Artificial Intelligence – Lecture 8 – Rabbi Michael Abraham
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Table of Contents
- Opening the series on artificial intelligence and its introduction — the Rabbi places this lesson within a broad introduction to thought, consciousness, creativity, and types of inference, before turning directly to AI after the break.
- A review of the three classical forms of inference — deduction, induction, and analogy are defined by the direction of movement between universal and particular, and distinguished in terms of necessity and the addition of information.
- Certainty versus information and the implications for computer science — a kind of “constant-sum game” is presented between certainty and quantity of information, leading to the distinction between classical computing as deductive and AI as an empirical field.
- Computer science: from mathematics to science — the claim is that in the past computer science was a branch of mathematics, and only with contemporary learning systems has it actually become a field grounded in observation.
- Hume’s problem: causality and induction are not products of observation — the Rabbi returns to Hume’s empiricist crisis, which showed that basic principles of science are not derived from direct observation.
- Kant’s distinctions: a priori / a posteriori and analytic / synthetic — Kant’s two distinctions are explained, including why before him people thought these were really two overlapping classifications.
- Formulating the problem of the synthetic a priori — laws of nature are presented as claims that add information about the world but are not derived from observation alone, and are therefore both synthetic and a priori.
- The crisis of empiricism and the need to go beyond it — if science itself goes beyond mere observation, then the empiricist is forced to admit that there is knowledge about the world that cannot be reduced to empirical data.
- Kant’s “theological” method — the Rabbi explains why moving from the conclusion back to the premises is not necessarily pragmatist, but rather an uncovering of implicit assumptions that ground an existing intuition.
- Discussion of students’ questions about intuition — objections are raised concerning the subjectivity of intuition, changes in people’s views, and the non-one-to-one nature of moving from conclusions back to premises.
- The Kantian solution: phenomenon and noumenon — Kant is presented as distinguishing between the world as it is in itself and the world as it appears to us, and on that basis explaining synthetic a priori judgments.
- Criticism of Kant and the search for another solution — the Rabbi argues that the Kantian explanation of laws of nature as derived from forms of perception is implausible, and therefore does not really solve the basic problem.
- The Rabbi’s proposal: “cognitive thinking” and intuition — he proposes rejecting the dichotomy between thinking and cognition, and recognizing a non-sensory intellectual faculty that grasps causality, lawfulness, and insights about the world.
- Abduction as a prime example — through black-body radiation, Planck, and quantum theory, the difference is explained between induction, which generalizes data, and abduction, which generates an explanatory theory.
- Philosophical and Torah precedents — the Rabbi links his idea to Maimonides’ “eyes of the intellect,” Rabbi HaNazir’s “auditory logic,” and Husserl’s “eidetic seeing” as support for an intellectual cognitive faculty.
Summary
General Overview
This lesson continues the introduction to the series on artificial intelligence, but now deals with a more basic question: what is human thought, and how do we acquire knowledge about the world at all? The Rabbi presents the structure of different kinds of inference, the philosophical crisis created by Hume regarding induction and causality, Kant’s formulation of the problem of the “synthetic a priori,” and finally offers his own solution: recognizing that human beings possess a faculty of “cognitive thinking,” or intuition — that is, a non-sensory yet real way of knowing the world.
## Inference, Information, and Certainty
At the beginning of the lesson, the Rabbi returns to a review of the three accepted modes of inference: deduction, induction, and analogy. Deduction moves from the universal to the particular, and is therefore necessary; it does not add real information beyond what is already contained in the premises. By contrast, induction and analogy do add information, and therefore always involve an element of doubt.
From here the Rabbi proposes a basic principle: there is a tension between the amount of information added and the level of certainty. The more information an inference adds, the less certain it necessarily is. That is also why logic and mathematics rely on deduction, whereas science relies on induction and analogy.
## Computer Science and Artificial Intelligence
Against this background, the Rabbi offers an interesting distinction: the classical computer belongs to the world of deduction, and therefore classical computer science is really a branch of mathematics. By contrast, with the appearance of artificial intelligence and learning systems, our knowledge of the capabilities of such systems has become observational: we see what they do, rather than proving mathematically what they are capable of doing. Therefore, only now does “computer science” truly become science.
## Hume, Kant, and the Problem of the Synthetic A Priori
The Rabbi returns to Hume’s problem: principles such as causality and induction do not arise from observation, even though they are essential to science. From here Kant’s question emerges: how are synthetic a priori judgments possible — claims that add information about the world, yet do not arise from observation alone?
Kant’s distinction between a priori / a posteriori and analytic / synthetic is meant to sharpen the problem. A law of nature, such as gravity, is not analytic, because it cannot be inferred merely by analyzing the concepts involved; but neither is it purely a posteriori, because from observing only a few cases one cannot by itself derive a universal law.
## The Kantian Method and Moving from Conclusion to Premises
The Rabbi emphasizes that Kant did not ask whether science is possible, but how. His starting assumption is that we trust science. From there, one can work backward and ask which implicit assumptions make such trust possible. The Rabbi explains that this is not a pragmatist mistake, but a legitimate method for exposing foundational assumptions already embedded in our intuitions.
## Kant’s Solution and the Critique of It
Kant distinguishes between the phenomenon — the world as it appears to us — and the noumenon, the world as it is in itself. Science, on his view, deals only with the phenomenon. Thus one can understand how we have a priori knowledge about the world: not because we know the world as it is in itself, but because we know our own forms of perception, which shape the way the world appears to us.
But the Rabbi rejects this solution as implausible. For example, it is hard to accept that concrete laws of nature, such as Newton’s second law, are the result of the structure of our consciousness rather than of the world itself. In his view, the Kantian solution replaces one difficulty with another no less serious one.
## The Rabbi’s Proposal: Intuition as a Faculty of Cognition
From here the Rabbi proposes another solution: the problem is born from a mistaken assumption, namely, that there is a sharp dichotomy between thought and cognition. In his view, human beings also possess a faculty of “cognitive thinking” — non-sensory cognition by means of the intellect. Therefore, when we grasp causality, lawfulness, or an explanatory theory, this is not merely a thinking habit or a subjective structure, but a real cognition of the world by means of intuition.
## Abduction and Its Meaning
At the end, the Rabbi presents abduction — moving from cases to an explanatory theory — as a powerful illustration of this idea. Through the example of black-body radiation, Planck, and quantum theory, he shows that science does not settle for inductive generalization, but penetrates through the phenomena to a theory that explains them. According to the Rabbi, this ability rests on genuine intellectual intuition.
He connects his position to Maimonides, who spoke of the “eyes of the intellect,” to Rabbi HaNazir, who spoke of “auditory logic,” and to Husserl, who spoke of eidetic seeing. The central conclusion is that trust in science requires recognizing the existence of a non-sensory human faculty through which we know truths about the world.
Full Transcript
Last time I was really dealing with the three accepted forms of inference: deduction, induction, and analogy. Deduction is moving from the universal to the particular, induction is from the particular to the universal, and analogy is from particular to particular or from universal to universal. On the face of it, these seem to be the only three possible forms of inference, because combinatorially there aren’t any other options. But I said there’s another one, and that’s what we’ll talk about a bit more today — there’s also another method called abduction. Abduction is moving from cases to a theory, not to a general law — but I’ll talk about that today.
I just want to remind you that deduction is basically inference from the universal to the particular; that’s a necessary inference. Right? All human beings are mortal, Socrates is a human being, conclusion: Socrates is mortal. So that’s a necessary inference. Logic and mathematics are all basically engaged in deduction, in deductions. Induction and analogy are non-necessary forms of inference, because you move from one case to many cases, or from one case to another case. In every case, the result is not contained within the premises from which you started. And because of that, the result contains a speculative dimension, as we saw — a dimension that adds information beyond what’s in the premises. Therefore induction and analogy are really the domain of science. If deduction is the domain of logic and mathematics, then induction and analogy are the domain of science. Science is engaged in adding information, in gathering information, and therefore it uses forms of inference that add information; and by the very fact that they add information, doubt always accompanies them.
We spoke a bit about a principle of logical uncertainty, let’s call it that, or philosophical uncertainty, which says that the amount of information you accumulate times the certainty you have in that information is constant. Right? Meaning, if you want a high degree of certainty, you need to reduce the level of speculation — in other words, reduce the amount of information that the inference adds. If you’re willing to accept a lot of information, then it becomes more speculative and comes with less certainty. So there’s a tradeoff between the level of certainty and the amount of information you allow yourself to add. When the certainty is absolute, as in deduction, that basically means you added no information at all. Right? The added information is zero if certainty is one. So the claim is that there’s some kind of tradeoff here between the amount of information I add and the certainty I have in that information.
And for our purposes, what’s important — and we’ll see this later — is that a classical computer, an early computer, a Turing machine if you like, all concepts we’ll get to later, are machines that basically deal in deduction. And in that sense they belong to logic or mathematics. That’s why the term “computer science” always bothered me. Computer science isn’t part of the sciences; computer science is a branch of mathematics. But once artificial intelligence appeared — neurons and LLMs and all sorts of things of that kind, again, we’ll get to them later — then we really moved into the domain of science. Now computer science really is a science. Why is it a science? Because now the information we have about these systems is mostly not the result of mathematical theorems. It’s the result of observations. We simply look and see what these systems know how to do, and all the time new surprising things get published about just how much they manage to do. But it’s surprising because we don’t have theorems that tell us that these are indeed their capabilities. In other words, we don’t have mathematical proof that such a system can do this kind of task. I mean, there are bits and pieces here and there, but that’s really marginal. Most of the information we have today about computerized systems is scientific information. It’s information that results from observation, and less from mathematical proofs. So paradoxically, in my opinion at least, only in these years is computer science actually becoming a science. Before that, it was a branch of mathematics, not of science. And that’s because now it really is the result of observation. Before that it was the result of mathematical theorems that one could prove. In other words, we proved certain theorems and that’s how we knew what these systems could do.
Now this leads me to what we actually ended with last time. Last time I talked about the question whether it is possible to add information not by means of observation. What Kant called the problem of the synthetic a priori. So I said this starts with Hume, who as an empiricist — that is, as someone prepared to accept only things that are the result of observation — basically found himself in trouble when it came to some of the most basic foundations of scientific thinking. Chief among them, especially, the principle of causality and the principle of induction. These are the two prominent examples. They are two principles that essentially have no observational basis, certainly not a direct one. And so Hume argued that we cannot accept them, because as an empiricist he was prepared to accept only things that come out of observation. And we spoke about why causality and induction cannot really be extracted from observation. Although people think these are principles that come from observation, they are not. They are principles that we bring to observation. They do not come out of observation itself.
And therefore Hume really did undermine the validity of these principles, and by doing so he shook the philosophical foundation of science, the logical basis of science. And Kant, in order to solve Hume’s problems — and that’s where we ended last time — proposed two classifications of the claims that exist in our language, in our logic. There is a classification along the epistemic axis, the cognitive axis, and that is the distinction between a priori claims and a posteriori claims. A priori claims are claims that I know without observation; a posteriori claims are claims that I know by means of observation. Kant’s second classification is on the logical basis, not the epistemic one, and that is the distinction between analytic and synthetic claims. Analytic claims are claims I arrive at by analyzing the concepts involved in them. Synthetic claims are claims I cannot arrive at by analysis — analysis means analysis, so these are analytic claims. Synthetic claims are claims that require additional information beyond what is embedded in the definitions of the concepts that compose them. That’s why they’re called synthetic, because I need to synthesize additional information together with what is embedded in the concept definitions, and only then do I arrive at the claim.
I gave examples. If I say that this ball is round, that’s an analytic judgment, because from the concept of a ball I know it’s round. I don’t need anything beyond the information in the concept of a ball. Ignore balls that aren’t perfectly round — it’s just an example. And it’s also an a priori judgment, because it doesn’t require observation. By contrast, “this ball is heavy” or “this ball is orange” is an a posteriori claim; it requires observation. I need to look — there are also balls that aren’t orange. So if I say that this ball is orange, that’s basically the result of observation. And second, it’s also a synthetic claim because it adds information beyond what is embedded in the concept of a ball. Its being orange is not part of the information embedded in its being a ball. I need to add some further information here; that’s a synthesis with additional information.
Now from these two examples I argued — and this was really the very end of last time — that before Kant, and I’m not claiming this, Kant already pointed it out, I’m just describing it — before Kant it was customary to identify these two distinctions. Even though on the face of it they seem independent — one is epistemic and one is logical — in fact, when you think about it, they completely overlap. They are two angles from which to look at the same thing. Why? Because every analytic claim is obviously a priori, right? Because if I can get to a claim by analyzing the concepts involved in the proposition, then that analysis is enough to arrive at it; I don’t need additional observation. Therefore an analytic claim is an a priori claim. But the reverse is also true: an a priori claim is also analytic. Why? Because if the claim is a priori and I don’t need observation, then I ask myself: so where do I know it from? If not from observation, then from where? Necessarily, apparently, from understanding the concepts involved in that claim. Or in other words, if it is a priori, then it is analytic.
Now once I say that if it is analytic it is a priori, and if it is a priori it is analytic, that means there is an equivalence between these distinctions. So of course we don’t even need to talk about synthetic and a posteriori. If it’s two-way, then synthetic and a posteriori also go together. Okay? Therefore the claim is that before Kant at least, people thought these distinctions were overlapping distinctions. Every analytic claim is a priori, every synthetic claim is a posteriori, and so on.
Now Kant puts his finger on something and says — and this is where we ended — let’s reformulate Hume’s problems. The formulation he proposes is this: whether, or how, synthetic a priori judgments are possible. Notice: in the earlier classifications that couldn’t happen. Synthetic was a posteriori, a priori was analytic. Kant says no: there are judgments that are synthetic and a priori, and the question is how that is possible. That is really a reformulation — not a solution, but a reformulation — of Hume’s problem.
Let me define the matter a bit more. When we talk about a scientific law, for example, a scientific law usually deals with infinitely many situations or cases. When you say that two bodies with mass attract one another, that deals with infinitely many situations. Any two bodies you take, if they have mass, they attract one another. So a scientific law is by definition a law that deals with infinitely many situations. But we arrived at that law by means of observation, and the observation was made in some specific situations — I don’t know, five, ten, a hundred. Okay? But very far from the totality of the situations covered by the law. So how did I get from the observations to the law? Basically I’m performing some kind of generalization here. Or in other words, it is not correct to say that the law is an observational, a posteriori, empirical claim. I do indeed use observations, but the observations by themselves are not enough to generate the law. The observations tell me what happens in these and those cases that I saw. But how do I get from there to the general law? Therefore this is really an a priori claim, not an a posteriori one. The observations are not enough to give it to me. I need some additional information here, not by means of observation or beyond what observation gives me.
On the other hand, it is a synthetic claim. Why is it synthetic? Because the claim — suppose I say that every two masses attract one another — that claim cannot follow from an analysis of the concepts of bodies with mass or attraction. Even someone who knows those concepts and analyzes them well will not arrive at the conclusion that there is a law of gravitation in the world. In order to know that, you need I don’t know what — to observe the world, or think, or do something else — but analysis of the concepts alone is not enough. Therefore the claim is on the one hand synthetic, because it contains information about the world beyond what is embedded in the definitions of the concepts. Or in other words, it is a claim that tells me something about the world. An analytic claim tells me nothing about the world; it merely analyzes the concepts involved in it. A synthetic claim is a claim that tells me information about the world. On the other hand, it is not the result of observation. It is a priori. So it is synthetic and a priori.
Now up to this point, as I said, there was no such category. Synthetic was always a posteriori, a priori was always analytic. This combination of synthetic on the one hand and a priori on the other, Kant says, is really the whole set of problems raised by Hume. How are synthetic a priori judgments possible? In less heavy philosophical language, that basically means: how is it possible that we accumulate information not by means of observation? That is basically the interpretation of the problem of the synthetic a priori, right? Synthetic claims are claims that bring information to my knowledge, or reflect or express information about the world, make a claim about the world — and yet they do not arise from observation, or not only from observation. So how is it possible that I accumulate information about the world not by means of observation? Where does that information come from, if not from observation? Seemingly, what does not come by way of observation is only conceptual analysis, and conceptual analysis does not add information about the world. We spoke about how the analytic is empty — analytic judgments are judgments that contain no additional information about the world beyond what is embedded in the definitions of the concepts that appear in them.
Therefore Kant’s problem is really a reformulation of Hume’s problem of induction, or of various earlier versions of it: how is it possible that we accumulate information not by means of observation? How is it possible that the laws of nature tell us something about the world when I cannot base the laws of nature on observation? Because observations give only a few cases, while the laws of nature speak about an entire range of cases. So that is the Kantian formulation of the problem.
Now Kant says that Hume really awakened him from his dogmatic slumber. Before Kant — or before Hume, really — everyone calmly accepted scientific progress, was very impressed by science, everything was fine, and nobody noticed that there was actually a very big mine buried in the foundations of scientific thinking. Something here doesn’t make sense. How can we accept the fruits yielded by scientific inquiry? How can that be? There’s something here that isn’t observational, yet it tells me something about the world.
Now generally — and this is Hume and the empiricists, especially the British empiricists, though others too — empiricists claim that we can accumulate information about the world only by means of observation. Rationalists said no: I can make claims about the world even without observation. Okay? Now suddenly the empiricists are saying — and empiricists always went along with science, science being the way to discover information about the world — therefore, for example, an empiricist will generally be an atheist, because the claim that there is a God is not supported by observations. You can’t anchor it in observation; it’s not a scientific claim. Okay? Therefore empiricists generally tend to deny that claim, because they are willing to accept only observations as the basis for the information they adopt.
But now suddenly it turns out — this is the root of the crisis Hume provoked — that scientific results also do not come out of observation. So if you are an empiricist, then not only do you need to abandon belief in God, you need to abandon everything you know — every interesting thing you know about the world — apart from a few specific examples that you directly observed. But that’s not really interesting. The really interesting claims are general claims, laws of nature, things that speak about whole structures of knowledge — not a claim like “I now saw a phone here.” Fine, that’s information about the world I know by observation, but it’s uninteresting information; it’s particular information. It’s a specific fact, not really interesting. All the interesting information we have about the world is information for which observation is not enough.
And now the empiricists find themselves with nothing left. Because now the question is: we thought we had thrown rationalism into the trash — Descartes made some heroic effort to reestablish it, but it got thrown into the dustbin of history — and then empiricism ruled, and suddenly a terrible crisis emerged. Suddenly empiricists discovered that they have no real alternative; they have to go back and admit that the rationalists were right that one can make claims about the world not by means of observation. Anyone who accepts science, at least, has to understand that he must go beyond empiricism. Science forces us to go beyond empiricism. Understand the seeming absurdity here, the crisis this is supposed to create.
So Kant says: fine, what do we do in such a situation? First of all — and this is a point that’s always raised when people study Kant — Kant did not ask whether synthetic a priori claims are possible. He asked it in another formulation: how are they possible? What does that mean? His starting point was that he trusts science. He was not asking whether to believe science. Obviously I believe science. The whole question is how I can ground that. And I’ve spoken about this many times before, and written about it too. The entire fourth conversation in The First Existent is devoted to this matter.
Kant was really the first philosopher to put on the table what I called theological proofs or theological arguments — uncovering arguments. That is, arguments that assume some truth and then look for the assumptions that can ground that truth. Usually I start with a joke I once heard: what’s the difference between philosophy and theology? The philosopher assumes premises and derives conclusions from them. The theologian assumes conclusions and derives premises from them. He assumes that God exists, and now he looks for an argument to prove God’s existence.
The purest expression of this — which has taken a lot of abuse — is the opening of Anselm of Canterbury’s argument, the ontological argument, in the Proslogion. There he opens with a prayer to God, asking Him to enlighten his eyes so that he may discover the proofs of His existence. Now if you already know He exists, why do you need proofs? You’re praying to God before you’ve proved His existence. So everyone laughs at Anselm. And anyone who laughs at Anselm simply has no clue about philosophy. Not only because Anselm’s text is, in my view, a magnificent philosophical text, but beyond that, it’s just a misunderstanding. Since Kant, it seems to me, everyone understands that a great deal of philosophy is actually built in the way Anselm built his argument. You basically assume that science is reliable, and then you ask: yes, but how can I ground that? What argument could justify the trust I have in science?
And I explained there — and this is something people often don’t grasp because it’s a very subtle distinction — that at first glance this looks like a pragmatist argument, and in my view pragmatism is a pejorative term. Even though it’s a respected school in philosophy, pragmatism to me is a term of reproach. Pragmatism is basically the subordination of what is to what ought to be. For example, if you say: why is morality valid? Because without it we couldn’t run a society. That is a pragmatist argument. You haven’t actually shown me that morality is valid; you’ve shown me why it would be very useful for me to think it is valid. Or if I say: come become religious, because look how wonderful it is — you’ll stay with us, there are Sabbath candles and a Sabbath table and a marvelous family. Okay, and therefore you should repent? That’s a pragmatist argument. Because in order to repent, you need to believe in God. Now the fact that religious life is supposedly very pleasant — let’s say we accept that claim — is not a reason to repent. To repent you have to believe in God, believe in the revelation at Sinai, and in obligation to the commandments. So whether in the end it also gives you a better life or not is another discussion, but utility does not define reality; the desirable does not define what exists. Therefore the approach called pragmatism, which is very characteristic of American philosophers, William James and others, is in my view simply synonymous with a philosophical failure, failed philosophy.
That’s on the one hand. On the other hand, what Kant is doing here is ostensibly exactly that. He says: look, I trust science, I want to arrive at the conclusion that science is correct, let’s look for assumptions that will let me ground that. That’s exactly the same thing, apparently. It seems like a pragmatist argument. It basically says: I’m looking for truths, supposedly, but how will I adopt these truths? How will I decide whether to adopt them? If they’re useful to me — if they give me a basis for believing science. If you don’t believe science, then don’t believe it. The fact that it’s very convenient for you to believe science, that you want to believe science — fine, so what if you want to? What does that prove? Does that mean your assumptions are correct, the ones that in the end will ground your trust in science? Of course not. If the assumptions are true, then fine. But if you determine the truth of the assumptions only because they lead you to a conclusion you want to be true, that is a pragmatist fallacy.
So I argue no. Why not? Because the point is that since I have an intuition saying that science is reliable — I believe science, I trust science — that is an intuition. It’s not that I want to believe science because my life will be more comfortable if I do. No. I have an intuition that science is right. Now I ask myself what that intuition means. Presumably, if I have such an intuition, then there are certain assumptions that must be made in order to arrive at the conclusion that science can be trusted. So if I have such an intuition, that probably means that implicitly I really do assume those assumptions. I’m simply discovering in myself assumptions that I apparently make implicitly.
And therefore this is not a pragmatist fallacy; it is a perfectly legitimate philosophical argument. It is an argument that says — we’ve spoken about this in previous lessons — that every logical argument begins with premises. And you can always ask what the premises themselves are based on, right? You can always attack an argument: wait a second, but you assume premise A, B, C — so you haven’t proved anything to me. Every logical argument is like that. There is no logical argument without premises. Right? Every logical argument starts from premises, so you can’t attack an argument for having premises. But still the real question is: where does my trust in the premises come from? How do I know?
We spoke about that. I said there is some sort of human faculty called intuition. Intuition is the tool that allows me to recognize the truth of claims, and those claims can serve me as premises from which, by means of logic, I derive conclusions. Think, for example, about Euclidean geometry. Where did I get the assumptions that exactly one straight line passes through two points, or that parallel lines do not meet, and so on? Where did I get those assumptions? My intuition tells me they are true. And then logic or mathematics helps me derive conclusions from those assumptions. Okay? So every logical argument begins with intuition, which gives us premises, and from there continues by means of logical tools to derive conclusions — or theorems, if you like, in geometry or in any other mathematical field.
Now, what usually happens — one second — is that the movement is normally from the premises forward to the theorems. In a kind of thinking like Kant’s, what I called uncovering thought or a “theological” argument in quotation marks — nothing to do with God, I’m only calling it theological because of its form — this is an argument that goes backward. It goes from the conclusion to the premises. But in fact the conclusion is my premise. I assume the conclusion is true because I have such an intuition, namely that science is reliable. And now I’m looking for the assumptions that ground that intuition, because I know that if I trust that intuition, then apparently I also implicitly believe those assumptions. Therefore moving from the conclusion to the premises is no accusation. It is simply a fully valid philosophical method. I have no problem with it, and it has nothing to do with pragmatism. Pragmatism would be if I had no trust in science, but my life would be much more convenient if I did, so I adopt trust in science de facto and look for assumptions to support it. That would be pragmatism. But if I start from the fact not that I want to trust science, but that in fact I do trust science, intuitively I understand that it is true, then I can certainly ask myself: wait, what is that based on? If it has no basis at all, then I should just throw that trust into the trash. I need to explain to myself what I myself base my trust in science on — something that until now was unconscious, and now becomes conscious through this inquiry.
[Speaker C] But if so, then aren’t you, Rabbi, answering Kant’s question by saying that synthetic a priori is possible because I add my intuition to the a priori, and there you have a synthetic judgment that is not analytic?
[Rabbi Michael Abraham] Wait, slowly, slowly, we’ll get there. I’ll get there at the end. Anyone else?
[Speaker D] But I have a problem with this whole thing where you’re now basing everything on intuition. Isn’t intuition something completely subjective — dependent on the person, on his education, his values, everything he has? It’s not objective. So now you’re basically starting to base scientific matters on something very personal, very subjective, and not universal.
[Rabbi Michael Abraham] So I’ll argue that it isn’t — that’s exactly my point. We’ll continue. Intuition is definitely not something subjective, not personal, nothing of the sort. It’s a fully legitimate cognitive and intellectual tool. But I’ll get to that later. I just…
[Speaker D] So just one question about that: why doesn’t the atheist have the same intuition that the believer has?
[Rabbi Michael Abraham] There are disagreements. There are disagreements in many areas. There are disagreements in science too. One person is right and the other is wrong, but that doesn’t mean intuition is not a tool for recognizing truth. But let’s leave that; I’ll get there.
[Speaker B] Rabbi, can I ask something? This whole process of premises, then logical inference, then conclusion — it seems like a very closed system. I mean, if now we take a person who is an atheist, and he has premises and conclusions, it’s like a closed system. What happens when a person changes his mind? And now that same atheist accepts the yoke of Torah and commandments?
[Rabbi Michael Abraham] Very good question. I’ll get to that later too. All right?
[Speaker B] You understand what I mean, that it feels like a closed system? Like it’s not…
[Rabbi Michael Abraham] Okay. Yes, yes, that will definitely come up. With God’s help, we’ll get there. Thank you.
So I want to — there was another question here. Avi Lin asked something in the chat. Avi, do you want to ask? I don’t remember what it was now. Ah, yes. He asks: who says that this reverse engineering from conclusion to premises is one-to-one? I didn’t say it was one-to-one. And it definitely may not be one-to-one. By the way, induction going forward isn’t one-to-one either. A scientific generalization from facts — I can generalize in many ways. The move from facts to theory is also not one-to-one. Not every inference we make is one-to-one. But maybe that too will become a bit clearer later.
So now, here’s where we are. We’re looking for the justification or possible basis for our trust in science. How is it possible that we accumulate information beyond observations? Right? Observations alone are not enough to give me all this information, so the question is: how can I believe it if it doesn’t come from observation? Then from where?
Now all kinds of answers have been given throughout history to this question. This is really the basic question of epistemology. This is the fundamental question of the whole field. There is a book by Hugo Bergmann called Introduction to the Theory of Knowledge, and in chapter 9 of that book he calls this “the rationality of the world.” And that is basically an engagement with this very question. How is it that by means of the intellect we manage to understand what is happening in the world, not by means of observation? Intellect as distinct from observation — not that observation is stupid, but intellect as a faculty as opposed to observational faculties.
Now he goes through all the answers given to this question throughout the history of philosophy, and rejects all of them. None. No answer that really holds water has been given in the history of philosophy to this question. So Hume’s problem really is a very, very difficult problem. He also goes through answers that were given even before Hume. In other words, there were earlier formulations, before the problem had yet been formulated as it is now, but the problem certainly troubled people — how we accumulate information about the world.
In any case, Kant himself tried to offer an answer which many regard as the only answer that maybe does hold water, the one answer given to this question in a way that perhaps does make sense. And Kant’s answer was the following: he made yet another distinction. Typical Kant — in order to answer, he first of all performs conceptual analysis, makes distinctions, and then somehow the whole story seems to fold up and suddenly you see there isn’t really any question at all. It’s a very Brisker yeshiva method, if you know the style.
There’s a famous story about Rabbi Chaim of Brisk and his father, the Beit HaLevi. They both taught in Volozhin for a certain period; both were heads of the yeshiva there. And the Beit HaLevi rebuked his son and said: listen, your lessons are total desolation. I present ten difficulties, then raise some brilliant conceptual principle and solve all the difficulties in one stroke. Everyone is dancing with joy in my lesson. You can see examples in the responsa of the Beit HaLevi. By contrast, in your lessons, you make some analysis, some distinction, and distinctions like this, and one can say this way or that way, and it branches out into a whole tree — right? You split it into all sorts of possibilities. And that’s it. No questions, no answers, nothing dramatic happens. Each early authority just ends up located on one branch of the tree, and that’s all. No difficulties, no resolutions, nothing. And I think that expresses exactly what I’m saying here: once you do the conceptual analysis, and I tried to demonstrate this in the past with various Talmudic passages, if you do the conceptual analysis properly you can give up all sorts of pilpul, all sorts of elaborate dialectics, because you simply don’t need them. The solutions emerge on their own.
And in this context — actually in this same context there’s another story. My son studied in Yeshivat Grodno in Be’er Yaakov, a Haredi yeshiva. At some point he decided to move to the Gush. And then, as they say in Rabbi Nachman’s world, there was a great uproar in the worlds. Everyone was shocked and angry and so on, and at some stage they threw him out of the yeshiva. Doesn’t matter. If he had just gone off the rails, that would have been fine. But he wanted to learn Torah. Someone who wants to learn Torah — him they have to throw out. Anyway, this ties a bit into the opening of today’s lesson, what we spoke about at the beginning.
At some point I got a phone call from a certain man who himself was a graduate of Midrashiya, thank God became religious, became Haredi, and he is a well-known yeshiva head. He deals a lot with dropouts and ba’alei teshuvah, and a lot of young people get sent to him. In their world, someone who wants to study Torah in another yeshiva is called a dropout. That’s obvious. So I spoke with him on the phone, and he said to me: listen, I hear miracles and wonders about Rabbi Lichtenstein at Gush Etzion — that’s where my son wanted to go. But I’ve read things of his, and it’s basic. He said, every yeshiva student in the Chazon Ish kollel or in Ponevezh kollel writes things a thousand times more brilliant. So I said to him — not exactly in these words, but that was the spirit — you’re talking like a child. Because this is exactly the dispute between the Beit HaLevi and Rabbi Chaim of Brisk. What do you mean? You’re so impressed by the brilliant moves in the essays of these married yeshiva scholars from Ponevezh or Chazon Ish, but when you hear a lesson from Rabbi Lichtenstein, the passage is laid out before you like a tree of possibilities, spread out before you like a garment, as they say. No question even arises, and there’s no need to look for clever resolutions. So who is really the learner on the higher level? The one who comes up with some dialectical flourish that strings everything together — and who knows whether it’s right or not — or someone who really lays out the logic of the passage before you? You come away with a full picture of all the approaches, all the possibilities, all the implications, and not one chosen path just because that’s where you had an interesting novelty. That isn’t professional. It isn’t serious. It isn’t mature learning.
A professional learner — yes, it’s more boring — when you learn professionally, you learn like Rabbi Lichtenstein. You do the conceptual analysis, and then indeed the questions don’t come up in the first place. Too bad, because the most fun is when there’s a terribly difficult question and then suddenly you get a wonderful, brilliant answer and you dance with joy. But dancing with joy is nice. If you want to know the passage, then to know the passage you have to learn it properly, professionally — not with some particular novelty you want to say. Maybe it’s correct, but still it’s some particular novelty you want to say. As anyone who knows sees immediately, the whole lesson is built around that. You build all the questions in such a way that in the end you can say the novelty you wanted to say. You’re not teaching the passage; you’re saying some novelty you have in the passage, and you collect the questions only so that you can resolve them all with your own novelty. That’s all. The goal is not to learn the passage; the goal is to say the novelty, and everything is built for that.
And that’s exactly the point. In that sense I think Kant really is very exhausting and very boring — but for the same reason. He makes very heavy, annoying, nitpicking conceptual analyses, but in the end he really presents a kind of map. Not for nothing is he considered the greatest philosopher of modernity.
All this is…
[Speaker C] It’s not so simple. The analytical approach — the objective one that analyzes things and checks all the possibilities, as you described with Rabbi Lichtenstein — sounds very impressive, but it creates the feeling that the whole enterprise is some kind of laboratory analysis. You’re a scientist, you don’t want to take sides, you don’t want to show any involvement, you have no agenda, you come in cold, like a man of science who is supposed to be detached and distant — and the results follow accordingly.
[Rabbi Michael Abraham] I’ll answer briefly because it’s not our topic. I don’t think you’re right. The question whether you involve emotion is one question — and don’t drag me back into that argument — and whether you have an agenda is another question. You can certainly have an agenda, and still, in order to support it or show it or ground it, you do an objective analysis of the matter, show considerations in both directions, and arrive at what seems to you to be the correct conclusion. So I think you’re right on the practical level: in practice, people who learn this way often don’t issue Jewish law rulings, and probably also don’t succeed in issuing Jewish law rulings, because they don’t reach a conclusion about what is correct; they succeed in explaining all the possibilities. In order to issue a Jewish law ruling, you need to decide on one possibility as the correct one and the others as less correct. But I don’t think that’s a fate decreed from heaven; it’s not necessary. You can do the analytical work properly and still arrive at conclusions. But that’s really another topic, and I don’t want to go into it here.
So I return to Kant. In the end, here’s what I’m saying. Kant makes an initial distinction. He says this: when we deal with the world, the claims we make about the world are not about the world as it is in itself, but about the world as it appears to our eyes. Okay? Now what does that mean? For example, when I speak about colors, speeds, physical properties of one kind or another, I’m really speaking about the ways in which I perceive the world. But there is also the world as it is in itself, not as it is perceived by me. What exists out there on the objective plane. Science doesn’t deal with that. Science deals with how human beings perceive objective reality. That’s what Kant called the phenomenon and the noumenon. The phenomenon is the world as it is perceived by me — phenomenal, the world of appearances — and the noumenon is the world as it is in itself, the thing in itself.
And therefore, for example — we spoke about this when we talked about Mary’s room in one of the earlier sessions — I asked: what is the color yellow? Bertrand Russell asks in his book The Problems of Philosophy: what is the color yellow? Usually you’ll hear the answer: it’s an electromagnetic wave of such-and-such wavelength. Of course that’s nonsense. An electromagnetic wave of such-and-such wavelength is a physical phenomenon. The color yellow is a cognitive phenomenon. Right? Remember we talked about philosophers’ purple, whether they see it as the same color, and we got badly tangled there. But for our purposes, what matters to me is just this point.
When I speak about the phenomena by means of which I perceive the world — that is, the representation of the world in my consciousness — science deals with those. Science does not know what to say about the world as it is in itself. The world as it is in itself is some abstract thing about which I have nothing to say. All I can say is only about its properties or characteristics as I perceive them. Therefore Kant first of all makes a distinction between phenomenon and noumenon. Second, he says science deals only with the phenomenon, not the noumenon — only the world as it appears before our cognition. Okay?
If so, says Kant, then clearly the scientific picture we perceive is not only a function of what is happening in the world itself, but also a function of my own forms of thought and cognition. Right? Because clearly, if I perceive something, then it will be a function of my perceptual apparatus. Remember the color yellow? Someone else who looked at the same electromagnetic wave might hear Beethoven’s Ninth Symphony there rather than see the color yellow. Why? Because his sensory apparatus is different from mine. The same could be true of different faculties of thought. Therefore the world of appearances is a world shaped by my faculties of perception, sensation, and thought. As opposed to the world in itself, which has nothing to do with me; it is what it is, I don’t know what.
Now, says Kant, if that is so, then it is no longer surprising that we can say things about the world beyond the facts we observed. Because those things are actually derived from our forms of perception. Think, for example, by analogy: suppose I’m looking at the world through red cellophane. Without even opening my eyes I can already tell you that everything I see will be colored red. Right? I don’t need to observe the world in order to know that. Why? Because if I know my perceptual apparatus, I can say many things about the picture I am going to observe, even if I don’t know what is happening in the world itself. But I know my own perceptual apparatus. And my perceptual apparatus imposes constraints, or colors in certain ways, the world I perceive. Since that is so, Kant says, it’s no wonder that there can be synthetic a priori judgments. There can be judgments that I know how to make about the world without having observed the world. Why? Because I am not making them about the world itself; I’m making them about the world as I perceive it. And the world as I perceive it is certainly something about which I can say things derived from familiarity with my own apparatus of perception. Kant calls these transcendental claims — claims that precede observation, claims that constitute conditions of my perception. Through familiarity with the system of constraints, or the system of my perceptual apparatus — sensation, thought, my whole way of perceiving — I can make claims about the world even without observing it, because I know how it will appear to me: in this way and not in another, simply because I know that my perceptual apparatus perceives in this way and not in another. And therefore, says Kant, that is the solution he proposes to the problem of the synthetic a priori. In brief and in a nutshell, but that’s the basic move.
[Speaker E] Sorry, Rabbi, may I? Why still wouldn’t this count as analytic and a priori? Because the red cellophane colors things red, I know in advance what the result will be. I know red. I know the phenomenon I’ll get when I look through red. So really it’s analytic too, not necessarily synthetic.
[Rabbi Michael Abraham] Why do you think it’s analytic? Suppose I’ll see the ball I’m looking at as red. So I say in advance: the ball will be red. Still, its being colored red is not a property of the ball.
[Speaker E] Right, right, but I’ve already experienced the way of seeing.
[Rabbi Michael Abraham] It’s a priori, but it’s not analytic. Analytic means something you extract from an analysis of the concept you’re dealing with. The color red doesn’t come out of an analysis of the concept of a ball. You’re right that it’s a priori; that’s exactly what Kant says. It’s a priori, meaning it doesn’t require observation. I can say it even without observation. That is exactly the solution he’s trying to offer — to make a new distinction between the analytic and the a priori. In other words, there can be something a priori that is not analytic; it is synthetic. Synthetic a priori. That’s exactly what Kant is trying to explain here. Okay?
[Speaker E] Yes, but I’ve already experienced the… I already know what red is. If I were like Mary in her room and had never in my life seen red, then right, it would be synthetic.
[Rabbi Michael Abraham] Right, fine, of course. But you observed the fact that you have red cellophane over your eyes; you didn’t observe the balls. In that sense it’s a priori. You could also say that a person’s observation of himself is also a kind of observation. In that sense, what I know about myself could also be called a posteriori. I observe myself. Usually, though, it’s accepted that when I know myself, that’s not a posteriori; it’s a priori. That is, I know myself from within, not from without. Schopenhauer, for example, argued against Kant — or not against him but following him — that the distinction between phenomenon and noumenon breaks down when a person looks inward. When a person grasps himself from within, he isn’t looking at the thing from the outside and seeing it as it appears to his eyes; he grasps the thing as it is in itself. You perceive me as I appear outwardly, but I perceive myself from within, not from without. That means I grasp the thing in itself, Mickey as he is in himself, not Mickey as he appears outwardly.
Fine — it’s a matter of terminology. I’m willing to accept your terminology too, but in the accepted terminology this is called a priori, but not analytic, and also not a posteriori. All right?
Now, you’re right that in the wake of the Kantian solution there is already a great blurring between all these categories of a priori and a posteriori and so on, because scientific claims really do become a priori claims. But we still use observation to get to them — only observation is not enough; we make a generalization after observing. So at that point who knows what exactly to call it? A priori? A posteriori? There’s already a very big blurring between these four categories, or these two distinctions — two that are four, if you like. Later on I’ll blur them even more.
I have a problem with the Kantian solution. The problem with the Kantian solution is that it is simply utterly implausible. Why? Let’s think, for example, about Newton’s second law. Newton’s second law says that force equals mass times acceleration. Force and acceleration stand in a linear relation; it’s a constant multiple. Okay? Now suppose that in the world itself the relation could have been different, but my cognitive faculties dictate — so Kant would say — that I cannot see any other relation between force and acceleration. A law of nature, then, is really a synthetic a priori claim. So Kant explains to us why I see this relation between force and acceleration in just this way: because that is presumably my form of perception. It’s something that is a function of my sensory faculties, not of the world in itself. It is only the world as it appears to my eyes.
Then it comes out that maybe in the world itself acceleration goes like force squared, but my eyes won’t grasp such a relation. My perception somehow dictates that the relation has to be linear, that F equals ma. Okay? Now that is of course implausible. Anything is possible, of course — there could always be some demon that keeps deceiving me and doing something else each time. But those are not the kinds of claims a serious philosopher should be making. What you’re really proposing here is something very implausible, and I don’t see what you gain by using it to explain another claim that is itself implausible — trust in science. The claim you use to explain it is no more plausible than the thing you are trying to explain.
Why? Because clearly, a body with a mass of two kilograms can be seen by me as moving with an acceleration of four meters per second squared — four. Okay? How would that happen? If I exert a force of eight newtons on it. Eight equals mass, which is two, times acceleration, which is four. So a force of eight newtons on a mass of two kilograms will give me an acceleration of four. Okay? So when that body moves with acceleration four, I’ll see it. Now if a different force acts on it — a force of three newtons — and it still moves with acceleration four, then all of a sudden I won’t see it? Why? The body is moving with acceleration four. Why shouldn’t I see it? What’s the problem? Because a different force acted on it? Why should I care? I don’t see the force anyway. What, does the force somehow act mystically on my faculties of perception, on my cognitive faculties, and prevent me from seeing that the body’s acceleration is now four? Where did this deceiving demon come from? This is a totally implausible solution.
Therefore I argue that the Kantian solution too should be thrown into the same trash can into which Hugo Bergmann throws all the other solutions in that chapter. There is no solution to this problem.
And as a result I want to claim — and this is the important move — that we have no choice but to reject the basic distinction that generates the whole problem. I too will now do a conceptual analysis. What am I saying? I’m saying the following: the whole problem arises because we make a distinction between thinking and cognition. Analytic and synthetic belong to thought; a priori and a posteriori belong to cognition. What I’m really saying is this: in order to know information about the world, you need cognition, or observation, right? That is the faculty that brings me information about the world. It belongs to the world of cognition, of the senses, of the means by which I know the world. It does not belong to the conceptual world of thought. Thought is not supposed to add information about the world. Thought analyzes the information, but only observation brings me information about the world. Okay? That is really the framework within which this whole discussion is being conducted. That is what created the whole problem — this sharp distinction between thought and cognition.
Now I ask — or rather I say: fine, so we didn’t find a solution. There is no solution to the problem. Well then, if we didn’t find a solution, something in the framework is probably wrong — in the framework that generated the problem. And I want to claim that this sharp distinction we make between thought and cognition is the root of the problem. The distinction is not sharp. There is some blending between these two kinds of human connections, thought and cognition. There is cognitive thinking.
What does that mean? There are things that seem to us like thinking because they are not the result of sensory observation — like the principle of causality, for example, in Hume. How do I know the principle of causality? It is not the result of observation. Okay? So Kant will tell us, what do you mean — that’s just how I think. It’s simply a constraint that comes from my perceptual apparatus. I can’t perceive things except causally. Okay? Though quantum theory shakes that a bit, but Kant didn’t know that yet. That is how Kant explained it.
So what am I claiming? I’m claiming no. I know there is a principle of causality because I see it. How do I see it? Not with my eyes, not with any senses, not with measuring devices, nowhere. There is some intellectual faculty through which the intellect observes the world. The intellect functions as a cognitive power, not as a thinking power. This is non-sensory cognition — call it a sixth sense if you like. Okay? It is non-sensory cognition that enables me to grasp certain insights about the world, so that they do not arise from observation in the narrow scientific sense — sensory observation or measuring instruments — but they are still the result of intellectual observation of the world.
In other words, I want to claim that if someone kicks, and I then see the ball fly as a result — Hume says yes, but observation doesn’t tell you that it’s because of that. It tells you that first you kicked and then it flew. But the relation of “because,” the causal relation between the kick and the flight of the ball — you cannot get that from observation. Observation doesn’t show you the “because”; it only shows you that this happened first and then that happened. So how do you know it’s because of that? Kant will tell you that this is an interpretation that comes from our form of thought. And I tell you that we simply see it, that there is a causal relation between them. Not with our eyes; we cannot see it with measuring instruments or with the senses. But we see it with the eyes of our intellect. We simply see it. It is a kind of abstract cognition, philosophical cognition, intellectual cognition, or cognitive thinking — call it whatever you like.
In simple terms, what this really means — one second — what this means is that the distinction between thinking and cognition is not dichotomous in the way people usually suppose. Because if you remain with a dichotomous distinction between thinking and cognition, there is no way to ground our trust in the information we accumulate — in science, especially in science. Therefore I argue that if I assume that I trust science, then I necessarily have to adopt this conception. And it seems to me that if you examine yourselves, all of you will see that this is obvious to you. It’s just that until it is formulated, people don’t take such a possibility into account at all. But to all of us it is obvious that we have this faculty. We understand that there is a causal relation between the kick and the ball. You’re not going to sell me the story that there’s no causal relation there, that it’s just that first this happened and afterward that happened, but not because of the kick that the ball flew. We all understand that it is because of the kick. So the skeptics will say: what does “because” mean? You’re just used to it, it’s simply your form of thought — but not really as a claim about the world, not that there is really a causal relation in the world between the kick and the flight of the ball. I claim no. There is a causal relation. How do I know? Because I see it with the eyes of my intellect.
And that seeing is what I call intuition. Intuition — I have an intuition that something is true. What does intuition mean? It means that I don’t see it, right? And yet I still think it is true. What is the meaning of that intuition? After all, when I say I have an intuition that this is true, what I really mean is that I truly think it is true in the world itself, not just that I’m accustomed to thinking it’s true. I claim it is really true, but it does not arise from observation. So on what basis do I believe it is true? Necessarily, all of us — I think — feel this way: we understand that we have some ability to know things in the world not by means of direct sensory observation. That faculty I call intuition. If you like, call it faith; in my view that’s the same thing, synonymous. Faith not necessarily in God — faith in the law of causality is also faith. Faith means something I know even if I do not see it with my eyes. I simply see or experience it directly in some way. And this is not a matter of subjectivity, emotion, or inner experience; rather it is an additional tool for knowing the world, for interacting with the world.
That is really my claim, and I think it is the only solution that really holds water to the problem of the synthetic a priori, to the problem of how we accumulate information and how we can trust our scientific conclusions.
[Speaker C] Wait. Yes. A baby before it is born — if it could think, and it hadn’t experienced anything at all in the world — it’s not clear that it would have this intuition. Nachmanides, who apparently in the straightforward interpretation thinks that everything is miracle, and if we were to experience reality as miracle and without causality, where at every moment God decides every leaf and every drop, then perhaps he too would experience reality differently. But beyond that, one can also go one step further in your direction, Rabbi: if we take a Hegelian approach where the human being doesn’t stand by himself but is part of the world, then when he sees himself, his cognitive apparatus, he sees the world, because he is the world.
[Rabbi Michael Abraham] Fine, that’s a possible formulation as far as I’m concerned. Explain intuition that way, I don’t care. But still, the claim remains that we need some ability to know things in the world not by means of observation in the narrow sense — observation with the senses, scientific observation. That is the claim. I don’t care right now about the mechanism, whether I’m part of the world or whatever mystical descriptions you want to use — health and happiness to you. I’m not getting into how exactly this mechanism works. I’m only pointing to its existence. That’s all.
Now I want to move ahead just a little in trying to sharpen what this really means. Look, I spoke about abduction as an additional form of inference beyond the three standard ones: induction, analogy, and deduction. Let me bring an example that may make it…
The classic example often brought up in these contexts is black-body radiation. Radiation of a black body — an ideal black body, that is. For theoretical scientists, not experimental scientists, a black body is a body that absorbs all light rays equally. Fine? Bodies that have colors — say a red object — are objects that do not absorb red light. Therefore the red light that strikes them is reflected, and so I see them as red. All the other colors it absorbs — or relatively absorbs, or many of them it absorbs. Okay? A black body is a body that absorbs all colors, and therefore reflects none. Likewise, when I heat this body, the body also emits all colors — black-body radiation. When the body is heated, it emits radiation.
Now this phenomenon has been known for many years. When you heat a filament or a piece of metal, it naturally emits light, right? We all know that. It’s that orange light, like fire. Okay? So that, for example, is a phenomenon of black-body radiation. Or the sun — the color of the sun is also a kind of black-body radiation.
Now the question was: what exactly does the emission diagram look like, or how much does it emit at each wavelength of light? Meaning, at this wavelength it emits at this intensity, at that wavelength at another intensity — what does that look like? There were various measurements that showed us how much it emits at one wavelength, at another wavelength, and so on. At a certain stage there were two hypotheses: one for the lower wavelengths and one for the higher wavelengths, and they didn’t converge, until Planck came along in 1900 and found a formula that connects the approximation for the long and short wavelengths — and that’s what is called Planck’s formula. Planck’s formula is the complete formula that tells us how a black body emits radiation. Okay? It simply gives a graph, a graph saying how much is emitted at each wavelength. Okay? You can also write this as an explicit function.
Now Planck himself already understood that if this is the form, then probably there is some theory here according to which light is emitted in discrete packets, not continuously — photons. And Einstein, five years later in 1905, argued that these photons are not merely some theoretical entity invented to explain something; they really exist. Light really is made up of photons. And then quantum theory began, basically — and the rest is history.
Now there were two very interesting and distinct stages here. There was a first stage in which we performed induction. We saw various measurements at various wavelengths. We see how much it emits at each wavelength; suppose we had five, six, seven such data points. Then we generalized and said: the whole graph is like this. Why is that a generalization? Because once I have the graph, I can say at every wavelength how much it will emit — even at wavelengths I did not measure, right? When I measure, I measure one specific wavelength. But how do I know the full picture, what happens at every wavelength? That is the result of induction. Induction is the generalization that tells me: now I know how much it emits at every wavelength. But that’s induction. It’s simply taking particular cases and finding a general rule of which those cases are instances.
But then there was another step, and that step is called abduction. This step basically says: I have a theory that explains why the graph is this graph. Understand that getting from the measurements to the theory is not a process of induction. Induction is straightforward generalization: you have several examples and you make a rule of which those examples are special cases. But the move from examples to a theory that explains — and in the end that means quantum theory, really — the move to the theory is not generalization in the usual sense. It is not induction. It is another kind of generalization: a move from particular cases to a theory, not from particular cases to a general law that holds for all cases.
For example, take Socrates. If I say that I saw Socrates die, so he is mortal, and Moishe too is mortal — okay, then probably all human beings are mortal. That is a generalization, that is induction, right? But if someone now comes and says: look, I can also explain why people die — because they have energy, and there are mechanisms that consume the energy, and the body wears out, and therefore people die — that is no longer a generalization. It is a theory that explains the generalization. The move to that theory is called abduction. The generalization is induction; the move to the theory is abduction.
Now beyond Hume’s problem of induction, there is also the problem of abduction: how do I know that this is really the correct theory? I could come up with infinitely many other theories that would also explain this graph. Of course they would be more complicated; this theory is simpler. Who says the simpler one is true? There are many ways to formulate this difficulty. And my claim is that I simply see that it’s true with my intuition. Abduction, I think, is an even purer expression than induction. Abduction is a distilled expression of the fact that we can look at cases in reality and they become almost transparent to us. Through them we see that behind them there is some theory generating them. That seeing is what gives rise to abduction. And that is what I was talking about earlier — seeing, or cognitive thinking, or intuition — which is basically the basis for how I arrive at synthetic a priori insights.
Now this has precedents. I won’t go into it because I’ve spoken about it before and written about it too. Rabbi HaNazir speaks of “auditory logic.” Maimonides speaks of the “eyes of the intellect.” Notice these are both striking combinations. Eyes belong to the world of cognition; intellect belongs to the world of thought. What are the “eyes of the intellect”? Maimonides, at the beginning of Guide for the Perplexed. What does “eyes of the intellect” mean? It means that there is in the intellect some faculty that is a faculty of cognition, not of thought. There is an intellect that knows, cognitive thinking. I use my intellect to know the world, not through the senses. The intellect knows how to look at the world and know it.
And Rabbi HaNazir’s “auditory logic” is the same kind of combination. Logic belongs to intellect, to thought. Auditory, hearing, belongs to the senses, to cognition. Again, a combination that says there is in our intellectual capacity a cognitive faculty as well. The distinction between cognition and thought is not sharp.
The third musketeer in this triumvirate is Husserl — Edmund Husserl, a French Jewish philosopher — who also spoke, perhaps actually in these very terms, of eidetic seeing. We have some kind of ability to see ideas. Now ideas are something abstract; we do not see them with our eyes. The idea of democracy, the idea of horseness, whatever. I do not see ideas with my eyes, but I see them in some intellectual sense. This is intellectual seeing. As opposed to those who think I think ideas. No — I observe ideas, I see them. Intuition is a cognitive power, not a thinking power. That is the claim.
And that is basically the solution to Hume’s problems, in my view the only possible solution: that we have a kind of sensory-intellectual faculty, if you like, or cognitive thinking. We have the ability to know things in the world by means of our thinking. Thought is not confined inside us, merely analyzing the information brought to it by cognition while having no interaction with the world. No — thought itself draws more information about the world. In thought, not through the senses, I can do this with my eyes closed. Okay? That is really the novelty here.
And I say again: anyone who trusts science, in my opinion, at least implicitly assumes this, even though it sounds terribly mystical and terribly non-rational. I think every reasonable person feels this and assumes it, even if he isn’t aware of it. Because without it, we could not have trust in many things that in fact we do trust.
All right.
[Speaker E] Sorry, Rabbi, sorry, a side question. What you’re saying, what you’re explaining, is that intuition brings me to choose the theory, in abduction, that explains the induction in the simplest way. So does intuition lead me to choose according to Occam’s razor? Or not necessarily?
[Rabbi Michael Abraham] It could be. I think generally it is Occam’s razor, in my opinion. I’ve done quite a bit of work on this and showed that many, many forms of our thinking are actually — we’re not even aware of it — based on Occam’s razor. And we spoke about this in previous courses and previous lectures: the a fortiori argument, inference from a common principle, inference from one verse, objections, generalizations, common denominator — all those things. I argued that these are the building blocks that map out all non-deductive thinking, and I showed that all of them are implicitly based on Occam’s razor. But that’s a topic for another discussion.
Okay, I’ll stop here. Any final comment?
[Speaker C] Rabbi, Rabbi, I don’t really understand this whole discussion if, say, we take Husserl. He says: focus on consciousness, on the phenomenology of what you absorb from reality. Then people come and ask: who says that this tells me anything about reality itself? Why does that even matter to me? It’s this sort of curious boredom that says: beyond what we can experience and grasp of reality, we’re interested in what’s behind the curtain. Why is that so interesting to you? Not only am I saying it’s not interesting — I’m saying it can’t be that smart people invested their whole lives in that, because it doesn’t seem to me that what really interested them was what’s over there beyond the curtain, where in any case we’ll never get in our cognition.
[Rabbi Michael Abraham] Let me explain. The claim is that I’m not now entering the question of whether we’re talking about the world itself or the world as it appears to us. I accept the Kantian claim that science deals with the world as it appears to us, not with the world itself. I accept that claim. The only question is what justifies trusting science. Even if it speaks about the phenomenon, it is still not clear what justifies that trust, because Kant’s transcendental argument does not provide that justification. So the question is: what does? And I claim that the justification can only be this — only intuition. Therefore I don’t need to get into the question whether scientific phenomena deal with the world itself or with the world as it appears to us. I tend to accept Kant’s claim on that issue. What I reject is the grounding he offered for it.
[Speaker C] But actually, our purpose in the world is first of all to survive in it, and somehow get through it with as little suffering as possible. And if intuition and our cognitive tools are giving us, for the time being, the best path for doing that, we can’t demand more than that, and we don’t demand more than that either.
[Rabbi Michael Abraham] You’ve gotten into things I’ve spoken about — not with you personally, but in general I’ve spoken and written about them a lot. But I’d need much more time to explain this. There are several points here that I think an argument like that misses, but I’d need time for it.
Okay, so we’ll stop here. Sabbath peace.
[Speaker B] Thank you very much.