Intuition in Halakha – Lesson 1
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Table of Contents
- Rationality, belief, and norms
- Rationality as inference rather than as a property of a claim
- Validity of an argument versus truth of the premises
- The source of premises: observation, general rules, and the problem of generalization
- Occam’s razor and the lack of any guarantee of truth
- Three modes of inference: deduction, induction, and analogy
- Blurring the line between induction and analogy and reducing things to two families of inference
- John Stuart Mill’s challenge to the power of deduction
- Skepticism about logic and the infinite regress of justifications
- Intuition as a fundamental tool for verification and validity
- Intuition, observation, and induction in science
- David Hume, Kant, empiricism, and rationalism
Summary
General overview
The text distinguishes between rationality in matters of belief, meaning the rationality of factual claims that are tested as true or false through correspondence to the state of affairs in the world, and rationality in halakhic or religious commitment, meaning the rationality of norms, which are assessed in terms of binding or not binding, fitting or unfitting, and not in terms of truth and falsehood. Rationality is defined here as dealing with inference, so there is no such thing as a “rational claim” but rather a “rational argument,” and the validity of moving from premises to a conclusion does not guarantee that the conclusion is true if the premises are false. From there arises the question of the source of the premises and the justification of generalizations and general laws, because observation provides only particular facts, while deduction already relies on general rules in advance. The proposed stopping point is intuition as the fundamental tool that grants validity both to the rules of logic and to trust in observation and to the justification of induction and analogy, while also presenting the historical problem of David Hume and Kant’s attempt to deal with it.
Rationality, belief, and norms
Belief is judged in terms of the rationality of factual claims, and factual statements are determined to be true or false according to the fit between their content and the state of affairs in the world. Halakhic or religious commitment is judged as the rationality of norms, and therefore it is measured in terms of binding or not binding, fitting or unfitting, and not in terms of truth and falsehood. The text states that when a person is “obligated” to do something, we are not talking about a fact but about a normative determination that is not directly compared to the facts of the world.
Rationality as inference rather than as a property of a claim
Rationality is defined as dealing with processes of inference, and therefore a claim in itself is not rational or irrational; rather, what can be rational is an argument that derives a conclusion from premises. A person’s rational action is defined as the optimal action for achieving his goals, whereas the goals themselves are not judged in terms of rationality but are chosen by the person. The text presents the goal as a premise from which ways of acting are derived, and therefore rationality begins only after the basic assumption has been placed on the table.
Validity of an argument versus truth of the premises
The text states that even a logically valid argument can lead to an unreasonable conclusion if the premises are not true, because validity concerns whether the conclusion follows from the premises, not whether the premises themselves are true. The premises are presented as claims, and therefore they are examined in the language of truth and falsehood rather than in the language of rationality, while rationality concerns the transition itself. The example is given: “All tables have wings, this tissue package is a table, therefore this tissue package has wings,” in order to show that an argument can be valid even when its premises and its conclusion are false, and it is stated that being rational and being correct are not the same thing.
The source of premises: observation, general rules, and the problem of generalization
Observation is presented as a toolbox that produces claims directly from contact with reality, like “I see that there is a wall here,” but it provides particular facts rather than general principles. The text states that generalizing from particular experience to a general law is not an act of observation but an act of inference, and that deduction requires general premises in advance and therefore cannot itself provide those general rules. The central question is formulated as a request for justification for our right to posit general laws that do not arise from observation and cannot be derived deductively.
Occam’s razor and the lack of any guarantee of truth
A proposal is raised involving “Occam’s razor” as choosing the simplest model, but the text rejects this as a binding argument and states that simplicity in itself does not guarantee truth, but at most convenience of use. The text emphasizes that even giving something a name like “intuition” solves nothing if no justification comes with it, and that there is still no guarantee of the correctness of a model or a rule.
Three modes of inference: deduction, induction, and analogy
The text presents a standard logical distinction between deduction as moving from the general to the particular, using examples like “All human beings are mortal, Socrates is a human being, therefore Socrates is mortal,” and induction as moving from the particular to the general by means of a non-necessary generalization that nevertheless serves science. Analogy is presented as inference at the same level of generality, from particular to particular or from general to general, and is illustrated through comparisons between different species. The text sharpens the point that not every move from particular to general is induction; induction requires that the particular be a member of the general class that contains it, whereas some such transitions are analogical because they move between different domains.
Blurring the line between induction and analogy and reducing things to two families of inference
The text argues that the distinction between induction and analogy is largely artificial, because induction can be viewed as a collection of analogies between particulars, and analogy can rely on a hidden generalization. From this there emerges a coarser distinction between deduction as necessary inference and non-deductive inferences, which include induction, analogy, and their whole family. The text adds that thinking that adds new information is analogical in essence, and that analogy can be broken down into a two-stage process of induction followed by deduction, formulated as “analogy equals induction plus deduction.”
John Stuart Mill’s challenge to the power of deduction
The text attributes to John Stuart Mill a challenge according to which deduction does not provide much epistemic value if the premises themselves are unjustified, because its necessity lies only in the conclusion’s following from the premises and not in the truth of the conclusion in itself. It states that the important question is not the validity of the argument but the truth of the claims, and that an argument is a tool for accumulating new claims rather than an end in itself. From here the text again emphasizes the need to clarify how we arrive at the general premises on which deduction depends.
Skepticism about logic and the infinite regress of justifications
The text describes the need to add the “inference scheme” itself as a premise in order to explain to an alien how the conclusion follows from the premises, and shows that the demand to justify the schemes can continue into second-order and third-order schemes in an infinite regress. It states that within logic itself there is no answer that terminates the chain through an internally logical move, and that there is a point where one stops at what seems self-evident. Trust in observation and in logical tools is presented as something that can in principle be challenged, but for the sake of the discussion observation is accepted as a reliable, even if not certain, tool.
Intuition as a fundamental tool for verification and validity
The text presents intuition as the supreme instrument by which a person validates, verifies, or rejects claims and schemes, and states that even trust in logical rules ultimately rests on intuition that “it’s obvious this is true.” It distinguishes between intuitions of varying degrees of strength and connects them to different levels of probability that intuition “quantifies” in an informal way. The text presents acceptance of intuition’s validity as a necessary stopping point in order to avoid an infinite regress, and formulates this as a conceptual threat: without intuition we are condemned to skepticism.
Intuition, observation, and induction in science
The text applies that same intuitive stopping point to trust in observation and to the justification for making generalizations, and argues that a final justification for induction cannot be supplied from within the tools themselves. It states that observation by itself is insufficient because it provides only particulars, and the move to a general law is a mental procedure that needs a non-deductive justification. Intuition is described as the basis for believing that “if I’ve seen enough donkeys with four legs, then apparently all donkeys have four legs,” while recognizing that the certainty is not absolute and that the probability assessment varies.
David Hume, Kant, empiricism, and rationalism
The text attributes to David Hume the casting of doubt on induction and the creation of a crisis for empiricism, because science relies on generalizations that cannot be justified by pure empirical means. It describes empiricism as a historical revolt against Aristotelian rationalism, which drew conclusions without experiment, but states that empiricism discovers that hidden within it are “mental leaps” that bring the problem back. It states that the whole philosophy of science sits on the question of the justification of induction and causality, and it presents Kant as one who came to solve the Humean problem through the framework of the Kantian problem of the synthetic a priori, as two equivalent presentations of the same point.
Full Transcript
[Rabbi Michael Abraham] I spoke about the issue of rationality in two contexts. One context was the context of belief. I said that there the discussion is about the rationality of factual claims. And the second context is halakhic or religious commitment, and there it’s rationality in the context of norms and not of factual claims. When I’m obligated to do something, that’s not a fact; it’s something normative. It’s measured in terms of binding-not binding, fitting-not fitting, and not in terms of truth or falsehood. We’re not comparing it to facts, to the state of affairs in the world, but to something else. I talked about that. Factual statements, on the other hand, are judged in terms of true or not true. When we determine that a factual statement is correct or true, that basically means there is a correspondence between what it says and the state of affairs in the world. In that case it’s a true statement, and if not then it’s a false statement. So in these two contexts I spoke about rationality, and I said that basically rationality, at least as it is commonly defined, deals with processes of inference. Meaning, there’s no such thing as a rational claim; there is such a thing as a rational argument. A claim is a claim; it says something. An argument derives one claim from other claims, a conclusion from premises. And when we talk about rationality, we’re talking about the question of how you moved from the premises to the conclusion. A person who acts rationally—let’s talk about people—a person who acts rationally is someone who acts in the optimal way to achieve his goals. But which goals are rational or irrational is not judged in terms of rationality. Everyone has his own goals. A person decides on his goals, but after he has already decided on them, there’s a way that will achieve them and a way that won’t, or that will achieve them better or less well. That’s where we can start talking about rationality. And again, it’s basically the same idea. The goal in this sense is some kind of premise, and from that premise I’m supposed to derive my ways of acting. So rationality begins only after I’ve put the premise on the table. Now once I sharpened this point, that rationality deals only with inference, with the transition from premises to conclusion, the question came up: okay, so if that’s the case, then everything depends on the premises. Because suppose we use a logical argument to move from premises to a conclusion, and that’s reasonable, that still doesn’t mean the conclusion is reasonable. Why not? Because there may be a problem with the premises. You can use logical tools very well to infer conclusions, but if the premises I start from are incorrect premises, then that argument won’t help me much. And therefore in the end, when I want to know something about the conclusion, it’s not enough to talk about the rationality of the path by which I got to that conclusion; I also need to talk about the premises from which I started out, on which I am applying the logical tools. And regarding the premises, as I said before, I don’t speak in the language of rational versus irrational, but in the language of truth and falsehood, because premises are claims and not arguments. Okay, so how do I arrive at my premises? That’s basically the question that came up at the end of last time, and because of it Judith isn’t here—she was really the one who raised it—and because of her we thought we’d talk a bit about intuition. That’s the series I want to start now, because I think the question of how we arrive at our premises, or how we can verify or reject premises, by what tools or in what category we operate, seems to me to force us into this concept of intuition. And why? In principle, we have two toolboxes we can work with in contexts of thought. One toolbox is the observational one, scientific if you like. Looking. I look, I see there’s a wall here. How do I know there’s a wall here? It’s not the result of an inference, I simply—well, you see. I have the ability to make contact with reality and through that to know what it is. So observation itself gives me certain claims; I can extract them from observation. That’s one tool. The second tool is inference, as I said before, but inference deals only with moving from one claim to another claim, or from one set of claims to another set of claims, and not with the claims themselves. So in fact inference won’t help me here. The logical toolbox doesn’t deal with the truth or falsehood of a claim, but with arguments. Okay? So what I’m left with is only observation. Now the question is whether observation is a sufficient tool. It’s pretty clear that it isn’t. That is, observation can at most yield particular facts. Say I see someone kick a ball and then the ball flies, so I say okay, what I saw was that when the ball was kicked, it flew. Can I infer from that that whenever you kick a ball it flies? No. What I saw was one specific event. Its extension or generalization into some broader law is not an act of observation. Okay? It’s an act of inference. Fine? In this case not necessarily deductive inference, but inference. So if that’s the case, observation usually—or maybe always, actually I think always—gives me particular facts, specific facts. Never general principles. Now usually inferences, and deductive logical inferences certainly, begin from general premises and not from particular premises. Take even a law of nature. We have a law of nature that every two bodies with mass attract one another. That’s a general law, and from it I can infer logically that if every two bodies with mass attract one another, then these two things too, which are two bodies with mass, also apparently exert force on each other. That’s a logical inference. Okay? But I made that logical inference because I moved from a general law to a particular case, to a particular case that exemplifies it. That’s deduction. Okay? So in order to use the deductive tool, I need to posit a general premise. But a general premise is never the result of observation. So if it isn’t the result of observation, then by what right do I posit it, or what justification do I have for positing it? That’s really the question. It doesn’t come from observation, and logic deals only with moving on from there, but it won’t give me the general law itself. So how do I obtain the general law itself? Well.
[Speaker B] Occam’s razor. What? Occam’s razor. What about it? That you look for the simplest model that will explain…
[Rabbi Michael Abraham] Okay, but Occam’s razor is not an argument; it’s an explanation. It’s a description. A choice, yes? I choose the simpler option. But do you have some argument for why the simpler one is also the correct one? Simplicity, on its face at least—unless you add all sorts of other things—simplicity in itself only says it’s convenient to work with; it doesn’t compel the conclusion that it’s true. What even counts as simple? That’s another question. We once talked about Occam’s razor; maybe I’ll get to that later on too.
[Speaker D] But no other model would guarantee correctness in that case either.
[Rabbi Michael Abraham] What do you mean?
[Speaker D] Even if you call it intuition, anything else also doesn’t guarantee correctness. Right. Right. So you can explain it in all sorts of ways. You call it intuition, I call it a pattern… no, no.
[Rabbi Michael Abraham] Calling it intuition doesn’t help at all. Names don’t provide an explanation. I mentioned intuition in advance, but I’ll get to it after I build this a bit more systematically. I’m not yet at the answer, I’m still at the question. Okay? Right. So observation really can’t give me this. Inference—at least deductive logical inference—also doesn’t give me general laws. So what does?
[Speaker C] Wait, even trust in observation is the question. Yes.
[Rabbi Michael Abraham] Of course, you can go backward even to trust in observation. You can also go backward, by the way, to trust in logical tools. There too you can ask everything: who says that if every X is Y and A is X, then A is also Y? It sounds to us like a necessary inference, but okay, if someone puts a question mark even on that schema, you can always raise question marks, you can always go all the way. I stop at the point where it is self-evident. Fine? Observation is not self-evident, but it is accepted. Fine? Good enough not to challenge it. So for the purpose of the discussion, let’s accept observation for now as something that is a reliable tool. I’m careful not to say certain, but reliable. Okay? So in the framework—I think I once talked about this, I mean, I talked about a large part of these things in the year when I dealt with… logic. Non-deductive logic, that was already a few years ago, I don’t remember. So I dealt a bit with these things, and some of what I’m saying now will be a repetition of what I said there. I no longer remember who was there and who wasn’t, so apologies to anyone who was and remembers—I ask forgiveness in advance. Okay, so first of all, I’ll stay for a moment at the level of logical description, even before the justifications—the beatings come later. At the descriptive level, we distinguish in logic, it is customary to distinguish in logic, three modes of inference. One mode is deduction, movement from the general to the particular. I gave the example before: all human beings are mortal, Socrates is a human being, therefore Socrates is mortal. So if all human beings are mortal, then Socrates in particular is also mortal; that’s moving from the general to the particular, that’s called deduction. There is movement from the particular to the general: if Socrates is a mortal human being, then apparently all human beings are mortal. The same generalization, right? That generalization is not necessary. There are some examples that don’t represent the whole, such that if I generalize from them I’ll make a mistake. Okay, but it’s still true that we use this tool. Meaning, generalization serves us, with the proper caution, but it serves us; it’s not a shot in the dark, it’s not something we have no trust in whatsoever. Okay, so that’s called induction. Moving from the particular to the general, or from several particular examples to the general. Science works by induction, as I said before. Observations give me particular information, private information about a particular event, and when I generalize and create from it a general law, what I am actually doing is induction. I’m saying that the examples I saw represent the general law. Fine? So that’s induction, movement from the particular to the general, the opposite direction from deduction. And then there is analogy, the third tool. Analogy is staying at the same level. Not moving from particular to general or from general to particular, but either from particular to particular or from general to general. Okay? But it’s at the same level, not changing the level of generality. That’s called analogy. For example, all donkeys are mortal, therefore all horses are also mortal. Okay, that’s an analogy. In this case it’s an analogy from general to general. But these are two distinct generalities, and all I’m doing is comparing them. Analogy is comparison, okay? Induction is generalization, analogy is comparison, deduction—you might call it specification, the term is less common but maybe you could call it specification. Or, I don’t know, if this donkey is such-and-such and is mortal, then that other donkey is also mortal. That’s an analogy from particular to particular. What about induction—if this donkey is mortal, therefore all horses are mortal? What about that inference? What kind of inference is that?
[Speaker D] That’s analogy because horses aren’t donkeys. Different height or ears, you don’t need to compare.
[Rabbi Michael Abraham] And it’s also not induction. It’s from the particular to the general—why? It’s both analogy and generalization.
[Speaker B] Why? From one donkey to the class of all donkeys.
[Rabbi Michael Abraham] Why do I need the generalization to all donkeys? I want to move directly from the individual donkey to horses.
[Speaker B] There are stages here. There’s a stage in moving from one to many, and a stage in moving from one species to another. Those are two things.
[Rabbi Michael Abraham] Yes, but not necessarily through the class of all donkeys.
[Speaker B] You could first go from one donkey to one individual horse.
[Rabbi Michael Abraham] It seems to me that the essential part—you can of course argue about definitions—the essential part of this inference is analogy and not induction. What? From donkey to horse. Now the fact that I do it for each horse separately, fine, but basically it’s still analogy. If I were doing it from the donkey to the class of all donkeys, that would be induction. And why? Because for induction it’s not enough to say that it’s movement from particular to general; rather, it has to be from a particular that is included in the general class to the general class that contains it. That’s called induction. In other words—just a second—I see the particular as something that represents the group to which it belongs. That’s the idea of induction.
[Speaker B] In other words, it doesn’t matter which individual we chose; this property of mortality is shared by the entire class. Yes, that’s what’s hidden here, so there’s also both analogy and generalization hidden in it.
[Rabbi Michael Abraham] No, actually not.
[Speaker B] In my opinion, you’re copying the property of being mortal from donkey to horse, and also claiming that it…
[Rabbi Michael Abraham] I’m copying it to the class of all horses. Directly to the class of all horses. What?
[Speaker B] So then it doesn’t matter which horse you chose. So therefore it’s induction.
[Rabbi Michael Abraham] That’s what I said. You can define it that way, but the essential part of this inference is not the induction, it’s the analogy. Fine? Because I’m basically making a comparison between donkey and horse. True, I’m doing it with respect to each of the horses, but that doesn’t matter. What I did in this example was simply to show that the move from the particular to the general is not just any move from particular to general, but from a particular that is one of the members of a class to the general class that contains it. Not every move from particular to general is induction; some of those moves are analogy. Fine? Because really I didn’t move from a particular. What I wanted to show with this example was that the move from the particular to the general is not just any move from particular to general, but from a particular that is one of the members of a class to the general group that contains it. Not every move from particular to general is induction. Some of those moves are analogy. Fine? Because really I didn’t move from particular to general, but from the world of donkeys to the world of horses. It doesn’t matter right now how many donkeys and how many horses. Did you want to comment, Arik?
[Speaker F] It seems to me a little like you’re forcing it into some edge case. Like, intentionally instead of saying that—because if I make an analogy from donkeys to all horses, then it seems kind of obvious that I would include all donkeys too. So I can simply say that I’m learning from the particular donkey to the general class of donkeys and horses.
[Rabbi Michael Abraham] Fine, but when I make the inference I want to learn about horses; I don’t need the generalization to donkeys in order to move to horses. I can make another inference to donkeys too, you’re right, but who cares? At the moment I’m dealing with the inference from the donkey to the horses. For that inference I don’t need to go through the class of all donkeys.
[Speaker F] Without going through the class of all donkeys, the moment I make one induction to the class of all donkeys…
[Rabbi Michael Abraham] You do that—you’ll make induction to all of them, and I’ll make an analogy to the class of all horses. That’s a different inference. You can say that this is a good inference and that is also a good inference, and that is a different inference. This inference that I described. What?
[Speaker F] It’s not plausible that someone would accept this inference and not accept the other one.
[Rabbi Michael Abraham] Okay, maybe. But still, in its essence this is analogy and in its essence that is induction. Fine? Now true, I think your intuitions do see some common basis to induction and analogy, and I think they’re definitely right. Because really, when you look a little more closely at how induction works—how do I know that what’s true of one donkey is true of the class of all donkeys? Not every thing. The donkey’s height is not true of all donkeys. The fact that it has four legs probably is true of all donkeys. There are properties with respect to which I make an induction, and properties with respect to which I don’t. So what is that based on? One could come and say it’s based on an analogy to each of the other donkeys separately. Meaning donkey A is similar to donkey B and also to C and to D and to E. That collection of analogies ultimately creates an induction. Okay? On the other hand, of course, you can look at it the other way around. When I move from donkey A to donkey B, why do I really think they’re similar? They’re both donkeys. Fine? Meaning in the background there’s actually some generalization about all donkeys, because after all there’s nothing special about donkey B in particular except that it’s simply a donkey. Okay? So in fact the analogy hides behind it a latent induction. Fine? And therefore the distinction between induction and analogy is to a large extent artificial. Fine? So if that’s the case, I’m now going to make a rougher distinction—not three modes of inference as logic usually does, but two. There is deduction, and there are non-deductive inferences: analogy, induction, and the whole family. Fine? For me that’s the important distinction. The difference between analogy and induction isn’t really necessary—and not necessary.
[Speaker C] The syllogism, yes.
[Speaker F] Is deduction supposed to include all logically necessary things?
[Rabbi Michael Abraham] Yes. I call all of that movement from general to particular—you’re right. For example, implication is also deduction. Is that a syllogism? If A then B. A? Yes. Conclusion: B. Yes. So that’s not movement from general to particular. Exactly. So why is it deduction? Fine, we call it deduction. Again, I’m not getting into all kinds of nuances right now—there are lots of nuances—but broadly speaking, necessary inferences. Fine? You could say that behind every deduction there sits a move from general to particular, but again, that’s hairsplitting; it doesn’t matter. When you say if X then Y, you’re basically saying that for every X, it must also be Y. Fine. Excellent. Okay. Right. So these are basically the two modes of inference. So now if I go back to the question with which I opened—how do I arrive at general laws? So I said deduction can’t give me that. Inference in the strict sense, because necessary deductive inference doesn’t give me that, because its conclusion is a particular conclusion from a generality. And now I’m asking: how do I know the generality from which I started? How did I get to it? That is basically Mill’s challenge to deduction. John Stuart Mill has a well-known challenge to deductive inferences. He basically says: what good is deductive inference? We think deductive inference is a very powerful tool because it gives us a necessary conclusion. But of course that’s not true. The conclusion of deductive inference is not necessary. The following of the conclusion from the premises is necessary. The conclusion in itself can be incorrect. There are valid deductive inferences whose premises are all false and whose conclusion is also false. Right? All tables have wings, this tissue package is a table, therefore this tissue package has wings. That’s a valid inference. Right? A valid argument. Both its premises are false, and its conclusion is also false. That means the fact that you used a valid inference—and here I return to the rationality with which I began—the fact that you operate rationally does not mean that you are right. And of course the reverse is also true: the fact that you’re paranoid doesn’t mean they’re not after you. The fact that you’re irrational doesn’t mean you’re not right. Okay, rational and correct are not the same thing. Fine? So therefore in the end, what matters to me is really the truth of the claims, not the validity of the argument. The argument is a tool to learn more and more claims. I want to know whether the claims are true or not; why should I care right now whether the argument is valid or invalid? It’s a tool, it’s not something that interests me in itself. Fine, I want to know claims about the world, to accumulate information, to understand, to know things. Fine? So how do I know that? So we said: logical inference, rationality, doesn’t give me this, because logical inference takes me from a general premise to a particular conclusion. But even if I say the inference is valid, I worked rationally, and so on, all that means is how I moved from the premise to the conclusion. How do I know that the premise is true? And that is the most basic and important question, and the question is from where I draw the premise. And without that I also can’t know that the conclusion is true, of course. Right? Even if the inference is valid. A valid inference takes true premises and derives true conclusions from them, but if the premises aren’t true you can’t know what’s with the conclusion. Fine? By the way, a valid inference can also derive a true conclusion from false premises—that can happen too. But yes, anything can happen; you just have no certainty that it does. The validity of the inference is not enough. You also need the premises to be true. If the premises are true and the inference is valid, then the conclusion is necessarily true. That is really the value of inferences. Okay.
[Speaker C] So in the terminology people use—even with “rational”—don’t they usually also talk about the premises?
[Rabbi Michael Abraham] Right. Philosophers don’t.
[Speaker C] And if not, then on the street they do.
[Rabbi Michael Abraham] On the street, yes, and they’re basically conflating rational with true, in my opinion. But they’re also conflating rational with
[Speaker F] having reasonable judgment, because they
[Rabbi Michael Abraham] think that reasonable judgment is…
[Speaker C] You can say that his premises—maybe he’s mistaken—but he’s still rational. There’s a reasonable premise even if I think it isn’t true. I’d still say it’s reasonable to think that way, like “these and those are both the words of the living God” from the Rabbi. I’d still say he’s rational; he’s just rational and mistaken. He assumes things that I understand how one might assume; they just don’t seem correct to me, and I would still call him a rational person, just one who is mistaken.
[Rabbi Michael Abraham] Okay, I’m willing to accept the correction. Meaning, there are several levels of reference here, but this is all everyday language, so that’s a question for linguists, not logicians. Meaning…
[Speaker C] Philosophers use it too.
[Rabbi Michael Abraham] To their sorrow, to their sorrow. But usually the more careful ones define these sensitive concepts before using them.
[Speaker C] I mean they use it as evidence.
[Rabbi Michael Abraham] Ah, as evidence that this is the common wisdom, that that’s how it is. Okay. Here it’s only terminology, so it’s not important. Okay, so basically the question is how we arrive at the general claim from which the argument derives the conclusion. So Mill essentially claimed that since I didn’t arrive at the premise by deductive means, what good does the valid argument do me, taking that premise and deriving a necessary conclusion from it? If the premise is shaky—shaky is the word, yes—if the conclusion rests on the premise and I did not arrive at the premise in a sufficiently convincing way, then how does that help? So how do we arrive at premises after all? We’re still at the logical description, again, before the beatings. The beatings come later. At the descriptive level, we use analogies and inductions. Usually—let’s call it inductions. Fine? For example, in science, when we arrive at a law of nature, we observe several cases, and once we’ve reached the conclusion that this is a general phenomenon—and how exactly we reach that conclusion is not important right now—we say, okay, then there is a general law of nature that says every two bodies with mass attract one another. Fine? That’s the general law. So how did I arrive at it? Not by a deductive argument, but by induction, because observation gave me the particular cases, induction created the general law from them, and now if I want to infer a conclusion about another case, there I apply deduction. Once I have a general law, I can particularize it to a given case and infer a conclusion from it. And then notice what I actually did here. In the end what I really did here was analogy. Because I took the cases I observed and derived from them a conclusion about another case I did not observe, and I said that it too ought to happen there. How did I do that? In a two-stage process. The first stage: from the cases I observed, I made an induction and created a general law. From the general law I made a specification to the case that interests me. So in fact the analogy here was broken down into two stages. The first stage is the stage that made an induction from the cases—starting, of course, from observation; before that is before logic. Logic is the two stages: generalization, creating a general law, and specification—that is, descending back down to some other particular case. So in fact it comes out that the three modes of inference… that logicians talk about are not three but one. There are only analogies in the world. It’s only that we build analogies in a two-stage process: first we do induction and then deduction. Take any analogy in the world—it’s built that way. This donkey is mortal, so donkey B is also mortal. I said that behind this there is basically sitting the fact that…
[Speaker G] There are only two: induction and deduction. And then analogy is induction plus deduction.
[Rabbi Michael Abraham] You can also subtract.
[Speaker G] Sometimes you do only induction—you formulate a law.
[Rabbi Michael Abraham] You can also subtract, but these modes—not only combine them. You’re referring to combination. You can also subtract. In the end, you can choose two. I think any two can lay out the rest. So what we’re basically saying is that thinking that accumulates information, yes? Our thinking that adds new information for us, unlike deductions, is generally—not generally, always—analogy. It’s just that along the way, when we make an analogy, in general we make a hidden induction and then a specification. When I move from this donkey, which is mortal, to that other donkey, which is mortal, implicitly I really assumed something about all donkeys, and then I specified it to this particular donkey. Okay? So every analogy can really be broken down this way. Once I presented this to two soldiers—I picked up hitchhikers, I was driving to… suddenly I remember. In the first year that I taught in Yeruham, before we moved house, we were still living in Bnei Brak, so I used to travel in Elul, the month of Elul—we moved in Cheshvan—so during Elul I would travel, once or twice a week, a bit, and drive to Yeruham. And I gave lectures there. It was in the car, and on the way this light bulb suddenly went on for me, the idea I’m describing to you now. The relationship between the three modes of inference—that really there is only one or two. It’s an equation: analogy equals induction plus deduction. It’s not three modes of inference. So I presented it there to two soldiers. I wore them out, poor guys. I gave them a ride on the way and enthusiastically told them about induction and analogy and deduction and all that. I didn’t notice, because they were sitting in the back, I don’t know whether they were asleep or not, but I remembered them now. May these words be for the elevation of their souls.
[Speaker D] And to this day they still tell the story about the idiot
[Rabbi Michael Abraham] who spoke all kinds of foreign words. I got there, I got there. It’s automatic pilot, you know, no need to look at the road. It’s… anyway, so…
[Speaker H] What? Near Eilat?
[Rabbi Michael Abraham] That’s not the point. For my purposes there’s no analogy between Yeruham and Eilat. Though my father’s aunt, a heavily Hungarian-American woman, used to say: “The only thing which is good in Yeruham, that it is near Eilat,” in a very pronounced Hungarian accent. Anyway…
[Speaker B] It’s near Eilat the way
[Rabbi Michael Abraham] Tel Aviv is near Eilat. By American measurements it’s near Eilat. On an American scale it’s a suburb of Eilat.
[Speaker H] Even if the two soldiers wanted to get to Yeruham.
[Rabbi Michael Abraham] No, no, they got out on the way, and apparently just in time. They asked to get out in the middle, or maybe they got sick of me and went back to hitchhiking to Yeruham. That could also be.
[Speaker D] There’s a military base
[Speaker H] on the way.
[Rabbi Michael Abraham] Okay, anyway… So on the theoretical level, the way we arrive at our premises—say in my case, the premises are the laws of nature, the general laws about reality. Fine, for the sake of simplicity let’s call them laws of nature. The way to arrive at laws of nature is actually by non-deductive means. And what Hume… so that’s a description. Because I haven’t solved the question I asked by means of that description. Descriptions solve nothing. Sometimes they clarify the picture, but they don’t solve a problem. When I ask what the justification is for making a generalization—and that is induction—so what? So what is the justification for making inductions? The fact that I gave it a name is not a reason; it’s not a justification.
[Speaker C] And breaking them down into more stages just confuses the questioner.
[Rabbi Michael Abraham] Yes, yes, that’s a well-known demagogic technique. My son always says: “Oh, that’s selecting, that’s sorting, that’s moving.” On the Sabbath, is it permitted or forbidden? “No, it’s moving.” Obviously. There’s an issue of moving involved. You say some kind of action-term like that and immediately: “Ah, of course, fine, if that’s the case then it’s forbidden.” Once you’ve said that, you’re exempt from giving any further justification. Anyway, basically what I’ve done until now is describe this process of arriving at general information about the world. But I haven’t justified it—that is, I haven’t explained what the justification for this method is. Logicians maybe… deduction is obvious to everyone, meaning it doesn’t need justification. It’s self-evident. Of course, you can always open your eyes and say, “What do you mean? Who says?” but that’s a kind of skepticism that’s not worth dealing with; it’s self-evident. The question, though—analogy and induction—that’s a skepticism with a lot more substance. Meaning, it really isn’t obvious why we’re allowed to use analogies and inductions. Okay? So that’s really the question. It’s a translation of the question I opened with. Yes, and we have to add it to the discussion of rationality from last time in order to present a full picture. Because rationality deals with inference—if rationality deals with inference, with moving from premises to conclusions—then the premises themselves have to be handled with other tools, not with logical tools. So that’s with empirical tools. But that doesn’t work either, because empiricism gives me only particular facts. So there’s another addition here that really belongs to the logical side, because it’s an intellectual addition, not an observational one. When I move from the particular cases I saw to a general law, that’s an intellectual procedure, not an observational procedure. Okay? In thought, I make that transition. But that thought needs justification, because it isn’t self-evident, it isn’t certain, it isn’t necessary, it isn’t deduction. Okay? But at least we’ve mapped the problem, or defined it more sharply.
[Rabbi Michael Abraham] So how can one justify such a thing? I’m going to do it in two parallel moves, and in the end I think they amount to the same thing. One of them is also somewhat semantic; I’m not even sure it’s really a justification. Why don’t we ask this about logical inference? Usually, most of us don’t. Because deductive logical inference is certainly correct. And there we don’t raise skeptical doubts. Why not? I once saw a logic book by someone named Evron Polkov. Logic for Thinkers and Computers. He was at Ben-Gurion University at the time; it’s an ancient book by now, I don’t know what’s with him today. So early in the book he says this: when I infer from, say, “All human beings are mortal, Socrates is a human being, therefore Socrates is mortal”—suppose some alien comes along and wants to know whether Socrates is mortal. I tell him: look, all human beings are mortal, Socrates is a human being, and therefore Socrates is mortal. He opens his eyes wide at me—but not about the premises. The premises he accepts for the sake of discussion. The conclusion—he doesn’t see how it comes out of them. He agrees: yes, it sounds like all human beings are mortal; if you say so, you probably know. And Socrates is a human being—fine, you probably know him. But who told you he’s mortal? asks the alien. What do you mean? It’s a necessary logical inference. Meaning, there are two propositions, and their combination necessarily yields the conclusion. How can you argue with the conclusion if you accept the premises? Notice: if you argue with the premises, fine. But how can you argue with a logical inference? That’s really the question.
[Rabbi Michael Abraham] So he says that in order to answer him, what would I really have to do? I’d have to add another premise to the argument. Premise one: all human beings are mortal. Premise two: Socrates is a human being. And premise three: if every X is Y, and A is X, then A is Y. The argument form itself is one of the premises that I assume. Now it’s valid. Meaning, after I’ve assumed the two premises and the schema, now I can say the conclusion follows necessarily. Fine. Now alien number two arrives—an alien from another planet. And he says: wait, no, no, I don’t accept that either.
[Speaker B] A kind of trilemma.
[Rabbi Michael Abraham] Yes, exactly, I don’t accept the trilemma either. What do you mean? True, I accepted the three premises, but how exactly did you derive Socrates from that? So of course you then have to add a second-order schema. Right? A schema that says that if—exactly—and if the schema, etc., basically a schema of schemas. Okay? This is really an equation, a functional and not a function. Fine? Meaning, it’s something second-order.
[Speaker B] Gödel’s treatment there.
[Rabbi Michael Abraham] Yes, Gödel’s treatment is a kind of, yes, second-order treatment.
[Speaker B] Back to understanding—an infinite regress.
[Rabbi Michael Abraham] In any case, of course you can answer him with a third-order schema, but there’s no point. There’s no point. So what is the answer after all? The logicians don’t have an answer. A little innocent child stood up and asked “why,” and all the logicians don’t know how to answer her. Because in the field of logic there really is no answer. There is no answer.
[Speaker B] Wait, logic is a profession within mathematics, meaning like geometry—half an imaginary world—and you simply posit primitive concepts, sets, and build a framework. In a mathematics department, let’s say A, B, C, and there you have it.
[Rabbi Michael Abraham] Most philosopher-mathematicians claim—
[Speaker B] No, no, but the “if… then…” is—
[Rabbi Michael Abraham] Universal, so it’s already—
[Speaker B] You’re suddenly using it in your natural language.
[Rabbi Michael Abraham] No, but the “if… then…” is universal, the “if…”
[Speaker G] “then…” is—
[Rabbi Michael Abraham] universal, it’s a branch of—
[Speaker B] mathematics. It’s like geometry, like a differential equation. Yes, yes—no—logic—
[Rabbi Michael Abraham] is a branch of mathematics, it’s a branch of mathematics, it’s only a branch of mathematics. Since Bertrand Russell, at least, it’s been customary to arrange mathematics as products of logic, meaning mathematics—
[Speaker I] is a branch of logic, and logic is not a branch of—
[Rabbi Michael Abraham] mathematics. Again: mathematics being a branch of logic—you have to show that that’s so. No, what do you mean, you systematically derive mathematics from axiomatic set theory—Russell and so on—what they’re really doing is only logic, nothing besides that. You derive all of mathematics from logic. That’s the claim, until Gödel came and showed they hadn’t succeeded in doing it. Not that they didn’t succeed—no, they got very far, only along the way they skipped over a few problems, and Gödel caught them red-handed, and there were major crises there.
[Speaker C] And even the sentence, those two statements, “all human beings are mortal,” so really the interpretation, the result, is not some extra thing—that’s what you said in the sentence. Meaning, that’s the meaning of the sentence. Okay, that’s what it says. Now if you don’t know what—
[Rabbi Michael Abraham] “all” means, you don’t know—
[Speaker C] what human beings are, whatever—then
[Rabbi Michael Abraham] the alien comes and says, “I don’t—”
[Speaker C] “know.” Fine, he doesn’t know what “all” means, so what difference does the alien make? Fine, fine, what will you answer him? Fine, you don’t speak the language, and that’s what I said.
[Rabbi Michael Abraham] Fine, fine, but still, suppose you want to teach him. What do you do?
[Speaker C] Then that’s what it means. I’ll tell him: that’s what the language means, accept it.
[Rabbi Michael Abraham] That’s exactly what I was about to say—it’s not language. Meaning, I think reducing this to language is problematic, because language can be translated. There’s a claim here, and it’s a claim about reality, not about language.
[Speaker C] But that’s what I said in the sentence. Instead of saying now—
[Rabbi Michael Abraham] You said it in a sentence, but the sentence makes claims about reality.
[Speaker C] Right, so I made a claim about reality in that sentence—that’s how I said it. I could say it that way, or I could start listing all the claims one by one.
[Rabbi Michael Abraham] I don’t follow. When you say this in the context of “that’s the convention of the language,” I think that’s imprecise. Rather, it’s the meaning of the utterance; and the meaning is not the language—the meaning is reality. Language is grammatical rules, how you construct words and sentences. I’m talking about the signified, not the signifier. Meaning, I’m talking about the content that language expresses. And that’s why I say this is very sensitive, what you just said, because analytic philosophers say exactly that, and I disagree with them so strongly that I’m being a bit insistent here. But never mind, it’s really just a nuance; I don’t want to—it’s not important here, only—
[Speaker C] It’s like asking why contradiction—why can’t I explain why contradiction doesn’t happen? Because you simply said something meaningless.
[Rabbi Michael Abraham] Yes, completely. But again, I’m saying that’s exactly the point. In the case of something meaningless, you can say it’s just language, because there is no signified. If it’s something meaningless, that means there’s nothing outside it that it signifies. You could maybe say a claim about the world—that there’s nothing in the world corresponding to that sentence—and then it’s still a claim about the world. Fine, never mind that… In any case, the point is that—
[Speaker B] I was trying to argue that logic is a mathematical framework, and the mistake, or the problematic thing, is taking the sentences of logic and using them—
[Rabbi Michael Abraham] No, no. So that’s where I hadn’t yet begun to disagree, and now I’ll continue to disagree, because the problem is not in applying logic to reality. I’m talking now about logic itself. I’m talking about the inference, not the premises and not the conclusion. The transition from premises to conclusion. The transition from premises to conclusion is a transition that is pure logic, even if the premises are premises about reality and the conclusion is a conclusion about reality. Okay? And someone who doesn’t agree with the transition—he doesn’t disagree with the premises—he is arguing with you on the logical plane, not on the plane of application to reality. And the question is: how can that be? How can a person argue with logic? Fact is, here’s this alien—he doesn’t agree, he doesn’t accept it.
[Rabbi Michael Abraham] Now of course we have to distinguish: what does it mean that he “doesn’t accept it”? If he really doesn’t think that Socrates is mortal, then there’s nothing to do with him except institutionalize him in a closed facility.
[Speaker D] He could claim that saying “all human beings are mortal” is a claim in mathematical space and not in real space, because “all human beings are mortal” means all the human beings we’ve encountered until today were mortal.
[Rabbi Michael Abraham] No, that’s what you can say empirically. But the meaning of the claim can be about all human beings. You can only ask me: how do you know? Fine, I didn’t say how I know. I’m saying: if that’s the premise, then that’s a—
[Speaker D] premise—
[Rabbi Michael Abraham] about human beings in the world.
[Speaker D] It’s not a claim about reality—it is a claim about reality.
[Rabbi Michael Abraham] It is a claim about reality. I may just have no way of knowing it; you’re claiming something else. I often make claims about reality without having a clear way to know them, but they’re still claims about reality. They will be judged against reality. For example, if you show me a human being who doesn’t die, then you’ve refuted my claim. Meaning, I’m making claims about reality. Yes, right, Popperian, right. So if he really doesn’t see how Socrates being mortal follows from here, then that’s in the department of… logic so—Ron Polkov following Lewis Carroll and so on—nonsense, yes, that’s what they translate it into Hebrew as: illogic. But if the person really does know what I’m talking about, and he’s asking a skeptical question—he says: who told you that the rules of logic are correct?—that’s another question. If a person’s brain is built differently from mine, or defective if you want to be more direct, fine? then there’s nothing I can do with him except send him to a brain surgeon. But if not—if his brain is built exactly like mine and he means to raise a skeptical claim, meaning to say “who says?” I also understand, and I’m also inclined to think that Socrates is mortal, and I understand that it follows from the two premises—I’m just casting doubt even on myself. Who told us? Maybe it isn’t true? Maybe we’re just built that way, but really it doesn’t actually follow from them? That’s a kind of skeptical claim. Here again there’s no good way to answer it, certainly not in the realm of logic. But here I’ll pull out intuition. Up to this point I’ll basically tell him: look, the highest instrument I have with which I can validate things, affirm or reject things, is my intuition. Even the logical rules—ultimately my conviction in the logical rules stems from the fact that my intuition tells me it’s obvious that they’re true.
[Speaker E] But everyone has a different intuition.
[Rabbi Michael Abraham] It depends. Regarding logical rules, I don’t think so. Most people I know—logical rules are—and even if so—
[Speaker E] that’s—
[Speaker D] his, and mine is—so—
[Rabbi Michael Abraham] I’m saying, the point is—
[Speaker D] that intuition—
[Rabbi Michael Abraham] is actually something we often tend to belittle, as though compared to logic. But in fact, when you look at it this way, intuition is more fundamental than logic. Even our trust in logic is grounded in our trust in intuition. And therefore we have no better instrument than intuition. Now clearly there are intuitions at different levels. I have an intuition that all tables have four legs, but even I myself understand that it could be otherwise—there are tables with three legs too, whatever, just an example of something not necessary. I have that kind of intuition. I also have the intuition that if every X is Y and A is X, then A is Y. I have that intuition too, and there I’m convinced.
[Speaker D] Why do you—why do you need intuition at all for something that is not a claim about reality but a claim in logic? Why is it that if A equals B and B equals C, then A equals C—isn’t that included in the very concept of equality?
[Rabbi Michael Abraham] So that goes back to Ido’s earlier comment. You’re reducing it to language, because mathematics is a language. But now I’m using it as a schema for speaking about reality. Now when I make claims about Socrates and human beings, I’m making claims about reality. I’m using a logical schema, but I’m making claims about reality. Now if that claim about reality is true, it means Socrates will die. So I’m committed to something that has to stand an empirical test. Fine? So in the end, true, the schema is a logical schema, but I insist on talking specifically about what it says in terms of reality, not about the logical structure in and of itself. The logical structure by itself can just be intellectual amusement. It says nothing, and if you don’t understand it, good health to you—so what? what difference does it make? There’s no real content here; it’s a schema, I’m amusing myself with something and you don’t know this game—fine, so what? But I’m saying no: logic does have some significance. Even though it is seemingly detached from reality, still it has significance. If you take two sentences that are true about reality and apply to them a schema that is valid in logical language, the result will be a claim that is also true about reality. So there’s something in logic that also touches reality. And that’s what I’m talking about. Okay? Not the schema itself, but what it says for me about the world, about reality—and it does say something about the world. It says that if these two claims are true, then necessarily Socrates will die.
[Speaker D] It says that whenever you have a claim in which something equals something, when you have attributes that you can link to such-and-such an attribute and such-and-such an attribute, then you can apply a certain pattern. Right. Fine. So that pattern is a pattern that has nothing to do with reality, and you can take patterns that don’t—
[Rabbi Michael Abraham] Now I ask: when I make this inference about Socrates the person, am I wrong or not?
[Speaker D] Meaning, I assume they’re true.
[Rabbi Michael Abraham] I’m talking about true premises.
[Speaker D] If it fits, if it falls into the pattern.
[Rabbi Michael Abraham] Why? But it’s a claim—I am ultimately claiming that Socrates will die. That’s a claim about reality. So what if it fits some logical schema? Why is reality bound by that?
[Speaker F] Because really in induction, you could say that just as you described earlier that analogy and induction are one thing, so really deduction too is part of induction. Once I made an induction, then I also implicitly assumed this. When I said I made an induction from several human beings, or from one human being, to all human beings, I really also made a deduction about all human beings. I said indirectly: Moses and Socrates and Plato are all mortal.
[Rabbi Michael Abraham] No, that’s the explanation we discussed earlier—that this is basically what it means. Okay. But that’s an explanation on the logical plane. Now someone comes along, the alien, and says to you: what? But who told you? Who told you that this is so?
[Speaker F] Meaning, I’m saying—that’s what I meant to say—how do I know they’re—
[Rabbi Michael Abraham] What you meant to say—that takes us back to language. “What you meant to say” is about language. I’m talking about reality. Who told you Socrates will die? Not what you meant to say.
[Speaker J] Nobody said he’ll actually die.
[Rabbi Michael Abraham] Of course they did! Of course they did! I can know. If the premises are true, I know that Socrates will die. Assuming the premises are true, assuming the premises are true—Elijah came and revealed the premises to me. I’m telling you that Socrates will die, unequivocally. How do I know that? It’s just a logical schema, isn’t it? Because the logical schema says that for any two true claims you place at the start, if you apply a logical schema to them, the result must also be true. If the premises are true, then the result must also be true—even about reality. That’s the only interesting thing about logic. If logic said nothing about reality, nobody would bother with it.
[Speaker J] But there’s some transition here that you’re skipping over, and that’s where you slip intuition in. When you move from logic to reality, it may be that in logic it’s necessary that he die, but in reality there could be a reality in which he doesn’t die there. Now I can—it’s not just language, because in mathematics, I can describe reality one way, and in a completely different way too, and both will fit perfectly with most of the cases I know in reality, and then one case will pop up that doesn’t fit. And that gap—where you transfer it from logic to reality—that’s where you insert intuition. There has to be some—so that bridge exists only because that’s how you’re built in reality, not because it’s necessary that logic be connected.
[Rabbi Michael Abraham] My intuition tells me that the logical schema can be applied to factual claims.
[Speaker J] No, I think the intuition says that when you move from logic to reality, then intuition gives you the feeling—
[Rabbi Michael Abraham] I’m not exactly moving; it’s not called moving.
[Speaker J] It definitely is moving, because they’re not completely connected. There’s one world that has logic in it, one world that has reality in it, and the world in which you do the thinking. Now to connect those three worlds—you can produce a logic that has nothing to do with anything in reality, and it will precede reality by a thousand generations. I’ll invent a logic, and he’ll have claims about reality, and in the end you’ll come and connect something I wrote before he even knew the reality, and apply it to reality.
[Rabbi Michael Abraham] That happened many times in the history of physics. It happened many times in the history of physics.
[Speaker J] Yes, where apparently a theory came first. Now when you say intuition, what you really want to say is that when I—when you connect me to him—there will be a bridge. Here that bridge is called intuition, but it isn’t necessary in reality, because everything could be true except for one case.
[Rabbi Michael Abraham] No, on the contrary. Intuition is not something necessary, but intuition says exactly this: that I can take the logical schema and apply it to claims about reality.
[Speaker J] Only because it works, but it isn’t necessary. If in logic it’s necessary, in reality it isn’t necessary.
[Rabbi Michael Abraham] I didn’t say anything was necessary. I said my intuition tells me it’s possible—
[Speaker J] to apply the logical schema to reality.
[Rabbi Michael Abraham] Only because it fits many cases for you. The necessity comes from logic, not from intuition. Right, but it’s not necessary—that logical necessity can be applied to reality. And it’s not necessary that this be true—that’s what I’m claiming along with you.
[Speaker J] Meaning, if my intuition is mistaken, then it isn’t true. Okay, and in that sense intuition is always mistaken somewhere in most scientific theories, I don’t know, at least the ones I know. In the end there was always some case that turned out to be an exception, and then they found another theory on the next floor up.
[Rabbi Michael Abraham] But here it’s not a logical schema. Because it isn’t a logical schema, and you have to be careful. I’m talking only about the logical schema. If you say, “all two bodies attract each other, and these two bodies have mass, therefore they too attract each other”—fine? It may turn out that there are two bodies with mass that don’t attract each other, let’s say. Okay, what did that refute? It didn’t refute the logical schema—
[Speaker G] it refuted—
[Rabbi Michael Abraham] it refuted—
[Speaker J] the premise that all two bodies attract each other.
[Rabbi Michael Abraham] It refuted the induction. Exactly. But if Elijah the Prophet told me that all bodies with mass attract each other, fine? then no opposite case can exist. That’s what my intuition says. It can’t be that the intuition is refuted. Right, I didn’t say it’s possible to refute logical intuition. Okay, well no, it is possible—why not possible? Because there is no case—give me an example. For instance, one plus one equals two.
[Speaker C] You can escape ad hoc—
[Rabbi Michael Abraham] but that’s already a decision.
[Speaker C] Not only can you—it will be obvious that you’ll say otherwise.
[Rabbi Michael Abraham] I don’t know. Elijah the Prophet comes—there are many people I’ve met who choose that option. In this case I choose your options. But many people—let me give you an example. Elijah the Prophet comes and says: all human beings are mortal. Fine? All of them. Elijah the Prophet comes, the Torah says death was decreed upon man, right?
[Speaker J] And then Elijah came and didn’t die.
[Rabbi Michael Abraham] Exactly. Now then Jacob our forefather didn’t die, I don’t know, or Elijah the Prophet ascended to heaven, and then someone says: wait, what do you mean? But there is a law that all human beings have death decreed upon them. Elijah the Prophet is a human being, therefore death was decreed upon him too—but Elijah the Prophet didn’t die. So there are two possibilities. Either you refuted the rule that all human beings have death decreed upon them—which is what I would choose—or he—
[Speaker C] wasn’t a human being to begin with. Yes, whatever—but in the factual premises. Or you refuted the logical schema.
[Rabbi Michael Abraham] Someone will come and say “the unity of opposites.” Right, or they’re confused and don’t think anything—neither this nor that. That’s what I think. But they don’t say that; they insist forcefully. Many people say otherwise.
[Speaker D] They simply don’t understand what’s troubling about the fact that logic applies to reality. Meaning, logic applies to claims about reality. And if—maybe I’m misusing the word “true”—logic applies to claims. If those claims are true, then in whatever domain they are true, logic applies.
[Rabbi Michael Abraham] I have no problem; nothing is troubling me. But why is nothing troubling me? Because the alien is troubled by it. Because I have the intuition that it’s true.
[Speaker D] Why do you need intuition? Logic is valid with regard to claims. If—
[Rabbi Michael Abraham] the claims are true—
[Speaker C] about reality, then it’s true.
[Rabbi Michael Abraham] You just stated a sentence there, you stated a postulate—
[Speaker C] But maybe logic, the logical schema—
[Rabbi Michael Abraham] “Logic is valid with regard to claims”—you stated a sentence. Logic is not valid with regard to claims. Logic is a set of rules of the game, as Ido said earlier. It’s a schema of game rules. But what—who said it’s true or false? Truth and falsity apply only to claims. Logic is games; there’s no true and false there. Once you move to true and false, by definition you’ve moved to claims about reality. That’s model theory in mathematics: reality is a model for this logical schema, fine? Now the question is what the relation is between the model and the theory. Fine? And that is really the question. And I claim that intuition says the model must fit the theory completely—meaning, whatever is true in the theory will also be true in its model, “theory” here in the mathematical sense. Fine? And for that you need intuition. You can’t bring a mathematical proof for that, because obviously it’s outside mathematics. And if the model is reality, then you’ve moved entirely into physics—that’s no longer mathematics. A logician dealing with model theory is a mathematician. Fine? So what I’m trying to show here is that, unlike the bad name intuition got—or to counter the bad name intuition got as against logic—I think that bad name is undeserved. Intuition is the queen of thought. Meaning, without it there is nothing, not even logic.
[Speaker B] It’s no accident that in Hebrew it’s in the feminine; Hanoch gave her a compliment.
[Rabbi Michael Abraham] Yes, although I disagree even with that characterization, that women have more intuition than men. I think the opposite is true, but that’s just my intuition. They have common sense, not crooked sense. So that’s one route that leads me to intuition. And now of course I can take this instrument—which is very easy for me, say, to persuade you of its validity through the arguments about logic—and now bring it into science, into observation. And then someone asks me: who told you that what you see really exists? Because I have an intuition that the vision I see reflects reality correctly, even though there were philosophers who cast doubt on that too. Okay, so there were. But I don’t doubt it; I have the intuition that what I see is probably true. And again, maybe I made a mistake. I’m not saying it’s certainly so. But I have the intuition that it’s true. Yes, there’s a mirage, sure. But okay, still, I have the intuition and that’s good enough for me; I think it’s true. Now what about the particular case—I see the wall here. What about the general law? There too I say the same thing. Basically what happens is that I have an intuition that if I’ve seen enough donkeys with four legs, then probably all donkeys have four legs. Fine? What’s the justification? I don’t know what kind of justification you expect. Once I give you the principle of justification, you’ll ask me: and what’s the justification for that principle? In the end we’ll have to stop somewhere. Where will I stop? This really takes us back to the previous class. Where do I stop in the end? I have the intuition that it’s true, period. I have nowhere else to stop.
[Rabbi Michael Abraham] Now, does such a thing count as justification? What I just did—this little trick of saying otherwise we get into an infinite regress. I proved to you by contradiction that you can’t arrive at anything if you don’t trust intuition, because the only alternative is infinite regress. If this isn’t true, then it’s true because of that; why is that true? because of that. Okay—where does it stop?
[Speaker C] So maybe you can’t arrive at anything.
[Rabbi Michael Abraham] Yes. So either skepticism—either skepticism. But if you are not a complete skeptic, you have no choice but to accept the validity—I don’t know if certainty, but the validity—of intuition. Fine? That there is something in intuition, some faculty we have, by which we can apprehend the truth of claims even though it’s not the result of direct observation.
[Speaker J] So this intuitive faculty—to believe in them—it’s not about their truth, but about believing the claims, I mean.
[Rabbi Michael Abraham] And not what? It’s not—
[Speaker J] about their truth. It’s believing those claims, I don’t know.
[Rabbi Michael Abraham] Their truth. Why not their truth?
[Speaker J] Their truth—
[Speaker C] of it. I believe that this claim is correct. I think it’s probable, yes, probable, not true.
[Speaker J] I’d say certain—
[Rabbi Michael Abraham] even—
[Speaker C] I’d even say certain.
[Rabbi Michael Abraham] But what I’m claiming is that the claim is true. I’m just claiming it at a certain level of probability.
[Speaker J] Fine, okay, percentages, percentages.
[Rabbi Michael Abraham] What is the relation between probability and intuition? What? Intuition basically determines the degree of probability of the information. Because I have intuition, and intuition sometimes sees something as very probable and something else as probable but, I don’t know. There are many generalizations we make where we say: maybe it’s true, but we understand that we definitely wouldn’t be surprised if it turned out not to be true. There are generalizations that seem completely far-fetched. There are generalizations that seem almost self-evident to us, like all human beings are mortal, for example. Okay? All of these are just different levels of probability that our intuition somehow quantifies. I don’t know how. We have some kind of faculty that succeeds in quantifying different levels of probability for claims. Now, you can accept that or not accept it. You can cast doubt on all of it and remain a skeptic. But if you’re not a skeptic, this is a proof by contradiction: if you’re not a skeptic, then either infinite regress or stopping at intuition. Intuition is the point at which you stop.
[Speaker C] And if you really are a skeptic, you probably shouldn’t do very many things.
[Rabbi Michael Abraham] Yes, not that you shouldn’t do many things, but fine.
[Speaker C] But to claim that you can’t believe anything—isn’t that itself a statement that needs some justification?
[Rabbi Michael Abraham] He’ll also tell you that he’s not sure of that.
[Speaker C] Okay, he’s also not sure that you can’t—
[Rabbi Michael Abraham] Yes, he’s not even sure that everything is doubtful. That too is doubtful. Fine, these are old arguments against the skeptic.
[Speaker C] Fine, also that he’s not sure… fine.
[Rabbi Michael Abraham] No, it’s either regressions of infinite justification—
[Speaker C] Why justification? Also that he’s not sure that he’s not sure—is that not justification?
[Rabbi Michael Abraham] Not justification, not justification. I’m not sure of this, but I’m also not sure of that. One doesn’t justify the other. Of course not. I have no problem claiming—
[Speaker C] Are you sure that you’re not sure? What? No. So still—again, another claim now—
[Rabbi Michael Abraham] Right, another claim, no problem. I’ll claim about anything you ask: I’m not sure. But it’s not that one justifies the other. The failure of infinite regress is an infinite chain of justifications. Here it isn’t justification. I’m not sure of this, and I’m not sure of that, and I’m not sure of that. There’s no connection between them. I’m equally unsure of all of them. Meaning, there’s no hierarchy here. It’s not that one justifies the other. Okay?
[Speaker D] It doesn’t have to be binary; it can be on a continuous scale. What? There are things I’m 100% certain of, and things I’m 90% certain of.
[Rabbi Michael Abraham] Right, so I’m talking—
[Speaker C] No, I just wanted to ask whether skepticism is consistent.
[Rabbi Michael Abraham] Yes, I’m saying at the level of—what does “consistent” mean? You know, if contradiction is consistent—it depends. By their standards, yes. Because fine, they have no problem with contradictions. It’s a somewhat context-dependent question.
[Speaker C] You have no need whatsoever to be consistent about anything, because there’s nothing to be consistent about.
[Rabbi Michael Abraham] Consistency is a relation between claims. He doesn’t claim anything. He doesn’t even claim “I am a skeptic,” because even that is in doubt. He claims nothing, so what does consistency even mean? Okay. In any case, that’s one direction. A direction that says: basically we have two options—either be skeptics. It’s really more of a threat than an argument. Just know that if you don’t accept the validity of intuition, you are doomed to be skeptics. That’s it. Now decide. It’s basically a threat. Yes, exactly. More than that, I don’t know how to argue.
[Rabbi Michael Abraham] And that brings me to the other side of the coin. I said I’d present it from another direction too, and that is the Kantian problem of the synthetic a priori, which is entirely equivalent to what I’ve said up to now. Kant presented it somewhat differently. It starts with David Hume, who cast doubt on induction—he’s our alien. He casts doubt on induction, not on deduction, but fine, he’s alien number two. So yes: how do you derive general conclusions from specific observations? That was David Hume’s question, and in doing so he caused a lot of heartburn for the empiricists, of whom he himself was one.
[Speaker C] Did he accept deduction?
[Rabbi Michael Abraham] Deduction yes, and observation too.
[Speaker C] He was a strict empiricist. Why did he accept observation?
[Rabbi Michael Abraham] Just because. Because that’s obvious. You see it.
[Speaker C] Intuition… that’s what he said?
[Rabbi Michael Abraham] Yes, you see it, it’s obvious. Okay. But this generalization—who knows, maybe yes, maybe no. After all there are generalizations—
[Speaker C] But he doesn’t see that.
[Rabbi Michael Abraham] No, again: when I see something, it’s obvious that it’s true. I’ve never seen something and then it turned out not to be true, David Hume would perhaps tell you. He never went through the desert, never had a mirage. I have no reason to doubt that. But in induction I know there are generalizations that have failed. I made generalizations in the past that turned out to be untrue.
[Speaker C] Is that what he says?
[Rabbi Michael Abraham] No, no, I’m trying to justify him. I don’t know a statement of his like that. But maybe that’s what lies behind it. There is some basic doctrine… fine, no, it’s not a failure but… okay. The question is how far you take skepticism.
[Speaker C] But we explained—it has to be total skepticism.
[Rabbi Michael Abraham] No, no, no. You can say, look, I have no reason—
[Speaker C] or that he doesn’t believe these intuitions?
[Rabbi Michael Abraham] Exactly, exactly. Not all intuitions. Okay, so—
[Speaker C] Anyway, so those were the intuitions.
[Rabbi Michael Abraham] So that was David Hume’s problem, which basically—you can—
[Speaker I] say intuitions I trust 100%—those he accepted. Intuitions that are less than 100%, then from his point of view—
[Rabbi Michael Abraham] In short, it stuck the entire empiricist project in philosophy, because all empiricism, which began say in the 15th–16th century יחד with modern science, was trying to offer an alternative to what had ruled until then: rationalism. Rationalism is the view that says you can derive conclusions about the world from thought processes alone, without observation. Aristotle’s physics was basically rationalist physics, because he was willing to draw conclusions without doing experiments. That’s why, for him, a heavy stone falls faster than a light stone, even though the experimental means at his disposal would have allowed him to do that experiment with no problem. You don’t need a particle accelerator for that.
[Speaker B] Including even the number of teeth a person has.
[Rabbi Michael Abraham] Yes, I don’t know. But not long ago I once saw in some book an explanation of the expression “from the horse’s mouth.” You know that expression? “I heard it from the horse’s mouth.” As if it’s obvious. I never knew where that came from. I saw in some book—not a scientific book, just some book, incidentally—that “from the horse’s mouth” meant that scholars in the Middle Ages argued over how many teeth a horse has. One said fifty, one said forty, whatever. He has this kind of logic, and the head is large, so he has more than a human being and less than—lots of sophisticated logical arguments. Until somebody came and said, okay, let’s open his—open it up. And he says to them, “Gentlemen, the horse has sixty-three teeth—that’s from the horse’s mouth. I saw it in his mouth.” Fine? That’s supposedly the obvious thing. Huh? Was that accepted? Even that I don’t know—maybe it’s just a legend. I have no idea. Because afterward I looked online for the source of that expression, “from the horse’s mouth,” and I saw all kinds of speculations, but nobody brought—I didn’t see a source.
[Speaker F] It reminds me of the Mishnah Berurah—not about the horse, but… actually yes, about the horse—about sixty horse-breaths—
[Rabbi Michael Abraham] where they say—
[Speaker F] that one should not sleep during the day more than the time of—kind of a recommendation for a pious person to be stringent with himself and not sleep during the day—
[Rabbi Michael Abraham] more—
[Speaker F] than sixty horse-breaths, if I remember correctly. Because it has to do with the horse’s breaths. That’s how it goes.
[Rabbi Michael Abraham] And you also have to wash your hands. After sixty breaths you have to wash your hands. And the Vilna Gaon never slept sixty breaths, and all kinds of—
[Speaker F] And they bring all kinds of sources. The Ari slept that way, so apparently it’s a longer time.
[Rabbi Michael Abraham] When the horse breathes like that, then we have indications. So it’s like “the hand recoils.” You know what “the hand recoils” means? There’s that experiment of Shlomo Zalman there—the Mishnah Berurah, I think, mentions it—where he arrived at some lower threshold of forty-something degrees, forty-five degrees I think, through some, I don’t know, goose blood from a goose they had slaughtered… he had some kind of… he managed to reach some sort of threshold. Instead of putting your hand there and noticing when the hand recoils and when it doesn’t recoil. But for us you need numbers and indications and science.
[Speaker F] And then among other things he also brings some testimony from someone who counted and said that a horse’s breathing is not more… that sixty breaths of a horse are no more than three minutes or something like that, and then it doesn’t fit with the sources.
[Rabbi Michael Abraham] The Ari, of blessed memory, apparently didn’t breathe like horses. Okay, in any case, nature has changed. What, the Ari…
[Speaker F] Horses breathed…
[Rabbi Michael Abraham] Obviously. Nature has changed, the horses… decline of the generations among the horses. Exactly. The horses’ lungs. Yes, exactly. They also ate eggs accordingly, you know, after all… no wonder. Anyway, so Hume’s problem, yes—what is the justification for induction, causality, and all the foundations of science?—basically brought the empiricist project to a halt. Because that project really came to offer an alternative to rationalism. In the Middle Ages, Aristotelian thought dominated, and it basically looked down a bit on experiment. They did do some experiments—it’s not that nobody did at all, Aristotle also did experiments, by the way—but he didn’t see any necessity to do experiments. Meaning, if something was very logical, then as far as he was concerned that was enough; he didn’t need to run an experiment. So in that sense he was a rationalist. Now in the fifteenth century, a revolt against rationalism began. How can that be? Just because your mind is built in a certain way—so what? The world doesn’t owe you anything, right? It was here first, as Mark Twain says. So the fact that your mind is built in a certain way means the world behaves that way? What’s the connection? If you had been born with a different mind, would the world behave differently? In other words, the fact that the mind is built a certain way proves nothing. If you want to know reality, you need to check what happens in reality itself, not what you think or what seems logical to you. Okay? And then empiricism began to develop, and that basically opened the door—it was the philosophical platform for the development of science. Modern science really began in the sixteenth century following the… empiricist revolution, but philosophers don’t rest on their laurels, and then another hundred or two hundred years passed—the British empiricists, yes, Locke, Hume, Berkeley, and the whole gang. And each of them narrows empiricism more and more; it becomes more and more radically empiricist. But suddenly it became clear that to be an empiricist means to be a skeptic. Which was really true from the beginning, but it’s a very long historical process before that rises to the surface. And why? Because empiricism is grounded in skepticism. It basically says: what my mind tells me—who says that’s true? I want to see it straight from the horse’s mouth. So he’s a skeptic. But now the straightforward empiricist—and David Hume was, all in all, a straightforward empiricist—basically starts examining himself in the same way, and he discovers that within the empirical method there are a great many hidden jumps, and they are conceptual jumps. Who says they’re valid? Like induction. Science, after all, is based on induction. I observe things and from that create a general law. Fine, observation is great, accepted, we’re empiricists. But what about the generalization? When you’re an empiricist, you’re not a rationalist. Generalization is an intellectual process. Your head thinks this is the correct generalization—fine, what does the world owe you? So you’re actually in the same mess as the rationalists; what alternative is there here? And then all kinds of contortions begin, to this very day, by the way. The whole philosophy of science sits on this question, and only on this question, in my opinion. Pretty much the whole philosophy of science is only about this. And there are all kinds of attempts to twist this way and that—there really isn’t a good answer to Hume’s questions to this day. What there is, is this or that kind of maneuvering, and possibilities and nuances; philosophers know how to do that. But basically the question is: how is science suddenly valid? That’s really the question. And the cornerstone of science is induction, causality, induction—those are connected to one another too, but never mind.
[Speaker J] The fact that the mind is part of the world doesn’t, I don’t know, solve it?
[Rabbi Michael Abraham] That too is an interesting inference. Who says it’s valid?
[Speaker J] I agree, I’m only saying, the fact that the mind is part of the world.
[Rabbi Michael Abraham] That’s part of the answers, but even that isn’t free of problems, because that inference itself you also made with your mind. Who says it’s valid? You won’t get out of it.
[Speaker J] No, I agree.
[Speaker E] The direction of induction—meaning after you’ve formulated the experimental law, you need to prove it from another case.
[Rabbi Michael Abraham] Test it, not prove it. Yes, to give a prediction, a prediction, and put it to a falsification test. Fine, but before you’ve done that, do you get on the plane? Maybe it’ll crash. Maybe the laws of mechanics aren’t correct.
[Speaker J] No, on the contrary, because I rely on mechanics, you—meaning—you agree that in principle with laws you need, there’s some kind of belief, because all these minds are built the same way and they—
[Rabbi Michael Abraham] The world doesn’t owe them anything. The plane won’t crash because of minds; the plane will crash because our mechanics is incorrect. Who says it’s correct?
[Speaker J] It really was incorrect many times, and they adjusted it to something more correct.
[Rabbi Michael Abraham] So why do you get on planes? That’s what I’m asking.
[Speaker J] Because experience created enough belief in me.
[Rabbi Michael Abraham] But really there’s no justification for that. It’s just psychology.
[Speaker J] A belief was created in you.
[Rabbi Michael Abraham] I don’t know if it’s entirely psychology; planes don’t crash, all in all. Every now and then it happens, but all in all, planes—there is some basis for that belief.
[Speaker G] They don’t crash because the law turned out
[Speaker J] to be incorrect.
[Rabbi Michael Abraham] Right. Yes, so that’s exactly the question; these are always ad hoc solutions. That too is a problem in the philosophy of science. But in any case, the point is that Kant basically came to solve the Humean problem. All right? But the Humean problem is basically this: what is the justification for generalization? What stands at the basis of science? Science doesn’t really offer an alternative to rationalism; science too assumes intellectual procedures that bring us to.