Learning from Experience – Lesson 5
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- The three arguments against rigid empiricism
- The graph: facts, theory, and simplicity
- Actualism: theory as an organizing tool and not a claim about the world
- Informativism: theory as a source of information about the world
- Intuition, subjectivity, and the similarity between the two scientific processes
- Predictions, probability, and a scientific decision against actualism
- Popper, confirmation, and the identification of actualism with thin falsificationism
- Desires, biases, and an attempt to justify the reliability of intuition
- Overfitting, experimental errors, and filtering relevant facts
- The formation of intuition, Chomsky, and innate linguistic capacity
- Wittgenstein, the rule-following problem, and the difference between mathematics and the natural sciences
- Interpreting the Torah, interpretive intuitions, and Brisk
Summary
General Overview
The text argues that rigid empiricism, according to which scientific knowledge can be built only from observations, is an illusion, because the move from facts to theory requires rationalist assumptions and intuition. Through the example of a graph with five points, it argues that observations alone do not decide between infinitely many possible theories, and therefore choosing the simpler theory rests on a non-observational consideration. From there it presents a dispute between actualism and informativism, and says that the dispute can be decided scientifically by means of a statistical argument from the history of science showing that the success rate of experiments is not zero. It later argues that excessive attachment to observations leads to overfitting and error, and that even the acquisition of rules and language requires an innate structure that precedes experience, as emerges from Chomsky and from Wittgenstein’s rule-following problem.
The three arguments against rigid empiricism
The text states that it is impossible to build comprehensive scientific knowledge solely on the basis of observations, because already in collecting the facts relevant to a theory there is filtering that is not observational. The text states that the division of facts into different scientific fields is done before there is a fully formed theory, and therefore it relies on a rationalist component. The text adds that the same set of facts can fit infinitely many theories, and therefore observations alone do not yield general information about the world without conceptual assumptions.
The graph: facts, theory, and simplicity
The text describes five measurements of the relation between force and acceleration as points on a graph, and the straight line as a theory that explains them. The text argues that infinitely many lines can be drawn through those same points, and therefore there is no purely observational way to prefer the straight line over a dashed line or any other line that fits the facts. The text says that preferring the straight line relies on simplicity and elegance, which are elements of thought and not of observation, and therefore the move from facts to theory includes intuition.
Actualism: theory as an organizing tool and not a claim about the world
The text presents a rigid empiricist view according to which every legitimate claim about the world is only the product of direct observation, and anything beyond that is speculation. The text states that according to this view the straight line is not a statement about the world but a convenient way to organize five observational facts, and therefore one chooses it because of its efficiency and simplicity and not because of its truth. The text defines this as actualism, following Zeev Bechler, in which scientific information is only what is actually present before the instruments of observation, and what is not present in that way is not scientific.
Informativism: theory as a source of information about the world
The text presents informativism as the view according to which a scientific theory is a hypothesis that contains information about the world and not merely an efficient organization of facts. The text says that the informativist too admits that theory is not observation but the product of intellectual processing, yet sees that processing as a legitimate tool that yields a claim about the world. The text argues that the informativist chooses the simple theory not only because it is efficient but because simplicity is an indication of correctness with greater probability, even without certainty and while remaining subject to empirical refutation.
Intuition, subjectivity, and the similarity between the two scientific processes
The text states that the actualist attacks the informativist with the claim that simplicity depends on the structure of the mind and on taste, and therefore cannot teach us about the world. The text presents the informativist’s answer that intuition is a cognitive tool similar to vision, and that just as one can cast doubt on vision and still assume its reliability until it is refuted, so too with intuition. The text says that both sides conduct science in the same practical way, by adopting a theory, testing it, and discarding it if it is refuted, but they disagree in interpretation over whether theory is a claim about the world or only an organizing tool.
Predictions, probability, and a scientific decision against actualism
The text argues that in an actualist world there are no predictions in the sense of expecting the result to fall on the line, because the line is no more correct than any other line and therefore every future result is equivalent. The text proposes a wager on an additional experiment and concludes that according to the actualist, if all possible results are equivalent and there are infinitely many possibilities, then the probability of a particular result on the line is zero, and therefore the experiment-success rate should be zero. The text states that this can be checked historically and statistically, and that the very progress of science and the fact that theories endure through experiments refute actualism, because if actualism were correct science would not progress and every experiment would refute the previous theory. The text adds that a consistent actualist should not get on an airplane or rely on a painkiller, because past success gives him no indication at all about what will happen next.
Popper, confirmation, and the identification of actualism with thin falsificationism
The text presents Popper, who defines a scientific theory as one that can be tested by refutation, and illustrates this with “all ravens are black,” which cannot be proven but can be refuted. The text states that a scientific theory is not necessarily true, like Newtonian mechanics, which is scientific even though it is not true, and adds that the theory “there is God” is not scientific because it cannot be scientifically confirmed, though the question of its truth remains open. The text brings a criticism according to which, in Popper, even after many successes one can only say that the theory “has not yet been refuted,” and it identifies this view as actualist, emptying science of any positive claim to truth, whereas a confirmation-based view claims that the more tests a theory has withstood, the higher the probability that it is correct, and in this way it expresses informativism.
Desires, biases, and an attempt to justify the reliability of intuition
The text confronts the claim that intuition is influenced by desires and therefore “we create reality as we want it,” and rejects it on the grounds that the statistical consideration shows that intuition does hit reality, because the success rate is not zero. The text admits that there are biases and subjectivity and presents scientific tools to minimize them, such as comparing the work of researchers from different cultures and checking whether they converge on similar results. The text argues that even if there is abuse and localized deception, the actualist makes a stronger claim, namely that we have no possibility at all of being right, and the text states that this claim is false because science “proves itself” by working.
Overfitting, experimental errors, and filtering relevant facts
The text returns to the graph and adds another point that moves away from the line, presenting three possibilities: tailor a complex line that passes through all the points, draw a least-squares line, or delete the exceptional point as an experimental error and keep the straight line. The text states that exact fit to all results is overfitting and a bad method that leads to a mistaken theory, and that in actual scientific practice people tend to identify an exceptional point as something that “went wrong” and ignore it. The text connects this to the earlier arguments about choosing relevant facts and dividing scientific domains, and demonstrates that even before there is a final theory, a rationalist filtering already takes place regarding which facts belong to the law being investigated. The text concludes that not only is intuition needed in order to move from facts to theory, but that without it, sticking to observations alone is a “proven guarantee of error.”
The formation of intuition, Chomsky, and innate linguistic capacity
The text presents a common claim according to which intuition itself is built from prior experience, and rejects it with the mathematical argument that for every set of facts one can build infinitely many theories, and therefore experience alone does not select the correct theory. The text argues that even if learning is not conscious, there still must be a rationalist component that mediates the generalization from the facts. The text brings Chomsky, who argues for an innate linguistic capacity that makes language acquisition possible, and explains that nobody encounters all possible sentences and yet children produce new sentences, so there must be a structure prior to the examples that filters the infinite possible generalizations. The text states that anyone who disagrees with Chomsky misses a mathematical point, because without such a structure everyone would form a different “language” on the basis of the same examples.
Wittgenstein, the rule-following problem, and the difference between mathematics and the natural sciences
The text describes Wittgenstein’s “following a rule” problem, according to which every rule is learned through finite examples, and from here arises the difficulty of how one understands that same rule when infinitely many rules fit those same examples. The text illustrates this with the sequence 3, 5, 7, which can continue to 9 as the odd numbers or to 11 as the primes, and adds that one can generate infinitely many rules that would yield a different continuation, so there is no “right and wrong” in mathematics independent of interpretation and the structure we share. The text argues that in science the situation is different because one can empirically test the generalization against the world, and it turns out that a large portion of generalizations succeed in experiments, so the innate structure does not merely synchronize us with one another but also fits reality. The text states that Wittgenstein gets tangled when he turns this into a “game,” and that in the natural sciences the world owes us nothing, so empirical success itself proves that actualism is mistaken.
Interpreting the Torah, interpretive intuitions, and Brisk
The text affirms that in every interpretive field there are intuitions that prevent drift into arbitrary interpretations, and rejects the claim that the only intuitions are moral ones. The text argues that even in the study of Kodashim and Taharot among the Briskers, intuitions operate of “what makes sense and what doesn’t make sense,” and that without them there would be infinite possibilities and not just the two possibilities of a conceptual inquiry. The text argues that Rabbi Chaim “throws out possibilities” that are not reasonable but refrains from deciding between the possibilities that passed an initial filter, and adds that Abaye and Rava did make decisions by means of an additional dimension beyond the consistent presentation of the two possibilities. The text concludes that disagreement over decision does not prove that the analysis is incorrect, but rather that there is an additional component that leads to preferring one possibility over another after they have been clarified.
Full Transcript
[Rabbi Michael Abraham] Last time we talked about—or I finished last time by talking about—three arguments, or three angles, all of which lead to the conclusion that empiricism, this feeling as though you can build complete scientific knowledge only on the basis of observations, is a kind of illusion. We saw this through the question of how we actually collect the facts relevant to a theory, how we divide the collection of facts at all into different scientific fields, how we group a fact or a set of facts that belong to the same field before you even know what that field is saying. And the third argument dealt with a collection of theories that explain the same set of facts—right, with that graph. And in all these arguments, what comes out is that observations alone can’t give us general information about the world, especially scientific information. Rather, in the accumulation of scientific knowledge—and really in the accumulation of knowledge in general—there are rationalist components. Not everything can be based on observation, or observation alone can’t give us the whole thing.
Now, I ended last time with an argument that I went through quickly, and I said I’d expand on it a bit today. It’s the argument connected to that graph, basically the last argument. The claim is this: let’s say we have a set of points marked here with empty circles, right, these five points: one, two, three, four, and five. We measured the relation between force and acceleration, and we got these five measurements, the empty circles. Usually we draw a straight line through these points. They all lie on a straight line, and therefore the scientific conclusion suggested by these five measurements is that the relation between force and acceleration is linear, a straight-line relation. That straight line is basically the theory that explains this set of facts. Right? The points are the facts we observed, what came out of observation. The straight line is the theory.
Now we can see that the facts alone aren’t enough to explain the theory. Why? Because these facts can be explained by infinitely many theories, or infinitely many lines, that pass through the five points. One of them is drawn here, this dashed line, right, this line that also passes through the five empty points. So seemingly that theory is equivalent to the theory of the straight line. Both of these theories explain all five measurements, and so we really have no purely observational way to distinguish between the theories or to prefer one theory over another. And yet every scientist you ask will tell you that we choose the straight line. Why? So there is some sort of consideration here that is not observational, because from the standpoint of the observations themselves, all the lines are equivalent. So when I choose one line out of infinitely many possible lines here, I’m choosing it not on the basis of observation but on the basis of what seems simpler to me, or something like that, more elegant, and therefore I choose it.
Now, simplicity and elegance are elements that belong to thought, not to observation. In other words, our intellect produces them, not observation of the world. So we see—this was really the third argument—that the path from facts to theory is a path that involves quite a few conceptual assumptions, not just observations and that’s it.
Now, that was the third argument, which came to show us the importance of intuition in the process of accumulating knowledge. But I already tried to make use of this diagram, this graph, in order to say something else as well. Because in fact there is a philosophical dispute—and that’s what I did quickly, and now I’ll do it a little more systematically and carefully—there is a philosophical dispute over how to relate to scientific theories.
There is a rigid empiricist view that says: everything I can say about the world is only what I saw, the result of observation. If that’s so, then what I can say about the world, in terms of the picture described here, is only that acceleration number one has force number one, acceleration number two has force number two—these five measurements. That’s what I can say in a verified way about the world. That’s the result of observation. Anything I say beyond that is speculation. So when I say that the relation between force and acceleration is a straight line, I actually cannot make that claim—that the relation is a straight line—on an observational basis alone, and therefore it isn’t legitimate. It cannot be a legitimate claim about the world. According to the rigid empiricist, the only legitimate claims about the world are just the products of observation, nothing more. That is, without adding anything to the observations. Every time I add something to the observations, that’s speculation. I can’t take it seriously as a claim about the world.
And what that means, basically, is that the straight line, or the theory, is not a statement about the world, does not claim something about the world. It is only a convenient tool for us to organize the facts we observed. We have five facts that we observed. They can be organized in many ways. They can be organized through this dashed line, or through many other lines that pass through these five points, and they can also be organized on the basis of the straight line. These are simply different ways of organizing the five facts. The facts are what I observed—that I know, that is established. That is empirical knowledge. The theory is nothing but an efficient form of organizing the facts.
Now if that’s really the case, then there’s no problem, because obviously I’ll choose the straight line, since the straight line is the simplest, the most convenient, the most effective, and therefore I choose it. But notice: I choose it because it’s convenient and efficient, not because it’s true. Because the theory—the straight line—is a theory. The theory is not a true claim about the world but a convenient way of organizing the facts I observed. And that is the simplest organizing form and therefore also the most convenient. So why choose a complicated organizing form if I have a simple organizing form that is equivalent to it? In other words, empirically there is no way to distinguish between them, so I choose the simple one. But I choose the simple one because of its simplicity, not because of its truth. It’s just more convenient for me. I can’t claim that the relation between force and acceleration really is a straight line. That would be an unscientific claim. I can say that all the results I’ve seen until now lie on a straight line. And that’s true, because that is a claim only about the results; it is not a claim about the line. I cannot claim that the line is a correct theory about the world. That’s from the strict empirical standpoint, right, which isn’t willing to depart from observation, isn’t willing to use anything that isn’t direct observation.
Now according to this view—I called it actualism, following Zeev Bechler, who wrote several books on philosophy; he’s a professor of philosophy of science, now emeritus, at Tel Aviv University. He wrote Three Copernican Revolutions, wrote several books, he even has a kind of trilogy on this topic, though the books are quite different. And there he defines actualism versus informativism. What I’ve described until now is basically what he calls actualism.
What is actualism? Actualism means that scientific information is only information that is actually present before my instruments of observation. And that means these five points on the graph. What is not actual, or not present in a tangible and direct way before the eyes, is not scientific. So that’s what he calls actualism.
When actualism looks at the scientific process, at the scientific outlook, it describes it in the same way we’re familiar with. Meaning, suppose now I do another experiment, and in this experiment I get, let’s say, I measured acceleration number seven and the force I got was this force, right here, corresponding to this point. In other words, it doesn’t lie on the straight line. What will the actualist do? The actualist will say not that it has now been shown that the straight line is not true—I never thought it was true to begin with—but rather that it has been shown not to be useful for explaining the facts known to me, the observational facts, because it doesn’t explain this fact. And therefore I need to give it up. I give it up because it stops being useful, not because it stops being true. True it never was. Only now it’s not useful, because it doesn’t—it doesn’t explain the facts, or rather, it doesn’t organize the facts, let’s put it that way. Not explain, but organize the facts. And therefore I give it up. In other words, the process of refuting a theory, or confirmation and refutation, what we call it, exists in the actualist picture exactly as we’ve always known it. Exactly the same.
So that’s one view. Let’s call it the actualist view. Opposed to it stands the informativist view. The informativist view says that the theory, not only the facts we observed, but the theory itself contains information about the world. When I say there is a straight, linear relation between force and acceleration, that is a claim about the world. It isn’t just a convenient way of organizing facts for me. I’m claiming that this is the law that correctly describes what happens in the world. Okay? That’s what’s called informativism. The claim that says that theories are not just tools for organizing facts, but theories are hypotheses about the world that I learn from the facts.
And informativism basically says that it is a view that is not rigidly empiricist. It is willing to accept claims about the world that are not the result of observation. Because you have to notice: even the informativist does not say that the theory comes only from observation. That is not his argument with actualism. He too understands that what comes from observation is only the five points we observed. The straight line is some result of mental processing that we do to those data. But he argues that this processing is a legitimate tool that can yield information about the world. And he doesn’t claim that it is observation—the theory is certainly not observation. But despite the fact that it isn’t observation, since he is not a rigid empiricist, then despite the fact that it isn’t observation, he is still willing to accept the product and to see it as a claim about the world. The product is the theory, right? The straight line.
Now ask the informativist: why do you choose the straight line and not, say, the dashed line we see here? He too will tell you: because it’s simpler. So the actualist will ask him: fine, simpler is very nice, but who says it’s truer? After all, you’re claiming not only that it’s a more efficient or simpler organizing tool. You’re claiming that it is also more correct. And now I ask: on what basis? You don’t have observations that give you that. The observations also fit this strange line. So what is it? You think it’s simpler. So I understand why you adopt this theory. I just don’t understand why you think this theory is a claim about the world, that it is true. All you can say is that this is the simplest way to organize the facts. Because if you don’t observe it in the world, you cannot make that claim, you cannot see it as a claim about the world if it did not come from observation. That’s what the actualist claims.
The informativist says no. Once it is simpler, I claim that simplicity is an indication of truth, and not only an indication of the efficiency of a theory, as the actualist says. The actualist says: I also choose the simplest theory. I choose it because it is the most efficient, not because it is the truest. The informativist says: no, I choose the simplest theory because it is the truest. Again, nothing is certain, nothing is definitely true. It could be refuted in the next experiment. But for now, in light of the data I have at this stage, as far as I’m concerned this is the candidate to be the correct theory. The highest probability. There is never certainty, but I claim that it is not equivalent to all the other theories. Its chance of being correct is much greater than that of any other theory. And now we have to do experiments to really see whether that’s true or not. If you asked me how I relate to it—this is the theory that, as far as I’m concerned right now, is the closest thing to the correct theory.
[Speaker C] But what is that? Is it emotion? What is it? He claims that what is simplest is truest, but how does he ground that?
[Rabbi Michael Abraham] He claims that what is simplest is truest. Not emotion, but intuition, a judgment, a rational insight. That’s what he thinks. Now really, this raises the question: on what basis? After all, the actualist claims against the informativist that the fact that something seems simplest to you is because your way of thinking, or your brain, is built in a certain way. Obviously if our brains were built differently, then something else would seem simpler to us. The question of what seems simpler to me than something else is a matter of taste. In other words, someone with a completely different kind of thinking from ours might find this strange dashed line simpler than the straight line. Right? Someone with crooked eyes will see the straight line as crooked, and some crooked line will seem to him the simpler straight line. So the question of what is simple and what isn’t simple is a function of how my thinking or my brain is built. Why should that say anything about the world? That is basically what the actualist asks the informativist.
And the informativist claims: my intuition tells me that this is correct. In other words, this is a certain kind of seeing of things, or seeing of the world, that yields scientific theory. That’s what the informativist claims: intuition is a cognitive tool. And we talked about this—it’s a cognitive tool, meaning a means by which I can know the world. And the recognition that the straight line is more correct is a recognition that is the result of intuition. My intuition tells me that the simpler thing is also the truer one.
Now, what would the scientific process look like from the informativist perspective? Exactly the same as from the actualist perspective. There is no difference at all. In other words, the informativist does not claim that the straight line is certainly correct. He adopts it for the time being. Let’s say if he now does the same experiment we mentioned earlier with acceleration number seven and finds that the force is here, right, this force, not on the straight line, he too will throw away the straight line. Right? The straight line has been refuted. We did an experiment and the experiment showed that the straight line is not correct. So the informativist too does not see the straight line as the last word, as something that is certainly true. As far as he’s concerned, there is a higher chance that it is true than any other theory, but of course it is still subject to empirical testing. The informativist agrees to that too.
In that sense he is not detached from empirics or from observations. He just isn’t a rigid empiricist. He doesn’t see observation as the only admissible thing on the path to scientific knowledge about the world. But clearly he is subject to observations. Whatever the observations do not confirm, whatever the observations refute, he will obviously discard. The informativist too will discard it. It’s not that he belittles observations.
So basically he too will behave in the same way as the actualist. He will posit the simplest theory, do an experiment; if the experiment confirms the theory, he will stay with it; if the experiment refutes the theory, he will discard it and look for another theory—for example, the theory of this curved line here, which really does fit the finding I got here, including this finding. So maybe he’ll adopt that theory.
[Speaker C] So Rabbi, what exactly is the dispute between the actualist and the informativist? Is it whether to give weight to intuition? Is that basically the dispute, or not?
[Rabbi Michael Abraham] Yes. Is intuition a hallucination—as the actualist claims—something subjective, just the way you’re built? The informativist says intuition is a tool similar to what the eyes are. After all, the great skeptics can tell me to cast doubt even on what I see with my eyes. And who says, after all, that your eyes aren’t deceiving you entirely? But the point is: to me it is obvious that when I see, it is also obvious to me that sight is a reliable instrument. In other words, what I see really exists. In the same way, with intuition, when the skeptical actualist comes and says to me, who says your intuition isn’t deceiving you? I’ll tell him: intuition is a kind of seeing. I see, and so it is obvious to me—or not obvious, but highly probable—that what my intuition tells me is also true, unless I measure and see that it isn’t. But with high probability, yes; for now I adopt it.
Even with vision, if it turns out that I suddenly have a fata morgana, then truly I also won’t accept what I see. But my basic assumption is that what I see does indeed exist. If there is an experiment showing that it doesn’t, then fine, I’ll have to change that assumption or decide that in that particular case it doesn’t work. The same thing with intuition. That’s what the informativist claims.
So that is actually why philosophers treat the dispute between actualism and informativism as a philosophical dispute. It cannot be decided scientifically. Science proceeds in exactly the same way whether we are in an actualist framework or an informativist framework. There is no difference. Science will proceed in exactly the same way. The question belongs to philosophy: how do you relate to the theory you currently have in hand? The actualist will say: I treat it respectfully—respect it but suspect it—but I don’t put any trust in it. For the moment it is the most efficient organization of the information in my possession, but it is no more correct than any other theory that fits the information in my possession. Right? The straight line is no more correct than this curved line. Both fit the information in my possession. That’s what the actualist will say. The informativist will say: no, the straight line is simpler, and therefore as far as I’m concerned it is also more correct.
So basically this just means doing exactly the same science, progressing in exactly the same way, doing experiments, discarding theories, confirming theories—everything proceeds in exactly the same way in the actualist picture and in the informativist picture. The whole difference is only in the interpretation of how I relate to the theories I arrive at through science. Are these theories claims about the world, or are they efficient organizations of the information I’ve accumulated until now? So this is basically just a philosophical dispute over how to relate to theory. But as to what the theory will be, the actualist and the informativist will agree. They will always choose the simplest theory.
[Speaker C] And according to the actualist, how do you make predictions? Again—according to the actualist, how can you make predictions?
[Rabbi Michael Abraham] He predicts, but he doesn’t relate to predictions as predictions. He simply says: this theory has not yet been refuted. Let’s put it to a test. If the experiment “succeeds,” so to speak—succeeds meaning it also stays on the straight line—that means I don’t need to throw out the theory; it is still efficient. Not that it has been shown to be correct, but that it is still efficient. If it turns out that it doesn’t stand up to the next experiment, then it must be discarded. But I do not claim that the next experiment ought to sit on the straight line. Because the straight line is no more correct than any other line. There are no predictions in the actualist world. All right? But again, that’s a philosophical difference. It doesn’t matter because he’ll do the same thing. Seemingly it’s only a philosophical difference.
Now, what I wanted to claim is that this treatment of the dispute as though it were a philosophical dispute that cannot be decided by scientific tools or by any tools at all—just a matter of what you think, whether you’re an actualist or an informativist, but there’s no way to discuss it, no way to decide the dispute because it’s a philosophical dispute, a question of your starting point—I think that’s wrong. This is a dispute that can be decided scientifically. Not even philosophically by philosophical arguments—scientifically it can be decided.
And what I propose is the following claim. I’ve now done these five experiments marked here by the empty circles, right? One, two, three, four, and five. Now I ask: I’m now doing one more experiment, let’s say point six. Okay? What do I do now? I’m an informativist and I have an actualist friend. Now I want to bet with him. Let’s bet on what the result of this experiment will be. Right? We’ll apply a force of a certain magnitude and see what—or we’ll bring the body to a certain acceleration and ask ourselves—because here acceleration is the independent variable, never mind, that’s not really how it happens in life, but that’s how it’s drawn on the graph—and let’s see what force we’ll get, what force produced it.
Okay? So what is the actualist supposed to answer to that? There’s no way for me to know. Right? Because the straight line is no more correct than any other line. It’s what fits the results I’ve gotten until now, and it’s also the simplest, so for the moment I adopt it. And I’m not claiming that it is more correct than any other theory. So from the standpoint of the actualist, this result and this result, or any other result you find here, doesn’t matter—they are equivalent. Fifty-fifty chance. Right? And since there are infinitely many results—okay? This whole line all the way up contains possible results—there are infinitely many possible results. So from the standpoint of the actualist, what is the chance that the result will be this one? Zero. Right? If all results are possible and have equal weight, and there are infinitely many results, then the chance of a particular result is zero.
The same thing here, right? Do experiment seven. What is the chance that the result will be this and not this or this or this or this—all the results on this line? Zero. Right? In short, the actualist is supposed to assign no chance at all to the next experiment succeeding. Succeeding meaning that it too falls on the line that describes the current theory, the straight line in this case, say.
Okay? And this is true for every line, it doesn’t matter. What will the informativist say? The informativist will say: I think the straight line, because it is simple, is also more correct. I’m not saying it is certainly correct. Future experiments may refute it. But in my eyes the probability that it is correct is much higher than that of any other line. Which means that if I now have to bet on what the result of this experiment will be—acceleration number six—whether the force will be here or here, say between these two options, the actualist will say fifty-fifty, I’ll wager one shekel against one shekel. Okay? The informativist will say, what are you talking about—ten to one. Or I don’t know, depending on how much confidence he has. The more results there are on the straight line, of course, the more his confidence grows. But for the sake of the discussion, let’s say I bet on it at ten to one. I think most likely the result will be this. It could be this, and then indeed it will refute the theory of the straight line. But most likely the result will be this.
Now notice: here it already starts to become a practical difference between the actualist and the informativist. Earlier I said there was no practical difference. But I need to show whether this practical difference can be tested experimentally. And the answer is of course yes. What does that mean? Let’s do the experiments and see how many experiments the current theory fails in, and how many experiments the current theory succeeds in.
According to the actualist, the number of experiments—or the percentage of experiments—in which the current theory succeeds is supposed to be zero. Right? Because there is no chance that the next experiment will give me a result that falls on the current theory, since that is one result out of infinitely many possibilities. So from his standpoint the probability is zero. Which means: if we take all the experiments ever done throughout history that tested some theory that was considered correct at the time, and then another experiment was done and it was tested—according to the actualist, all those experiments, maybe one by chance not, but in principle all of them should have failed. There is no chance that they succeed. Zero percent, right? The chance that they succeed is zero.
According to the informativist, clearly not all of them succeeded; there are theories that were refuted. But the number of experiments that succeeded is not zero percent. Maybe fifty percent, thirty percent, sixty percent, I don’t know, but a significant percentage, not zero. Okay? We said there is no certainty. A simple theory can be refuted, but the chance is not zero.
Now this can be checked. Let’s look at all the experiments done until now and check how many succeeded and how many failed. You understand that the actualist is obviously wrong. If the actualist were right, there has not been a single successful experiment in the history of science until today. And that also means that no scientific theory can survive even one experiment ahead. Every time we’d have to refute the scientific theory—the next experiment refutes the next theory, the next experiment refutes the next theory, and so on.
You understand? After we did, say, this experiment, all right, we got this result. Now we draw, say, this line, okay? What is the chance that this experiment will give this result? Now I hold that this line is the correct one, right? Zero, according to the actualist, right? Same thing, because it can give any result whatsoever; this line has no preference. So the next experiment too will fail, and then I’ll change the line again, and then the next experiment will fail too, and so on. In other words, according to the actualist, science cannot progress. Every experiment you propose fails.
[Speaker B] How many experiments do you need in order to have a straight line?
[Rabbi Michael Abraham] There isn’t—infinitely many.
[Speaker B] No, I mean, at what point—how many experiments do you need to show they’re on a straight line, and then you say this really is a straight line?
[Rabbi Michael Abraham] No, according to the actualist—
[Speaker B] You can never prove that it’s… No, I mean according to the informativist.
[Rabbi Michael Abraham] According to the informativist, you say, what, five experiments are already enough. But they’re enough with a certain probability. If you did more experiments, then your certainty that the straight line is the correct one is higher, and that’s all. But this isn’t one or zero. According to the actualist, you’ll never know that the straight line is the correct one. Never. The probability doesn’t rise; it stays zero. Say I did a hundred experiments, from one to seven, I divided it into a hundred points, and in all of them I got the straight line. Understand that I can still draw some crazy curve—not one crazy curve, infinitely many crazy curves—that stitch together all those points. You can never create a set that only one line strings together, right? Every discrete set of points has infinitely many curves that pass through all the points. That’s a theorem in mathematics. And since that’s so, there is no number of experiments that will convince the actualist that the straight line is also true, not just that it’s the simplest. There isn’t one. Now you understand: science doesn’t work that way. Obviously, if I did five experiments, or fifty experiments if you like, a hundred experiments, the scientist would stake his head on the claim that the straight line is the correct one. Now what am I saying? Could it be that it was just a coincidence that a hundred experiments succeeded? There’s practically no chance in the world. Maybe at high speeds it would change, but within the interval I tested, there’s no chance that it’s accidental. There’s no chance you’ll discover here, between one and seven, some point that won’t fall on the straight line if I measured, say, a hundred points in that interval. No chance in the world. No scientist would deny that; anyone who denies it is crazy. So what does that actually mean? It means that actualism is a philosophical theory that all of us—including the actualists themselves—clearly know is not true. A philosophical approach, yes? Or a philosophical conception; it’s not a theory in the scientific sense. But somehow, for some reason, this debate just keeps going forever and never gets settled. There is decisive scientific proof that resolves this debate. Statistical proof. The fact is that science advances. The fact is that a non-zero percentage of the experiments carried out throughout history succeeded. So how can one go on holding an actualist position? Fine, Bickel devoted books to this, but in none of them—in all his books—did he bring even one argument showing why actualism is not true. There are only attacks on actualism there, but there’s no argument showing that actualism is not true, or why actualism is not justified in its criticism of informativism. He doesn’t explain that either. I claim that he’s wrong because intuition is a cognitive tool. That’s the explanation. But I also have a proof for that explanation, because actualism is refuted by the history of science. The history of science refutes it.
[Speaker D] Rabbi, I don’t understand—does an actualist not get on an airplane?
[Rabbi Michael Abraham] Why are you coming as if I don’t understand? A consistent actualist, yes—if he’s serious about it—then he shouldn’t get on an airplane. He shouldn’t rely on any technological device, any scientific finding, because after all this is all only cognitive forms of organization of the information I have now, and there’s no chance that in the next experiment it will continue behaving the same way. So why assume the plane won’t crash on its next takeoff? There’s no indication. The fact that until now it worked, from the actualist’s point of view, means nothing. That’s Hume’s problem of induction. The actualist says Hume’s problem of induction is absolutely correct. I really agree: Hume’s problem of induction is a hard problem, and therefore the theory that comes out of induction is not true. It’s only an efficient way of organizing the information, but it’s not true in any sense. So that means you can’t rely on anything. How do you know that the next Tylenol you take won’t kill you? True, until now it lowered fever and everything was fine; it generally didn’t cause severe damage. But so what? If something happened until now, does that mean it will continue? Who said so?
[Speaker B] Sorry, but just to understand: once, say, there are now five points on the graph sitting, say, on the straight line, is the probability that the next point will also fall on the straight line, statistically, also infinite just like the probability that it won’t fall on the straight line, or is the probability now lower?
[Rabbi Michael Abraham] Probability has to be defined when you have a sample space and a distribution. Now you have to decide what the distribution of the theories is—of the lines. In other words, what is the chance that each line is the correct one? Okay? Assuming all lines are of equal value—that’s what the actualist claims—that all lines are equally correct, simplicity is not a criterion for truth, so from his point of view all the lines are equivalent. If all the lines are equivalent, then all the possible next results are possible too. And therefore the chance of getting one particular result among them is zero. By the way, that’s not the same thing—the chance of getting one result among all other results is not equivalent to the chance of getting one line among all the other lines—but those are paradoxes in statistics, I’m not going into them now. There are other interesting statistical paradoxes relevant to this.
[Speaker B] The informativist would say no.
[Rabbi Michael Abraham] The informativist would say: the pattern convinces me because until now it worked, so it’s probably true. Sometimes his plane will crash; sometimes he’s wrong. But the fact that that doesn’t always happen is an indication that informativism is the correct approach and not actualism. That doesn’t mean informativism gives me scientific certainty—there is no certainty in science—but it does mean that the scientific theory that has stood up to tests is the reasonable theory, the leading candidate to be the true theory, until proven otherwise. Okay? That’s basically equivalent to the Popperian conception. I mentioned Popper—I think I mentioned him. Popper defines a scientific theory as a theory that can be subjected to a falsification test. Because if you say the theory is that all ravens are black—well, you can’t prove that, because you can never know that you’ve seen all the ravens, but of course you can refute it: if you see one raven that isn’t black, you’ve knocked down the theory. So he says: if so, you can’t prove a scientific theory; you can refute a scientific theory. If so, when we want to define what a scientific theory is, the definition cannot rely on proof; rather, it has to rely on refutation. He says a theory will be considered scientific if it is falsifiable. Now a theory such as Newtonian mechanics is a scientific theory. As it happens, we already know it’s a scientific theory that is not true, but it is still a scientific theory. Why? Because it can be subjected to a falsification test. A scientific theory does not mean a true theory. That’s only the definition of whether it belongs to the scientific category or not. But the theory that God exists is not a scientific theory. Not because it isn’t true, but because it cannot be scientifically confirmed. It cannot be subjected to a falsification test. And still, the question of whether it is true or not is an open question. I do not identify scientificity with truth. But Popper’s definition is that a scientific theory is a theory that can be subjected to a falsification test. That is a scientific theory. Now one of the criticisms of him is that according to Popper, however many experiments you do, and all the experiments so far have confirmed the theory, all you can say about that theory is that it has not yet been refuted. You can’t say anything at all about it being true or more true. And that is a very thin conception of science. Because basically science only tries to refute theories, to throw theories away. Science can never tell me that the theory in my hands is true. It can only tell me that so far it hasn’t been refuted. But there are many theories that so far haven’t been refuted. There are infinitely many theories that so far haven’t been refuted. So what do I choose—the simplest one? But the simplest one is not the truest one. One criticism of Popper is basically, implicitly, that Popper is an actualist. Because Popper claims that the theory doesn’t really—at least on the scientific level—say something scientific about the world. Rather, it is a way of organizing the information I have. And therefore all you can do is refute a theory. Popper’s critics, for example, argue that a theory can also be confirmed. True, you can’t prove it—that’s obvious. But you can confirm it. If the theory has stood up to more tests, then it is better confirmed. The probability that it is true is higher. Because there is a difference between whether you did five experiments between one and seven, as we have here—or between one and five, sorry—as opposed to a situation where you did a hundred experiments in that interval. If you did a hundred experiments in that interval, clearly the theory is more grounded, more confirmed. According to Popper, no. It only means that so far it hasn’t been refuted, but I can’t say anything positive about it. Okay? So you understand that this debate between confirmation and falsification—whether there is such a thing as confirmation, or whether all there is is only falsification—is precisely the debate between informativism and actualism. It’s the same debate. Because what does confirmation actually say? That the theory, although of course it is a generalization and it doesn’t come only from observations, is confirmed. That means it is a good claim about the world. Not certain, but good. And the more tests it has passed, the better it is. So confirmation hides informativism behind it, and the Popperian criterion hides actualism behind it. That’s basically the…
[Speaker D] Rabbi, if in fact it comes out from this that intuition here is very, very central—in other words, our attitude toward scientific theory, how seriously we take it, how willing we are to take risks on its truth, on its correctness, basically depends on our intuition—and it’s quite reasonable that our intuition is influenced by our desires, then the Rabbi is really explaining very clearly why we create reality the way we want it, since we really
[Rabbi Michael Abraham] describe
[Speaker D] and understand it according to what we are—according to intuitions, and intuitions are very much connected to our desires and our beliefs and our world.
[Rabbi Michael Abraham] Wait, wait—exactly the opposite. My whole argument—what he just said—is an attempt to show you that our intuition is true, not why we adopt intuition. Rather, this is a proof that intuition works. Because the fact is that the percentage of experiments that succeed is not zero. So that means we are hitting reality itself. On the contrary: all I came to prove is that my use of intuition isn’t only because that’s how I’m built—that’s what the actualist claims.
[Speaker D] No, no, I mean to say—obviously—but Rabbi, when you adopt that intuition, when you imagine it and define that intuition, it is certainly influenced by your desires.
[Rabbi Michael Abraham] That’s the actualist criticism, and therefore he says don’t trust it. And I’m showing him…
[Speaker D] No, but we agreed he doesn’t exist—after all, he himself flies on airplanes—this is a nonexistent personality. But I’m talking about informativism: how much an informativist…
[Rabbi Michael Abraham] What difference does it make? The criticism you’re raising exists. It’s an actualist criticism.
[Speaker D] No, I’m not saying criticism, I’m saying facts. I think that’s reality.
[Rabbi Michael Abraham] No, your facts are mistaken. You think that’s reality, and you’re wrong. Here—your intuition was mistaken here. Why? Because I showed you by a statistical consideration that you’re wrong. It works. Otherwise it wouldn’t be expected to hit the results of experiment.
[Speaker D] No, but you test it after you’ve created that theory. You create the theory on the basis of intuition. And if you didn’t have that intuition from the start because you wanted exactly the opposite—let’s take an extreme example—you’d go to some racist professor in Nazi Germany and he created an entire doctrine of racism, and he has all the proofs and theories, and you tell him, listen, maybe create another theory—no, the intuition…
[Rabbi Michael Abraham] Not beforehand—wait—I’m not telling him to create another theory. I’ll do an experiment and show him he’s wrong. But when I create my theory, he won’t be able to find an experiment that refutes it. Maybe he will, but not at a high percentage. That’s an empirical claim. That’s exactly the point. I’m not arguing why it is worthwhile to adopt this intuition—not a psychological claim about why people adopt intuition. I’m trying to show that intuition works, that it is true. Although apparently it is influenced by desires and wishes and interests and biography and environmental and social influences—all true. The fact is that despite all that, all that is included a fortiori, as Tosafot say on the Talmud, right? Despite all these flaws, this theory works—meaning this approach, sorry, works. It explains the facts. So that means this criticism is not correct, this criticism that desires distort intuition, and so on. It’s true that in science they developed all sorts of tools—which are all non-empirical, by the way—but tools to minimize the subjective influences on intuition, which certainly do exist. How? For example, let’s take people of different types, from different places, from different cultures; they’ll all work on the same scientific fields and we’ll compare the results. If we all arrive at the same theory and the same results, that means apparently it’s less likely to be influenced by our subjective environment. And then we’ve cleaned away, at least partially, these influences. At the end of the day, after we do all that, science is a good instrument; the fact is that we make progress, we succeed in building things, things that work. So you can’t deny that. And if actualism were right, and if it weren’t justified to trust intuition because it is influenced by all kinds of biases, as the ethicists say, then we wouldn’t have science today. And the fact that we do have science today—and that is exactly the strength of this argument. This argument doesn’t explain psychologically why I adopt intuition. The actualist will explain that; he claims it’s a psychological phenomenon. I claim no: I have proof that it is correct, it works. That’s exactly the point.
[Speaker D] No, but a large part of our biases is survival—that planes should fly and theories and telephones should work and science should work. But when we have those corners where we want science not to work because we want to do something else
[Rabbi Michael Abraham] we
[Speaker D] may fall into that.
[Rabbi Michael Abraham] Listen to what you’re saying. We have a tendency to be right, and therefore we are right. What kind of argument is that? The fact that it works, the fact that we really survive. We want to survive, but the question isn’t why we want to survive; the question is how it can be that we succeed in surviving. Since we want to survive, and therefore we adopt good scientific intuition that gives a good scientific theory. But what does “good” mean? According to an actualist there is no such thing as good; it’s not within our reach. We have no way to know which theory
[Speaker D] is good. I’m not supporting the actualist. I’m talking about the informativist: when he chooses for himself that theory to which he gives a certain trust until then—and gets on airplanes—he usually wants to survive, wants the economy to work and the machines to work, and therefore it
[Rabbi Michael Abraham] works in the test of the outcome.
[Speaker D] Excellent—no, that’s perfectly fine. I also think, rightly, that it stands the test. But I’m only saying that in those corners where he wants something else—when he’s a Nazi and decides that he wants to be racist and see the Jew as a subhuman—then he’ll be able to find in science all the explanations and proofs for the theory.
[Rabbi Michael Abraham] That doesn’t touch us in any way. I’m talking about the question whether our intuition gives us theories that work, that are true. And the answer is yes. You claim there are situations in which intuition misled us or will bring us a theory that isn’t… true, I agree. Who said not? I said so. Sometimes even without distortions, intuition isn’t right—not because of distortions but because we missed it. And the next experiment will show us that we’re wrong. No problem—I didn’t say intuition is a perfect tool. I didn’t say our environment or our desires don’t influence intuition. What I said is that intuition is a tool for reaching truth, and it’s not a shot in the dark. With all its limitations—and it has limitations—we don’t have a better tool than this. And not only do we not have a better tool than this, but this tool proves itself quite well. Even if not with certainty, and even if not always. That’s the claim. The fact that there is misuse, that there are tendentious people, that sometimes people are mistaken—obviously, all true, we’re all human beings. But the actualist claims something stronger. He claims that we are always wrong. That is, we have no possibility whatsoever of being right. That isn’t true. Okay, so that is basically the argument in more detail, the argument I gave last time. But it says a great deal for our subject in terms of learning from experience, because it means that everything I said in the previous lessons—that intuition is a cognitive instrument, that I adopt it because adopting it is actually the only thing that can justify the trust I place in the information I have accumulated—now we simply see it in a scientific form, or a more quantified form. Okay? So what I’ve now shown is basically a proof of this point, that it works and is not just a hypothesis or a proposal. Until now I had only offered a proposal; I said: if one wants to believe in science, then one need not get excited by empiricist and skeptical attacks. One can say that my intuition is a cognitive tool and trust it. And therefore that is at least a possibility. Now we’ll choose it philosophically; whoever believes in it will choose it, and that is legitimate. And whoever doesn’t believe in it won’t choose it, and that too is legitimate. But I, as someone who believes in intuition, need not be alarmed by empiricist attacks. That was the situation up to this argument. What this argument shows is that not only do I not need to be alarmed by these attacks and am legitimate like they are—no, I am more right than they are. Not that I’m legitimate like they are. This is not survival in the sense that they didn’t succeed in destroying me. I succeeded in destroying them. In this we have advanced one more step beyond the philosophical arguments I gave until now that led to trust in intuition. Until now, those were philosophical arguments: you can adopt it, you can choose not to adopt it, depending on your philosophical outlook. What I’ve now shown is that it’s not only that trust in rationalism is possible, but that rationalism actually works. There is statistical evidence that it is correct. And that is a strong claim, okay? Now I want to show something else on the same graph, another important point—because all these things will serve us later, so for now I’m just laying the groundwork. I’m bringing back the graph. Let’s now look—suppose we did not five experiments but six. Fine? So we did one, two, three, four, five, and six. Leave seven aside for the moment. We did one through six, okay? And the results came out as all the white empty circles and this and that. That’s what we got in the experiment, that’s what came out. Okay? Now the question is: these are my results—what is the theory? Or what is the line, actually, that I’m going to draw? There are several possibilities. Someone could come and say: I’ll draw the dashed line, what is drawn here. But of course there are infinitely many such lines that pass through—this time I already have six points. Think of this too as an empty circle, yes? So I actually have six empty circles representing my observations, the empirical facts. These six circles can be stitched together by infinitely many lines. And in this case, the line I drew here is not even the simplest among them. Okay? So that is one possibility: to move to other lines and try to look for the simplest among them. What one usually does in science is not that. What one usually does in science is say: if this whole thing looks like a straight line, then maybe it’s not exactly this straight line but a straight line that passes roughly like this, and the results—of course there are experimental errors. So the results didn’t fall exactly on the line but in its vicinity. And then one draws what is called the least-squares line. Yes, I draw a line and I look for a line such that its distance from all the points I got in the experiment is minimal—the sum of the distances, the sum of the squares of the distances, is minimal. Yes, that’s the mathematical definition; it doesn’t matter. I draw the straight line that is optimally close to all the results I obtained. Okay? That’s what they often do. Because overall, in experiments, results—an experiment never falls exactly on the line. If someone comes with a graph that worked and all the results fell exactly on the line, know this from a former teaching assistant and lecturer: he copied it or faked it. It never falls on the line. It falls in the area. So the line basically symbolizes for you more or less where it should have fallen. But in practice the results always fluctuate—effects of air, friction, heat, it always deviates a little from the line. Therefore you draw some line that is the optimal line, the one closest to the entire set of points. They define some criterion for what counts as closest—it’s least squares for those who know—but it doesn’t matter. They define somehow how the minimal distance comes out, and that’s what defines the line. But—and this is more familiar to people in machine learning and those areas, though scientists know it too—if really, say, I got these five results. And this result too—here too there’s an empty circle. What would we actually do? We wouldn’t draw a least-squares line. We would draw this line and say that this was an experimental error. In other words, we would erase this result; apparently there was some problem here, some involvement of an element we didn’t take into account—we’ll erase it. Because the rest of the points fall on a straight line. It’s not likely that five points would coincidentally lie exactly on a straight line and one would suddenly fall far away. If one fell far away, that means something went wrong here, and my theory is this straight line. Fine? To draw a line that stitches together all these points, including this point too—that is what in the language of machine learning is called overfitting. Overfitting is the attempt to fit the line, to force the line, to match completely and exactly all the experimental results. And as is well known, that is a very bad way to arrive at the correct theory. A very bad way. This method will usually bring you to the wrong result, even though supposedly it is the most precise. It’s the line that most precisely stitches together all the results I got in the experiment. And everyone will tell you that whoever does that reaches a clearly, unequivocally wrong theory. He will reach a wrong theory. Why? Because life is more complicated. There are results that really slipped because something interfered there and we didn’t notice—there was some mistake in this specific experiment, experiment number six. Doesn’t matter what. Something interfered there that wasn’t there in the other cases. And since that’s so, if everything else falls on a straight line, it is reasonable to assume that the straight line is the correct one and this is an experimental error. Much more reasonable than this overfitting, and even more reasonable than the straight least-squares line, which would come out something like this roughly—something passing here with a slightly steeper slope. That’s the least-squares line. In other words, basically among the three possibilities—either this crazy line, which is the overfitting, or the straight line that is least squares, which is this line, or this straight line, which simply doesn’t fit this point at all and ignores it—the result that is probably correct is this straight line. Now notice: what this overfitting actually means is exactly what I showed in the first consideration. Remember with Napoleon and with Semmelweis, with the question of which facts are relevant to the theory? Because that is exactly what I did here. I have six facts, and now I want to build a theory. What do I do when I erase this fact and claim that only these five are relevant? I am basically choosing five out of the six facts and declaring the sixth an irrelevant fact. In this case because of an experimental error or something else that was involved here, but not because of the law I’m interested in; it doesn’t belong to the law I’m interested in. That is exactly what a historian does when he examines why Napoleon lost at Waterloo, and exactly what Semmelweis did when he examined what caused puerperal fever in his ward. He took various facts—he had no idea which facts were relevant—but he decided in advance that some facts were not relevant, he erased them, and some facts were relevant, and he tried to build a theory on the basis of the relevant facts. He constructed the relevance of the facts before he knew the theory. He had some intuition about what the theory might be; that’s how I explained it there. Basically, notice that the logic at work here is the same logic as overfitting. Because what I’m doing here is: I still don’t know what the theory is, I have results. This result, this result, this result, this one, this one, and this one. I have six results. Okay? Now I need to decide what the theory is. I still don’t know what the theory is, and lo and behold, without knowing what the theory is, I tell you that this point is an experimental error and erase it. And I choose a subset of the facts that are the relevant facts. And now I have a theory that explains them—that’s the straight line. And it turns out, astonishingly, that this works much better than those who cling to empirical observations—that’s the overfitting—those who try to create a line that will fit all the facts we observed, who are unwilling to do any rationalist filtering of facts. We only have observations. What you think is relevant or not relevant—speculation. That’s not interesting. Let’s see the facts. And here through the back door you have another indication that relying on facts, first, is not enough to understand the correct theory, and second, whoever relies too much on facts will usually arrive at the wrong result. You have to decide which facts are the relevant facts with which you can build your theory. And these are two… If now in this graph I proved or demonstrated the third argument, then in the overfitting, where I collected this point, I demonstrated the first two arguments, which told us how we choose some of the facts as the relevant ones for explaining the phenomenon, and how I divide the facts in the world into different domains, each of which will be explained by a different theory. Why is this physics, that chemistry, that biology? Or this thermodynamics, this mechanics, this electromagnetism—that’s the division within physics. Right? Those were the first two arguments that showed us there is a rationalist element here. That is exactly what is happening here. I choose some of the facts, throw out some of the facts that don’t fit, and explain only this part with the theory. These are the relevant facts to the theory. These are the relevant facts for determining the relation between force and acceleration. This fact is not relevant if I’m looking for the relation between force and acceleration, exactly as Napoleon’s mother’s height is not a relevant fact if I’m looking for the explanation of why Napoleon lost the Battle of Waterloo. Even before I have the explanation, I already say: this fact is not relevant. To rely on all the facts is overfitting. That’s not right, it’s not good. It will bring me to the wrong result. In other words, we see that this very… or this example—it’s not a model, it’s an example—this very simple example demonstrates the three arguments that show us why it is impossible to build scientific theory without intuition. Why science cannot rely only on observations. Not only is something more required—components beyond observations are required—but if you do not bring in those components, it’s not merely that you won’t have a theory; you’ll have a wrong theory. Whoever clings to observation is guaranteed to err. That’s quite surprising. Whoever clings to observation will make a mistake. You need intuition in order to prevent errors—not only to get from facts to theory, but to rule out wrong theories, to rule out irrelevant facts. And this goes very far, at first glance… after all, people are used to thinking that the best science is science that clings to observations and adds nothing to them. That is very bad science. Science that clings only to observations and adds nothing to them is science that wouldn’t work. It wouldn’t have advanced a millimeter beyond Adam if that’s what we had done all the time. All the time we are filtering which facts are relevant and which are not relevant, which theories are plausible and which are not plausible. These filters are not empirical; they are rationalist. Okay, that’s a remark about overfitting and the previous two arguments we saw. Now I want to…
[Speaker D] Rabbi, isn’t this intuition of ours, in the end, also influenced by a certain empiricism, in that we made some kind of generalization on the basis of…?
[Rabbi Michael Abraham] So I said—I talked about this in the previous lesson. I said there is the common approach—not only is there one, the common approach is—that our intuition itself was built on the basis of previous experiences. Built from experience. Maybe it wasn’t formulated that way, but basically somehow our brain got organized, or learned, from the facts we observed until now. Experience is what shaped our intuition. So I answered that last time: that cannot be true. Mathematically it cannot be true. Because there too, after all, that experience is basically building insights or theories on the basis of facts. But after all, on the basis of any set of facts you can build infinitely many theories. So how does unconscious experience select the correct insight from among infinitely many others? You have to assume that besides experience, we have some additional rationalist tool that accompanies learning from experience. And even if it serves us unconsciously, still, in that unconscious dimension that shapes our intuition—sorry—on the basis of our experience, there too a rationalist dimension is involved. Because there too, basically, what we are doing is generalizations on the basis of facts, only we do it unconsciously. But generalizations on the basis of facts always require additional components that are not factual, not observational. Therefore we do not escape this; we only retreat one step backward. But I’ll now raise the same argument regarding the formation of intuition, and I’ll show that even in the formation of intuition, intuition was involved. Always. There is no way—you cannot start from bare facts and arrive at insights. If you assume we are born tabula rasa, yes, with no prior assumptions, today we would still be with no general information about the world. Nothing. With the information of Adam.
[Speaker D] But if, say, the world were chaotic, for example—if the laws of nature changed randomly all the time, assuming one could survive in such a world—
[Rabbi Michael Abraham] You have science that explains them, and you have laws that give you laws. Who said science is correct? You understand that already in your question you assumed that the laws of science are correct. Because you’re saying that the laws of nature are stable, but that’s what science says. So therefore that doesn’t—it doesn’t help at all. In other words, at the end of the day, I don’t know what would happen to my intuition in a chaotic world. It could be that my intuition would grasp that the world is chaotic and that I have no way to understand it. I would reach the correct conclusion; it just wouldn’t help me at all. Yes, I’d be a mathematician—big deal. You reach the correct conclusion, except that it doesn’t help us at all. I don’t know whether I would develop intuitions there and they would get shattered. No, it could be that I would develop the correct intuition that this world cannot be understood, that it has no laws. So of course you wouldn’t be able to manage there. We would die very quickly. Because we would have no way to deal with all the challenges—yes, all evolution would collapse in such a situation. In other words, we would have no way to deal with survival challenges. Okay. So these phenomena actually have—have further expressions. I think I already mentioned, I don’t remember if I mentioned here, Wittgenstein’s rule-following. I don’t remember anymore. In the past—and maybe not in this series, I don’t remember if I did—and Chomsky, actually, on linguistic ability. So I’ll bring those two examples because they complete the picture. Chomsky argues—yes, Noam Chomsky, considered one of the greatest linguists, I think, Israeli or his parents were Israeli actually, but he himself was born in the United States, of course a great anti-Israel figure, as expected. And he claims that we are born with an innate linguistic capacity. Meaning, if we weren’t born with it, we couldn’t acquire language. This is a debate among linguists, but Chomsky claims that we have some kind of innate capacity. If we didn’t have linguistic capacity—and again, linguistic capacity is not a particular language, but rather the capacity in principle to absorb languages. Okay? Which language will I use? The one my environment teaches me. But my ability to absorb that language that my environment teaches me is linguistic capacity, and I’m born with that. That I did not learn. And that’s his claim. What I want to say is that this is actually equivalent to what I said here. If we didn’t have linguistic capacity, we would have no way to learn a language. Why? Because how do we learn a language? They give us examples. This is how you say this sentence, this is what this thing is called. Gradually we see how people speak, and from that we build for ourselves linguistic ability in a particular language—say, to speak Hebrew. After all, no one has ever encountered all the possible Hebrew sentences, right? We encounter certain sentences in the course of growing up, maturing, and that teaches us over time to speak very quickly. Already at a very early age we learn to speak. The examples we’ve encountered by age three are enough for us already to speak almost fully. By age three or four there are no—there are basically no speech errors. So that means that the inference we draw from the examples creates for us a linguistic theory, which is basically, say, the Hebrew language, and now we can use it and produce sentences we’ve never encountered. Now according to what I showed here, Chomsky is right on the mathematical level. Those who disagree with him are missing a mathematical point. In other words, those who disagree with Chomsky simply cannot be right. This is not a philosophical dispute. It can be decided scientifically, or in this case mathematically. If we didn’t have linguistic capacity, we couldn’t speak. Because any collection of facts we encounter could be explained in infinitely many ways. The straight line, the dotted line, everything we saw—of course these are metaphors; in this case these aren’t really lines, but the lines represent the theory that tries to explain the facts. In this case it’s a linguistic theory or rules of language that explain the examples I encountered. And I use those rules to produce new sentences that we haven’t encountered. Now if I didn’t have linguistic capacity, then every discrete set of examples I encountered could be explained by infinitely many different systems of rules, and each one of them would lead me to speak a different language. So how do we all grow up speaking in the same way? How do we understand each other in sentences we haven’t heard before? That means that we all formulate the language in the same way, even though each one of us—one person should have drawn a straight line between the points and another, if he were built differently, should have drawn a broken line, right? If we all draw the straight line or form the same linguistic rules on the basis of our examples, that means there is within us some innate structure that precedes the examples, which I use in order to understand the examples and generalize them and produce the skill of speech. And therefore there must be, as I said earlier about intuition, there must be some such innate capacity in us. This example parallels what Wittgenstein called the problem of following a rule, in the later Wittgenstein, in Philosophical Investigations, not in the Tractatus—that’s the early one. So there he says that basically whenever we learn some rule, that rule is always taught to us through examples. You can never teach us the rule directly. Let’s say you learn to count, so you do one, two, three, four, five, ten, eleven, twelve, twenty, and so on. You learn how to skip the tens, how to skip the hundreds, and that’s it—what, are they going to count with you to infinity? But in the end you can already use it and count millions, billions, and whatever you want. Okay? We make generalizations from examples. You can’t teach us the rule top-down, meaning teach the rule from above and then we’ll apply it to the particular cases. It’s always learned bottom-up. It always starts from the examples below, from which we understand the rule, and then we apply it further. Then Wittgenstein says: but something here doesn’t make sense, because every set of examples you give me has infinitely many rules that can explain it, which I can infer from them. So how can it be that you give me a finite discrete set of examples and I correctly understand the rule—exactly what you wanted to convey to me—and I use it correctly? I count to infinity exactly the way you would count, even though you would expect that from ten thousand onward each of us would continue differently, because there are infinitely many generalizations. And again, you understand that this is exactly the same problem? How do you produce a law from a discrete set of examples, when every discrete set of examples can be explained by countless laws? So how is it possible to convey a law to me through a discrete set of examples? How do we learn rules? So Wittgenstein argued that it’s some kind of game, a language game or a linguistic game. Okay? Basically there is no right and wrong answer in this context. There is no correct and incorrect rule. If someone is built differently, then from his point of view the rule is a different rule. Okay? But we have an agreed-upon game, because we are all built in the same way, we have some agreed-upon game, and the fact is that we succeed in conveying rules or generalizations to one another. And therefore—but this is a structure embedded in us, and only through it can we convey rules to one another. If someone came with a different structure inside him, he wouldn’t be any more stupid than I am, and he wouldn’t be more mistaken than I am, but I simply wouldn’t be able to teach him anything. Yes, for example, if I take the sequence three, five, seven, and now on the psychometric exam they ask you what the next number is: three, five, seven, and… what do you say?
[Speaker D] Nine.
[Rabbi Michael Abraham] Nine, right, everyone will say nine. Why? Because you assume that it’s the sequence of odd numbers: three, five, seven, nine, right? But maybe it’s the sequence of primes: three, five, seven, eleven. Nine isn’t prime; it’s three squared. Three, five, seven, eleven. Now if one person writes eleven and another writes nine, who is correct? There is no “correct” here. It depends on how you interpret the rule governing the first three examples—three, five, seven. After all, you have to derive a rule from that, and then from the rule understand what the next number is. But there are infinitely many rules. I brought you two that are trivial, intuitive, but I can generate infinitely many other rules for you, each of which will give a different result. I can tell you that the next number is minus seventeen and a third. I have no problem generating the rule that will give me three, five, seven, minus seventeen and a third. There is absolutely no problem generating such a rule. Very simple. And there’s no right or wrong here. What does that mean? It means that when we generate a general rule from a discrete and finite set of examples—not finite, rather discrete, discrete is enough—a discrete set of examples, something is intervening here besides the examples themselves, which is empirical, yes? The examples I know. Something in the form of thought, something embedded in us, something I assume, something I bring from home, I do not derive it from observation, and it is involved in the transition from the examples to the general rule. Without it there would be no way to define one general rule out of the examples, because there are infinitely many possibilities. Now with regard to the world, this is unlike mathematics, where there really is no correct answer. Three, five, seven—what’s the next number? There is no correct answer. Decide what the rule is. With regard to the world, our generalizations can be tested empirically, because our generalizations about the world are the laws of nature. The laws of nature can be tested by experiment. And it turns out that a large portion of these experiments, as I said before, work. So that means that with regard to the world, the system embedded in us is not only that the same system is embedded in all of us—that’s what you can see in mathematics, that everyone writes nine at the end. But not because everyone is right, rather because everyone is synchronized; we are built in the same way. But when we look at science, not mathematics, then we discover that not only are we synchronized, we are also correct. Because there you can conduct an experiment and see whether the generalization is correct or not, and in a great many cases it turns out to be correct. So in science we discover something that in mathematics we could not discover. In mathematics we only discovered that we have some innate structure shared by all of us, but there is no way to speak of it as right or wrong—that’s the structure, that’s how we are built. With regard to science, actualists claim that it’s the same thing there too, that there too it is only a structure we are born with, but it is not correct in any way. And then what I showed earlier would not be right. But that isn’t so. This structure we are born with is also correct. Because the fact that the generalization it produces—the generalizations it produces—also work in a significant number of cases, not in zero percent of cases. Therefore this innate system is also correct. And that goes much farther than Wittgenstein’s argument. Wittgenstein, of course, got tangled up in these things, so he claims that it’s all a game; he was basically an actualist in the language I used earlier, and he treated everything as some kind of subjective language game. But that you can say in mathematics. With regard to science, though, science works, it stands up to experiments, so what kind of subjective game is that? You can test whether you’re right or not. These are not games where we merely check that we’re synchronized among ourselves; this is against the world, and the world doesn’t owe us anything, and the fact is that it works. Okay, I’ll stop here. Does anyone have a comment or question?
[Speaker D] Rabbi, that same intuition we’re talking about with regard to interpreting the world and scientific theories—can’t we say, by extension, the same thing also about, like the Rabbi brought Chomsky and Wittgenstein, can’t we also say it about the theory of interpretation in general? That when we come to interpret, we also operate with intuition, because there isn’t—so when we—so really it’s a slightly different question from the topic maybe of the course, but of the series—but if we approach interpretation of the Torah, we come with a deep intuition for interpreting it. Right. Otherwise we’ll end up in surprising and undesirable places, and therefore it must be that the Torah is based on the one intuition we have, which is morality; we don’t have anything else.
[Rabbi Michael Abraham] No, no, no—here you already made an Olympic leap. It’s true that we come with interpretive intuitions, absolutely true. Without them you could take any verse or any set of verses and generate from it whatever you want, on the theoretical level. And the fact is that there are interpretations that make sense and interpretations that make less sense. But that “make sense” is not really “make sense”; it’s the same thing as the straight line being simpler. In every field of interpretation I would say what I said here. You also assumed in addition that the only intuitions we have are moral intuitions—that is simply not true, factually not true. We have intuitions that are unrelated to morality, and they still make sense. Look, the best example of this is that the Briskers always say that we ask only “what” and not “why,” right? We ask what is written and not why it is written. That is of course nonsense—they ask why all the time. But in order to be comfortable operating with this strange ethos, it is no accident that they focus on sacrificial law and purity law, right? In Brisk they always study sacrificial law and purity law. Why? Because in sacrificial law and purity law it has nothing to do with morality and we’re not supposed to have any intuition there; there we can be mathematicians. We bring no intuition from home regarding impurity and purity or regarding sacrificial matters. But the fact is that even in Brisk, and in general when people study sacrificial law and purity law, at every step of the way—and elsewhere too—we use interpretive intuition. What makes sense and what doesn’t make sense. And that has nothing to do with morality in any way. That’s why the Briskers choose that area. We have interpretive intuitions independent of morality. Morality too is made up of intuitions we have, but it is not true that only morality forms our interpretive intuitions. Absolutely not.
[Speaker D] But when you go to a Brisker and say to him, okay, you described, you explained nicely the conceptual inquiry, the two sides of the dispute—fine, so tell me, what do you rule? Which side do you take? They never take a side. And why don’t they take a side? Because they didn’t really understand the root of the dispute from the moral side; rather they took some kind of conceptualization, an abstract conceptualization detached from life, and so in the end they’re left with an empty tool when they come to issue a Jewish law ruling, and they send it to Rabbi Elchanan to issue the Jewish law ruling, or someone else.
[Rabbi Michael Abraham] Rabbi Yitzchak Elchanan. You’re mistaken. They definitely toss out—they toss out many possibilities. There is no passage in Rabbi Chaim where you won’t see that he throws out possibilities that do not seem plausible to him. It’s not true that he lays out all the hypothetically possible options. There are lots of things that don’t make sense and he discards them. There is no passage in Rabbi Chaim without that. The illusion that he is engaged in mathematics is an illusion he sold to himself and to others, but anyone who reads it with unbiased eyes sees that it’s not true. At every step of the way he has intuitions about what makes sense and what doesn’t make sense. Otherwise there would be infinitely many possibilities, not two. It’s true that among those that remain he is careful not to decide, in order to preserve that same illusion that we understand nothing, we’re just mathematicians.
[Speaker D] Fine, but doesn’t that itself prove the point, Rabbi—that when in the end he remains without the ability to decide between the sides, after doing this impressive inquiry, doesn’t that prove that he didn’t… After all, Abaye did decide. Abaye didn’t say, I understood the inquiry, both sides are good, maybe Rava is right, maybe I’m right, I’m leaning a bit this way, I don’t know. He decided and banged on the table and said: I’m right. And Rava said the opposite. So that means Rabbi Chaim didn’t understand the root of the dispute at all. He conceptualized it in some detached way, but he didn’t get to the root of the matter. The fact is that he cannot decide. He cannot take a side.
[Rabbi Michael Abraham] Not true. Rabbi Chaim presents two possibilities, each of which is consistent and logical in its own right. He doesn’t know how to decide between them. But Abaye chose possibility A, and Rava chose possibility B.
[Speaker D] How? How can both… the inquiry is so successful, both sides are so logical, so how did Rava decide? How did Abaye decide?
[Rabbi Michael Abraham] About this successful inquiry you’re saying that it’s not correct? It is correct. It’s just…
[Speaker D] No, I’m saying it is correct, but it doesn’t reach the root of the matter. It’s on the surface. There are many levels. On the linguistic side, on the analytical side, everything is fine. But when you come to the root of the matter, they don’t…
[Rabbi Michael Abraham] He didn’t reach the root of the matter. Let’s try to separate between two things. To that claim I partly agree. Rabbi Chaim really does make a survey that is in a certain sense superficial. All in all he presents all the possibilities that pass the initial filter. There are still possibilities that he throws out, as I told you earlier. But he leaves the possibilities that passed the initial filter. Among them he does not allow himself to decide. By the way, it’s not certain that he didn’t have an intuition that would decide, but he did not allow himself to decide. Abaye and Rava did allow themselves to decide. But that doesn’t mean that Rabbi Chaim did not explain Abaye and Rava correctly. It only means that after he explained them correctly, there is an additional dimension that helped Abaye on the one hand and Rava on the other choose which possibility they preferred and which possibility they rejected. Okay? That Rabbi Chaim didn’t have. Agreed. That’s why he turned to Rabbi Yitzchak Elchanan. Anyone else? Okay then, have a peaceful Sabbath.
[Speaker D] Thank you very much.
[Rabbi Michael Abraham] Goodbye.