis Bacon, who claimed that this stands at the foundation of all science. He was basically the first to formulate what I told you earlier: that before Karl Popper, science basically worked on some kind of induction. Science cannot be founded on deductive inferences. Greek science, the old science, was in some senses a deductive science. And therefore it basically claimed nothing about the world. It tried to map the principles of thought that I come equipped with from home. Not to learn new things from the world, but to analyze things with which I come from home. And in many respects that was—it wasn’t pure deduction, but it worked like deduction. In other words, it did not make an integration or synthesis with knowledge coming from outside, but analyzed principles with which I was already equipped from the outset. It did not learn new principles from the world. I merely analyze. If I know that the element of fire is lighter, then obviously it rises upward. If the element of earth is heavier, then obviously it descends downward. Therefore every fire rises upward and every earth descends downward. I did not learn that from reality, apparently. One could come and say that yes, I do know it from reality, but from the standpoint of the scientific reasoning itself, it is some kind of speculative reasoning. It is merely an analysis of concepts with which I am already equipped, not an addition of information that comes to me from outside. I do not add things beyond what I already know.

So as we already mentioned—he himself already mentioned Francis Bacon in the introduction, page 4 of the book. There he says: “The new experimental philosophy opens with a new Organon.” New Organon is the name of Francis Bacon’s book. Aristotle’s Organon is Aristotle’s book of logic, the Organon. And the New Organon comes precisely to say that the sciences cannot be based on logic. The sciences need to be based on induction. Therefore he constructs the process of inductive thinking—how one does it despite the fact that it is speculative, but how one does it in a careful way that still tries to advance scientifically and not just through mere speculation. Okay? That is basically the heart of the argument of the New Organon. And that is what he is talking about here—this is “modern logic” or “the modern sciences.”

Now one more very important point must be noted. Below, in note 40, he writes as follows: Mill, John Stuart, A System of Logic, Ratiocinative and Inductive—that is the name of his book. He brings this example of “Socrates is mortal,” and so on. Then look at the last line of the note: “A critique of the example, for the conclusion is already included in the general premise.” In fact, Mill presented this as a kind of critique of the deductive process of thought. He says: what are you telling me stories about deductions for? Deduction is nothing at all. The result of deduction is merely a statement with which I was already equipped before I made the deduction, when I had already assumed the premises. So in what sense does deduction help me? It helps me in no way. All it does is simply repeat things I already knew. And there he continues: “For inference is comparison of one particular with another particular and with particulars, and the general rises from the particulars by way of induction.” Therefore we said that analogy sits at the root of induction. “In Book III, on induction, Part II, chapter 20, on analogy, page 96: every resemblance of one thing to another presupposes a basis for a number of other resemblances.” Right? That is what we discussed earlier. How do you find the resemblance between Socrates and our father Jacob? Through the fact that you are really speaking about other human beings too. In fact you say that all human beings are mortal, so really there is induction in every analogy. “For example, as the earth, so too the moon is inhabited”—that is an analogical proof. Because we have no way by which we could distinguish analogy from induction. Right? That is essentially the claim found in Mill.

But in Mill there is another claim, which he does not bring here, but for our purposes it is very important. Earlier we saw it implicitly. Mill also makes a claim against deduction—not only the claim we discussed here, not only the connection between analogy and induction. We said there are three forms of thinking: from the general to the particular—that is deduction; from the particular to the particular—that is analogy; from the particular to the general—that is induction. And we already identified the last two and saw that they are not really two different things. Mill also claims that the first one is not something different either. The first one too is not something different. So his first challenge is what he mentions here, which we read earlier: that deduction is not a different form of thought. It is simply repeating the same thing twice. To say “all human beings are mortal” and “Socrates is a human being,” and then to say “therefore Socrates is mortal,” is simply to restate what I already said. There is nothing new there; therefore it is not a form of thought.

And in my view he has an even more significant challenge to deduction—a challenge that says: let’s assume that even so, in deduction you really can get somewhere. After all, there is mathematics, there are logical things that we plainly would not have arrived at otherwise. Now the question is: how do you really arrive at them? Let’s take Mill’s example again: all human beings are mortal, Socrates is a human being, therefore Socrates is mortal. Mill asks us: how do we know that all human beings are mortal? They tell him: we saw all human beings. How—how do we know that all human beings are mortal? That is what he called the major premise of the argument, right? The major premise. What does “major” mean? It means the general one that says all human beings are mortal. An argument is usually structured like this: there is a major, general premise; there is a minor premise; and there is a conclusion. The major premise is “every X is Y,” all human beings are mortal. The minor premise is that the specific I is X—Socrates is a human being. Conclusion: Socrates is mortal, right? That is a major premise, a minor premise, and a conclusion—that is what we had above. Fine.

And how do you know the major premise? Mill asks. How do you know that all human beings are mortal? Past experience. Past experience did not encompass all human beings; you saw

[Speaker C] maybe the vast majority of them, but there are people alive now.

[Rabbi Michael Abraham] Hm? There are people alive now.

[Speaker C] But again,

[Rabbi Michael Abraham] not all of them you know.

[Speaker C] maybe from induction or analogy or a specific inference? Yes.

[Rabbi Michael Abraham] In other words, the general premise always itself comes out of induction, right? If there is a general premise, then it in fact came from observing a certain number of particulars and making an induction in order to reach the general premise. So what are you trying to tell me? You want to tell me that deduction is a stronger process than induction and analogy, that it is necessary? Mill says that’s throwing dust in people’s eyes. What do you mean? The deductive capacity itself is actually equivalent to induction. You want to infer that Socrates is mortal—how? By means of two premises: all human beings are mortal, and a second premise that Socrates is human. But your very first premise is based on induction. So you cannot say that deduction is an independent act of thought, stronger than induction. It is based on induction. Right? Hm? Could he have reached conclusions without induction? No, in my opinion no, and that is what enters into the conclusion so that it can serve as a basis.

[Speaker C] Fine, it’s an infrastructure, but it’s induction, it’s induction.

[Rabbi Michael Abraham] Obviously there are connections here in a certain sense, because you understand it, but it does not have mathematical validity. We’ll talk about that some more—yes, we’ll talk about it. So what comes out if we summarize? What comes out is what I told you before, but now it is sharper: induction, deduction, and analogy are not three forms of thought at all. They are three that are one. Not three that are two, certainly not three that are three. Earlier we said three that are two; it’s not even three that are two—it’s three that are one. And what we call deduction is simply a combination of induction—induction and that’s it. Induction plus a stage of focusing on one particular from within the general.

[Speaker C] An induction that says: I saw several particulars,

[Rabbi Michael Abraham] so I generalize and say all human beings are mortal. And afterward I focus on one particular who is a human being and say: fine, this one too is mortal. That is deduction. But that deduction includes an inductive element, right? So in fact what is there in this process? There is really one large analogy, right? As we saw earlier. There is an analogy from those few mortal human beings I saw to Socrates, who is also a human being, so I say that he too is mortal. How do I make that analogy? I go through a general law. I say: since there are several human beings who are mortal, I can infer the conclusion that all human beings are mortal, and from that conclusion I can infer in particular that if Socrates is a human being, then Socrates too is mortal. So in fact the whole world is simply analogy—analogy from the particulars I have observed to the particulars about which I want to infer the conclusion. It’s just that the analogy is composed of two stages. One stage is the induction that leads me from some particulars I saw to the general law, and the second stage is the deduction that says: okay, now you know the general law; let’s focus on one particular within the general law and know that this statement is true about him too. Okay? So deduction and induction are just a decomposition of analogy into two stages, but there is nothing in them that stands independently. Okay?

Therefore in fact human reason is, in some senses, something one can say is actually not complex. In other words, it is really one thing. You can break it down into stages and give each stage a different name, but these are not alternatives. It’s not that sometimes reason works this way, sometimes that way, and sometimes another way. Reason always works analogically. Sometimes you can break that into stages and call this stage induction and that stage deduction. But in fact it is all analogy. And that is basically the claim.

If so, let’s maybe finish with this: exactly the same claim applies to a fortiori reasoning as well. As I said before, a fortiori reasoning is not deduction. What do we do in an a fortiori argument? I mean the simple, classic a fortiori. There are also somewhat exceptional things that are called a fortiori too, but the classic a fortiori argument that appears in the Talmud is precisely analogy. And there are those who think it is deduction, and that is incorrect.

[Speaker C] It is exactly analogy, if you now understand this structure.

[Rabbi Michael Abraham] Because how does an a fortiori argument work? Let’s take the famous Mishnah with the a fortiori argument in chapter 2 of tractate Bava Kamma. What does the Mishnah say there? That if tooth and foot are exempt in the public domain, but horn is liable for half-damages in the public domain, and tooth and foot are liable for full damages in the injured party’s courtyard—okay? I want to infer that horn is liable for full damages in the injured party’s courtyard. Okay? That is how the Mishnah works, how the Mishnah stands. Leave aside for now whether “dayyo” applies; those are a bit more complicated matters. But the basic a fortiori argument—how does it work? It’s very simple. If tooth and foot, which in the public domain are exempt, in the injured party’s courtyard are liable for full damages, then horn, which in the public domain is liable for half-damages—that is more severe than tooth and foot—then in the injured party’s courtyard it also should not be less severe than tooth and foot; it must be liable for

[Speaker C] full damages.

[Rabbi Michael Abraham] Right? What did I actually do here? After all, what was given to me was three very particular facts. No general law was given to me. I was given three particular facts: tooth and foot are exempt in the public domain, tooth and foot are liable in the injured party’s courtyard, and horn in the public domain is liable for half-damages. Those are the three facts known to me. I knew nothing about who is more severe and who is lighter and none of that. What did I do? I said this: let’s look at the relation between horn and tooth-and-foot in the public domain and see that horn is more severe than tooth-and-foot, because after all horn is liable for half-damages and tooth-and-foot are exempt, right? So now I infer a general statement. I say: if so, then apparently horn—notice the induction here—I am now saying: if so, then horn, in everything, must be at least as severe as tooth-and-foot; everything that exists in tooth-and-foot will certainly exist in horn as well. Because horn is more severe than tooth-and-foot in every respect. How do you know that? All you know is that horn in the public domain is liable for half-damages and tooth-and-foot are exempt. You know two particular facts. How do you know that this is more severe than that in every matter? You are making a step of induction, right? Once you make that step, then it really is simple deduction. Once you say that horn is always more severe than tooth-and-foot, you move to the injured party’s courtyard. If in the injured party’s courtyard tooth-and-foot are liable for full damages, then obviously horn is also liable for full damages.

So apparently there is an appearance of deduction here, but that is not correct. Because how did you arrive at the premise—let’s return to Mill’s diagram, yes? How did you arrive at the major premise of your deduction? How did you arrive at that premise which says that horn is always more severe than tooth-and-foot, that general statement? By induction. Because that was not what was given to you. What was given to you was one particular fact: horn is liable for half-damages and tooth-and-foot are exempt in the public domain. By induction you arrived at some general conclusion that horn is more severe than tooth-and-foot in every respect. Once you formulated that general conclusion, of course everything looks like deduction, but the whole point is that you made an inductive move on the way to the general premise. Therefore the central point of the a fortiori argument is not the inference from the general statement to a particular conclusion, but the creation of the general statement itself. That is the central point of the a fortiori argument. What is new to us in the interpretive principle called a fortiori is that if I see that horn is liable for half-damages in the public domain and tooth-and-foot are exempt in the public domain—if I see two particular facts—I may infer from here some general relation that exists between horn and tooth-and-foot, namely that horn is more severe than tooth-and-foot in every respect. That is the point of the a fortiori argument. That is what was innovated in the principle of a fortiori: that if you see two particular laws that indicate the greater severity of one relative to the other, you can infer that one is more severe than the other in every matter, in every parameter. And then, consequently, infer additional laws. Okay? But the point that the a fortiori argument enables is not to infer the additional laws, but to infer the general conclusion from two particular facts. A fortiori is based on induction, not deduction.

The inductive stage is the a fortiori argument. No interpretive principle by which the Torah is expounded can be deduction. There are those who want to claim that a fortiori is deduction. Deduction was not given at Sinai. The thirteen interpretive principles are a law given to Moses at Sinai, usually—or according to most medieval authorities (Rishonim). Deduction was not given at Sinai. If it had not been given at Sinai, you would know it even without Sinai.

[Speaker C] I don’t need the principle of a fortiori in order to

[Rabbi Michael Abraham] use analytic processes in every sentence I study in the Talmudic text. I don’t need authorization from Mount Sinai for that, that I received the principle of a fortiori and therefore can use my reason. If I could not use my reason, I also would not understand what a fortiori means. Right. It is obvious that my using my reason is not because I got some authorization from Sinai. After all, it is obvious that that is how I function, and otherwise I cannot think.

[Speaker C] That is the correct order of thought.

[Rabbi Michael Abraham] So clearly, if the interpretive principles were given at Sinai, there is something in them beyond the trivial. There is something that says something substantive in those principles. It cannot be that the principles merely describe a logical thinking process. If they merely describe a logical thinking process, there would have been no need for Mount Sinai, and that is not the point. Therefore, if the principles are a law given to Moses at Sinai and were given at Sinai, they contain something—we’ll say in our language—they contain something synthetic. There cannot be any principle that is purely analytic. The principles contain something synthetic. There is something that the Torah, or the giving of the Torah, enables me to leap to beyond information I did not previously have, or to know additional things I did not know before. It teaches me how to engage in synthetic thought and not analytic thought. Okay? That is really the point.

Therefore, in the logic of the interpretive principles by which the Torah is expounded—and this is the last line—there must be a synthetic layer, because analytic thought I did not learn at Sinai. Every non-Jew knows it, and I knew it even before Mount Sinai. And I do not rely on the fact that Mount Sinai also told me to use it, because

[Speaker C] it’s impossible not to use it.

[Rabbi Michael Abraham] We said that even in order to understand that one may not use it, I use it. That has no meaning. Therefore, in the logic of the interpretive principles by which the Torah is expounded, it is clear that none of the principles—and with a fortiori it is best to start, because it appears to have the look of deduction—none of the principles by which the Torah is expounded can be deduction. For deduction, I would not have needed Mount Sinai. Therefore, in many respects, a fortiori belongs to the whole group of principles; all of them are basically some sort of analogical logic, not deductive logic.

The question is why, despite that, a fortiori still sounds somehow more reasonable to us. That is exactly the point: it is a kind of induction, a kind of topic that sounds reasonable to us. Right, not necessary, not mathematically compelling, but we use it all the time. Induction fits very well with the plain reasoning we use in day-to-day life. The other principles are somewhat subtler; you do not necessarily immediately see the application of everyday thinking in the other principles. And that is really the subject of the next sections.