Platonism – Lesson 37

Table of Contents

• Framework of the discussion: scientific Platonism, judging favorably, and Occam’s razor
• Actualism versus informativism in the philosophy of science
• The example of gravity: law versus a generating entity
• Agreement about scientific practice and the dispute over its meaning
• Induction, abduction, and David Hume
• The background: empiricism versus rationalism
• Philosophers of science, Kuhn and Popper
• Kant: analytic/synthetic and a priori/a posteriori
• The Kantian solution: phenomena and noumena, and the critique of it
• The claim of empirical resolution: the graph experiment and the probability of predictive success
• Critique of the actualist’s consistency, and the example of airplanes, medicine, and surgery
• Conclusion: informativism, scientific Platonism, and the decision against Aristotle
• Organizational notes and questions from the audience

Summary

General overview

The speaker concludes a series on Platonism and moves to scientific Platonism through the philosophy of science and Occam’s razor, while rejecting Matan Binyamin’s interpretation according to which “judging favorably” and Occam’s razor are pragmatic rules rather than factual claims. He presents the dispute between actualism and informativism as a dispute over the status of scientific theory: is it merely a convenient arrangement of observations, or is it a claim about the world and about theoretical entities such as the electron and gravitational force. He describes the empiricist versus rationalist background and Kant’s formulation of the problem through synthetic a priori propositions and his phenomenal-noumenal solution, and criticizes it as a speculative retreat that does not solve the difficulty. Finally, he argues that the dispute is decided empirically in favor of informativism through the success of scientific predictions throughout history, and concludes that on the scientific plane there is a decision in favor of scientific Platonism and against Aristotle.

Framework of the discussion: scientific Platonism, judging favorably, and Occam’s razor

The speaker places the lecture as a continuation of the series on Platonism, while he is in the middle of a discussion of scientific Platonism on the way to the mathematical realm. He ties the opening of the discussion to the trigger of “judging favorably” and to an article by Matan Binyamin that connects that directive with Occam’s razor. He says that he does not agree with Matan Binyamin, both regarding judging favorably and regarding Occam’s razor, because in both cases we are dealing with factual truth and not merely existential or pragmatic truth.

Actualism versus informativism in the philosophy of science

The speaker presents actualism as the view according to which a scientific theory is a convenient arrangement of facts that says nothing about the world, because only what is actually observed can count as a fact. He defines informativism as the view according to which the theory itself is a claim about the world, including commitment to theoretical entities that have not been directly observed, such as the electron. He explains that the actualist uses the assumption of electrons or forces only as a convenient organizational and explanatory tool, whereas the informativist sees the phenomena as an indication that there really are electrons in the world, or a force that generates them.

The example of gravity: law versus a generating entity

The speaker distinguishes between the law of gravity as a description of phenomena and observations of motion and acceleration, and “the force of gravity” as a theoretical entity that explains why the law is true. He says that the actualist accepts the law as a consistent description of motion but rejects the claim that there is a real “force,” because no one has seen the force itself, only its consequences. He presents the informativist as someone who accepts both the law and the existence of a gravitational force in the world, and sees the theoretical entity as an explanation that justifies the law and not merely a way of speaking.

Agreement about scientific practice and the dispute over its meaning

The speaker argues that there is no empirical difference between an actualist and an informativist in terms of scientific conduct: in both cases people create generalizations, build theories, subject them to tests of falsification, replace a failed theory, and continue this way in the progress of science. He defines the difference as a philosophical dispute over how to interpret the process, where the actualist sees theory as explanatory convenience only and does not speak about discovering truths about the world, while the informativist sees the replacement of theories as getting closer to factual truth.

Induction, abduction, and David Hume

The speaker distinguishes between induction as generalizing from particular cases to a general law, and abduction as finding an explanatory theory that adds theoretical entities. He explains that the challenge presented at the outset is aimed mainly against abduction, that is, against the move to theoretical entities, while an actualist can still accept induction as a valid tool for use even without committing to the existence of generating entities. He mentions David Hume as someone who challenges induction as well, but says that not every actualist is committed to that Humean challenge.

The background: empiricism versus rationalism

The speaker presents actualism as a consequence of empiricism, which recognizes only what is given in direct observation, and therefore rejects commitment to the existence of theoretical entities. He presents informativism as rationalism, which is willing to accept claims about the world even when they are not the product of observation, out of trust in processes of thought such as generalization, abduction, and the principle of causality. He formulates the point of dispute as the question whether the fruit of non-observational thought is a tool for knowing the world or only a description of the form of human thinking.

Philosophers of science, Kuhn and Popper

The speaker argues that an actualist view is more common among philosophers of science than among scientists. He presents Kuhn as an extreme expression of actualism, in that he sees scientific theory as a sociological creation of a community with its own language and norms. He presents Popper as someone who sees theory as something more objective than Kuhn does, but still remains committed to the idea that one can only falsify a theory and not confirm or prove it, and in that way preserves an empiricist dimension.

Kant: analytic/synthetic and a priori/a posteriori

The speaker describes Kant as formulating Hume’s problems through a distinction between a logical axis of analytic versus synthetic propositions and an epistemic axis of a priori versus a posteriori. He says that Kant claims that the philosophy before him mistakenly identified the divisions so that every analytic proposition is a priori and every synthetic proposition is a posteriori. He explains that laws of nature such as the law of gravity are synthetic because they do not follow from an analysis of concepts, but they also cannot be derived from observation alone because they require generalization and inference, and therefore they appear to be synthetic a priori propositions and give rise to Kant’s question: “How are synthetic a priori propositions possible?”

The Kantian solution: phenomena and noumena, and the critique of it

The speaker presents Kant’s solution as a distinction between the world as it is in itself (noumena) and the world as it appears in consciousness (phenomena), and says that the laws of science are claims about phenomena and not about noumena. He illustrates this through the tree that falls in the forest, where “sound” is a phenomenon in consciousness while pressure waves are what takes place in the world, so the description has a basis in the world but its appearances are categorical within consciousness. He argues that Kant pays the price of giving up full objectivity in favor of intersubjectivity, and brings a critique that tries to push this into solipsism by arguing that one cannot know that there are noumena beyond phenomena. He presents another critique through an example involving Newton’s second law, and argues that the Kantian explanation does not explain how the limits of cognition decide between alternative physical laws, and therefore it is seen as speculation that deepens the problem instead of solving it, in the image of an “English-English dictionary.”

The claim of empirical resolution: the graph experiment and the probability of predictive success

The speaker presents a graph of measurement points and shows that different curves can pass through the same points, while the straight line is chosen because of its simplicity according to Occam’s razor. He argues that the dispute between actualism and informativism becomes sharper in the question of what the chance is that an additional experiment will yield a point that falls on the simple line: the actualist is committed to the idea that the chance is almost zero, because there is no factual preference for the simple line, whereas the informativist is committed to the idea that the chance is significant, because simplicity serves as an indication of correctness. He says that one can decide this empirically through the history of science, because most experiments in practice confirm existing theories and theory replacements are rare, and therefore the rate of success fits not with “zero” but with informativist confidence.

Critique of the actualist’s consistency, and the example of airplanes, medicine, and surgery

The speaker argues that if actualism were correct, science would just spin in place without progress, and today’s knowledge would not surpass primitive knowledge, because predictions would fail almost all the time. He says that in practice no one lives as a consistent actualist, because people get on airplanes, take medicine, undergo surgery, and rely on concrete and steel without living in a “Kafkaesque” world of being unable to predict anything. He concludes that actualism is a “colossal philosophical mistake” and even a “scientific mistake,” and argues that its basic assumption is contradicted by the historical facts of science’s success.

Conclusion: informativism, scientific Platonism, and the decision against Aristotle

The speaker concludes that when one builds a scientific theory, it is not merely a statement about us but a claim about the world, including commitment to theoretical entities such as gravitational force and electrons. He argues that cumulative predictive success places science on a Platonic rather than Aristotelian foundation and provides a scientific decision in the ancient dispute between Plato and Aristotle in the sense of scientific Platonism. He defines scientific Platonism as the claim that the theoretical entities one reaches by theoretical tools are entities that exist in our world even though they are not directly observed, and announces that next time he will explain the significance for philosophical Platonism and conclude with mathematical Platonism.

Organizational notes and questions from the audience

The speaker corrects a misunderstanding about the lecture time and clarifies that with the switch to daylight saving time, the Friday lectures will be at eight-thirty, and he apologizes for the confusion. He responds to a question about Newton versus Einstein and quantum theory by saying that even if Newton is not correct in every domain, it is not arbitrary, and it remains as a valid approximate description at low speeds. He responds to the question that the actualist “also gets on an airplane” by saying that the actualist is not consistent, and presents the Kantian as someone who can formulate the concern in terms of phenomenal experience. He compares it to the question of determinism and free choice and the charge of “illusion,” and distinguishes between behaving in accordance with experience and the psychological implausibility of claiming extreme risk without actually being afraid.

Last time I started talking a bit about the philosophy of science, because I’m basically wrapping up the series on Platonism with a look at scientific Platonism and mathematical Platonism. So right now I’m in the middle of the discussion of scientific Platonism. We started with judging favorably, because that was really the trigger for this whole discussion. We saw that Matan Binyamin, someone who wrote an article on this topic, grounds the instruction to judge someone favorably in Ockham’s razor. He basically says that in both cases we’re dealing with pragmatic truth and not existential truth, and not truth in the objective factual sense. And I said that first, I don’t agree with his interpretation regarding judging favorably, and second, I don’t agree with his interpretation regarding Ockham’s razor. In both cases we’re talking about factual truth, not existential truth. So I spoke about judging favorably, and now I’m in the middle of Ockham’s razor. I gave a short overview of a dispute in the philosophy of science between what Bachler calls actualism and informativism. Actualism is an approach that sees scientific theory as some convenient arrangement of the facts that says nothing about the world. When I arrange the facts in the form of a scientific theory, that’s basically the most convenient way for me to look at the facts, but it’s not that I’m claiming that the scientific theory is true in some sense in the world itself. Why is it called actualism? Because actualism basically says that the only things I can regard as true facts in the world are the things I actually observed. The theory I built on the basis of those observations is not a claim about the world. It is not actually present before my eyes. It’s a theory sitting in my feverish mind, but it’s convenient for me to use it because it organizes the facts well. Informativism, by contrast, claims that the theory itself is also a claim about the world. When I construct a scientific theory, I am basically saying that in the world there are theoretical entities of the kind that this theory talks about, such as the electron. No one in the world has ever seen an electron. Even today, with electron microscopes, we see some kind of fingerprint of the electron, but not the electron itself. Nobody sees some little ball moving from place to place. So in that sense the electron is a theoretical entity; it’s not an object we observed. And as such, the actualist will say: I’m not claiming that there is an electron. I’m saying that the collection of facts I observed fits together in a way that is very convenient for me if I assume the existence of electrons, so it’s useful for me to do that, and therefore I use that theory. The informativist says no, I see this as an indication that in the world itself there really are electrons. That’s why these phenomena happen; that’s why I see these phenomena, because the electrons are what produce them. And therefore the informativist says that theory contains information about the world. That’s why it’s called informativism. In other words, not only what is actual before my eyes is a claim about the world, but also the theory, which I do not observe. How is this dispute related to the dispute between empiricism and rationalism? There is a connection; I’ll get to that in a moment. How is this dispute related to the dispute with empiricism? Yes, yes, I’m saying, there is a connection, I’ll get to that shortly. Just one simple example so we can understand the difference. When we talk about the law of gravitation—I may already have given this example—when we talk about the law of gravitation, the law of gravitation simply describes what happens when two objects with mass are at some distance from one another. The law says they attract each other with a force proportional to the inverse square of the distance. If the distance between them is r, then the force is proportional to one over r squared. So this is a description of the facts; you can see the law of gravitation as a description of the facts. I always see that when there are two objects with mass at a certain distance, they begin to move, and this law determines what the acceleration will be, how they will move, in what direction, with what magnitude of acceleration, and so on. So the actualist will say that’s all I can say about the world. The informativist says no: if they move, then I assume there is something causing that movement, and that something is called force—the force of gravity. The force of gravity is not the law of gravitation. The law of gravitation only describes the phenomena: that they move, with what acceleration, in what direction, and so on. The force of gravity is some entity that exists in the world and brings about the law of gravitation. Because there is a gravitational force, that is why the law of gravitation is true. So the actualist will say: gravitational force is just my way of speaking; no one has ever seen the force itself. What we see are its practical consequences, namely that the objects move, but nobody has ever seen the force itself. Therefore the claim that there is a force is not a claim about the world. It’s convenient for me to think about these situations by picturing something like a little demon called gravitational force that causes attraction between different objects. The informativist, by contrast, claims that not only is the law of gravitation true, but there is also in the world a gravitational force. And because of that force, the law of gravitation comes about, and the law of gravitation is true because there is a gravitational force in the world. So he claims that gravitational force, for our purposes, is a theoretical entity. The theory has created a certain entity that no one has ever directly observed, but we infer its existence because it helps us explain the phenomena. What we actually see is only the motion of the objects, not the forces, but we assume there are forces because that seems to us to be a good explanation of the motion of the objects. So the informativist claims that there is a gravitational force in the world, and the actualist says no: there is only a law of gravitation—not “there is” a law of gravitation, but rather the law of gravitation is true and describes the world; however, there are no entities, or at least I cannot claim that there are entities, that produce this law. It’s only my form of expression. It is convenient for me to think about things that way simply because my thinking is structured that way; it’s convenient for me to think in those terms. So that is basically the difference between informativism and actualism. Now, we saw that the difference between these two approaches is a philosophical difference. What does that mean? There is no empirical difference at all between them. Whatever those with an actualist view do, those with an informativist view will also do, and vice versa. According to everyone, when we have a set of facts, we generalize and build a theory—generalization, induction, and abduction, yes?—and construct a theory. According to both approaches, we will then subject the theory to a test of falsification, meaning we will try to perform an experiment that checks whether the theory predicts the results correctly or not. If it predicts correctly, we have corroborated it. If it does not predict correctly, we have falsified it. And if the theory is falsified, then we throw it out and try to find another theory that will also explain the experiment that refuted the previous theory, and so on. In other words, once we have the new theory, again we subject it to a test; either it survives or it is falsified. If it is falsified, we replace it with another theory, and that is how science constantly advances and builds theories that contain more and more, explain more and more observations. Okay? Regarding the description I just gave, neither the informativist nor the actualist disagrees; they both agree. The difference between them is only a philosophical difference. The difference is over the question of what this process means. The actualist says this process doesn’t mean very much. I’m simply collecting facts; now I have a larger accumulation of facts about the world. As for the explanations—the theory that explains these facts—that is a claim about me, not about the world. You can’t say that I’m now discovering more and more truths about the world, and that once I replaced the theory I discovered a truer theory. It isn’t truer; it’s simply more convenient for explaining more facts, that’s all. But I’m not asserting it as a claim about the world. The informativist, by contrast, says I am constantly getting closer to the correct theory, yes, to the factual truth about the world. So you see that the difference between informativism and actualism is philosophical. In terms of scientific practice, they both conduct themselves in exactly the same way. They will both replace theories to the same extent: if one replaces, the other will also replace; if one keeps it, the other will also keep it; if one generalizes, so does the other; if one decides the theory has been falsified, so does the other. The whole process. Why doesn’t the actualist take this all the way and say that even the law of gravitation itself—we describe it that way because it’s convenient for us, but it is not a claim about the world? That is David Hume’s question, where he basically says: not only abduction should be challenged, induction should also be challenged. Abduction—I’ve now remembered, I think I explained this—induction is a generalization from particular cases to a general law, and abduction is finding a theory that explains the general law, one that includes theoretical entities and all sorts of things of that kind. So what I presented until now is a challenge to abduction—who says the theory is true? But I assumed that induction—that is, the claim that the facts are also true in objects I didn’t observe—is valid. In other words, the doubt was only about abduction. In fact, of course one could also challenge induction, because who says that what you saw will in fact continue to happen? But that is not actualism. That is, an actualist can accept Hume’s induction as a true principle. What does “true” mean? In the sense that it is productive, that it is proper to use it—let’s put it that way. But he only claims that the theoretical entities generated by abduction do not exist. He too will assume that the next experiment will yield the same result. In other words, he accepts induction; he sees abduction as a claim about me. Okay, so Hume’s challenge certainly exists, but not every actualist shares Hume’s challenge. Sometimes he is only saying: I don’t trust theoretical entities; no one has observed them. But I do trust that any two masses will move according to the law of gravitation, because I do accept induction. If I’ve seen it until now, I have no reason to assume it won’t continue. It’s only when you tell me that this is because of some force—that’s an invention. You’ve never seen it, and you never will see it, so why assume it exists? So this is a more fundamental challenge than the challenge to induction, and therefore it is not certain he will share that. If you are Humean, then you also challenge induction. Now, what are really the reasons for this dispute? Why does the actualist restrict himself and the informativist not? So basically I already said it. In some senses, what stands in the background here—and this is what Shmuel remarked a moment ago—is empiricism versus rationalism. In other words, actualism is basically a consequence of an empiricist approach. That is, if you are an empiricist, you basically believe only in things you observed directly. And therefore obviously, regarding theoretical entities that I have not observed directly, I cannot claim that they exist. I can use them because it’s convenient, and so on—that’s related to Ockham’s razor—but I cannot claim that they really exist, that they are objective truth in some sense. The informativist is a rationalist. A rationalist means someone prepared to accept claims about the world even if they are not the result of direct observation. He believes in generalizations, in abduction, in our intellectual capacities, our thinking capacities, as tools for knowing the world. He does not see observation alone as a tool for knowing the world. Someone like that will also allow himself to treat the products of our thought, our intellectual analysis, as claims about the world. So basically, the basis of the dispute between actualism and informativism is the question of how I relate to non-observational processes. How do I relate to findings or claims that are not the product of observation alone, but whose formation also involves thought? Can I see such claims as claims about the world? Okay? Now, just as a side comment, it seems to me you’ll see a very clear difference between how scientists relate to their science and how philosophers of science relate to it. Among philosophers of science, an actualist view is very common. I don’t know who is the majority and who is the minority, but an actualist view is common there—a view that says theory is basically a claim about people and not about the world itself. The extreme expression of that is Kuhn, whom I talked about last time, who basically sees scientific theory as some kind of sociological creation. That is, the scientific community is also a sociological community; it is a collection of people, and a collection of people develops a language and accepted norms and all kinds of things like that, and basically he sees scientific theory as some kind of… some kind of sociological creation. And that is an extreme expression of actualism. Popper, by contrast, who sees theory as—not that he points to a connection between theory and the sociology of the community—he does see it as something more objective, but still he too says that a theory can only be falsified, not corroborated, and certainly not proven. And therefore, in some sense he too assumes empiricism. That is, something that is not the result of empirical observation he is not prepared to accept, and empirically one can only falsify a theory; one cannot corroborate or prove it. But he does not tie this to sociology, but to—I don’t know what—to the form of our universal thinking. It is not a convention, as Kuhn presents it, but it is still subjective. Subjective in the sense that we are compelled to think that way. And that really brings me to the problem as I presented it earlier. If in fact the discussion here is a philosophical discussion, then let’s try to focus the problem for a moment. After all, science really proceeds in the same way both in the actualist picture and in the informativist picture. There is no disagreement about how science should proceed or how it actually proceeds. The disagreement is only over what this process means, and that disagreement is philosophical. Because it has no impact on practical life. It is only a philosophical dispute, and this philosophical dispute is basically rooted in rationalism and empiricism. Now here we discover something a bit new. We discover that the empiricist will perform the same processes as the rationalist. He too will make generalizations, he too will assume the principle of causality, he will do everything. He will only treat all these assumptions as assumptions of his mode of thinking, not as claims about the world. The informativist relates to the world itself as if the law of causality exists in it, or as if induction is a valid tool for knowing the world. The actualist says no: I will use all these tools, but I will use them simply because this is the way I think, not because this is true of the world in any sense. The point of philosophical dispute between them—and this is not scientific, it is philosophical—is the question of how I relate to the fruit of my thinking. Is my thinking a tool for knowing the world, or is the world known only through observation? Yes, that dear Mark Twain whom I keep quoting: the world owes you nothing; it was here before you. In other words, the fact that you think in a certain way does not obligate the world to behave that way too. Your brain is built that way, your intellect is built that way. So what? Fine—use it, because that’s how you work, but don’t assume that it really reflects something happening in the world itself. That is basically the claim. Therefore the focus of the discussion is the question of how to relate to the conclusions of thought processes, as opposed to observational processes, where everyone agrees that if I observed something then presumably—they are not solipsists, they are not skeptics—if I observed something then it is probably true. That applies both to the actualist and the informativist. But what about the things that I generated through thought-processes based on the observations? In other words, I have observations, I make some kind of generalization, abduction, I arrive at the law of gravitation, gravitational force, field theory if you like, it doesn’t matter, all kinds of theoretical things that I create through intellectual, conceptual tools, not through observational tools. The question is how I relate to those products. Are they claims about the world or not? Do I trust thought as a tool for knowing the world or not? Now, once I formulate it in that way—I’m doing this rather telegraphically, but the ideas are already familiar because I have discussed some of them in various contexts—once I formulate the dispute this way, we immediately come to Kant. Because Kant, when he gathered together all the philosophical problems David Hume had presented, formulated them generally as follows: first, he made a distinction between two ways of relating to claims. One is on the epistemic axis, the axis of knowledge: how do I know the claim is true? And the other is to relate to the content of the claim itself in the logical sense. What is the content of the claim? What is the claim actually saying? These are two different questions. Now, on the logical plane he divided between synthetic and analytic claims. Analytic claims are claims that analyze the subjects appearing in the claim. For example: this ball is round. That is an analytic claim, because its being round follows from the very definition of a ball. I do not need to look at the ball in order to see that it is round; I analyze the concepts that appear in the statement, and that way I know it. Therefore it is an analytic claim. By contrast, “this ball is heavy” is a synthetic claim. Why? Because not every ball is heavy. To know that this ball is heavy, I need observation. Right? In other words, it is not enough for me to analyze the concept “ball” in order to conclude that this ball is heavy. Therefore it is not an analytic proposition—analytic means analyzing—but a synthetic proposition. And synthetic means a proposition that contains information, that makes a synthesis, yes? additional information beyond the information latent in the definitions of the concepts themselves. So those are analytic and synthetic propositions, and that is the distinction on the logical axis. There is also a distinction on the epistemic axis, the axis of knowledge. How do I know that this claim is true? Here Kant says I have a priori claims and a posteriori claims. A priori claims are claims prior to observation, and a posteriori claims are claims that come after observation, claims I learn from observation. At first glance these distinctions seem independent. One is a logical division, the other is an epistemic division. What is the connection between them? But Kant says it is not so. In philosophy before Kant, philosophers basically identified these two divisions with each other. Try for a moment to think about the examples I gave. Let’s say “this ball is round.” I said that is an analytic claim. It is of course also an a priori claim, right? It does not require observation, because I can analyze the concept “ball” and understand that this ball is round. I do not need to observe the ball to see it. So that claim is analytic, and because it is analytic no observation is needed to discern it; it is enough to analyze the concepts, which is a thought process. Okay? By contrast, “this ball is heavy” is a synthetic claim. It is not enough to analyze the concept “ball” to conclude that this ball is heavy. That is a synthetic claim, and of course how do I know that this ball is heavy? By observation. So in other words it is also an a posteriori claim. Therefore, Kant says, in philosophy up until me—that’s how he put it—it was customary to identify these two divisions with each other, even though they are supposedly two perpendicular axes, yes, orthogonal. But in practice, it was customary to identify the two divisions with each other. Every analytic proposition is a priori, and every a priori proposition is analytic. In other words, this works in both directions. And similarly with a posteriori and synthetic. So basically these are two viewpoints on the same division between claims; that is how it was accepted until Kant. And Kant basically says that this is the focus of all of Hume’s problems. What does that mean? When we look, for example, at the laws of nature, at scientific generalizations, those scientific generalizations are propositions that on the one hand are clearly synthetic, right? They are synthetic because it is not enough to analyze the concepts involved in them in order to know the proposition. For example, all objects with mass attract one another with a force inversely proportional to the square of the distance—Newton’s law of gravitation. To know this law, I need observation. Right? In other words, it is not enough to analyze the concepts in order to know this law. Even if I understood the concept of mass, I would not arrive at this law just from analyzing the concept of mass. Right? It is not an analytic proposition; it is a synthetic proposition. Now I ask, that is in the logical sense. So it is a synthetic proposition. In the epistemic sense, how do I know that this proposition is true? In the naive empiricist view I say because I observed it. But now we already know that this is not true. Observation does not give the general law. Observation gives the cases that I observed, the cases that I saw. How do I know the general law that all objects with mass attract one another? That is a generalization, that is induction—I did not observe that. It is a thought-process. And since that is so, it turns out that the law of gravitation is a proposition that is, on the one hand, synthetic, and on the other hand a priori. A priori in the sense that you cannot arrive at it through observation. There are observations we make on the way to it, but the observations are not enough to get there. You also need a thought-process: induction, abduction, and so on. A posteriori? What? A priori, yes. A posteriori then? A priori. A posteriori? No, the opposite— a priori. A posteriori? The opposite, a priori. In other words, I… there are observations there, but the observations do not bring me to the law of gravitation. I analyze the observations, make generalizations, make abductions, all of which are thought-processes, not observational processes, and only that way do I arrive at the general law. So it turns out that this general law actually falls into a category that did not exist before Kant. On the one hand it is a synthetic claim—it contains information beyond the definition of the concepts involved in it. On the other hand it is not the product of observation, or not of observation alone. In other words, observation is not enough to give me this. And then the question comes back: if this is a thought-process, the world owes me nothing, so why assume that if my thought says such-and-such, that is also what happens in the world? So what Kant claims is that all the interesting claims in science, all the laws of nature, actually belong to a category that supposedly does not exist. They are synthetic but a priori claims. We know that every a priori claim is analytic and every synthetic claim is a posteriori. There are no claims that are both synthetic and a priori—claims that both contain information and are not arrived at through observation. So if it contains information, how do I know it without observation? Therefore there cannot be synthetic a priori claims. So this Kantian analysis of the different systems of propositions places the whole set of Hume’s skeptical problems into a more general perspective. And Kant formulates it and says: synthetic a priori claims—how are they possible? How can it be that there are such claims? How can it be that I can know synthetic claims without observation, in an a priori way? This basically represents Hume’s empiricism and the skepticism that accompanies it. Now, throughout the history of philosophy, all kinds of proposals were made to resolve this difficulty. This is really the most fundamental problem in epistemology, I think—certainly in the philosophy of science. And in Hugo Bergmann’s book called Introduction to the Theory of Knowledge, in chapter nine—the chapter is called “The Rationality of the World,” rationality with a shin and a kaf—in that chapter Bergmann goes through all the philosophical solutions proposed for this problem and rejects them all. There is no solution, including the solution Kant proposed. But the solution Kant proposed is essentially the only solution that was ever seriously proposed for this problem. So now we have to pay close attention. I’ll try to describe it briefly and also explain briefly why I think it does not solve the problem. The difficulties are not mine; I’m only summarizing. So Kant basically says this: in order to solve this problem, he makes a distinction between the world as it is in itself and the world as I perceive it. What are called the noumena and the phenomena. Phenomena—phenomenology—is the way I perceive things, the way they appear to me. Phenomenon means appearance, and noumenon is the world as it is in itself, not as I perceive it. And Kant basically says that all the scientific claims we make are not claims about the noumenal world. They are not claims about the world as it is in itself; they are claims about the world as I perceive it in my consciousness. In the end, the facts I explain by means of a scientific theory—what are these facts? These facts are not something that happens in the world itself. They are something I perceive about the world itself. They are something that basically happens in my consciousness. Now, my consciousness is activated by the world, but still the phenomenon to which I relate is a phenomenon of consciousness. So the example of this, I think I may have given it in this series too, is the tree falling in the forest. The question is whether a tree falling in the forest, when nobody is there, makes a sound. The answer is of course no, it doesn’t make a sound. At most it sets pressure waves in the air in motion. It moves pressure waves in the air, and when those strike my eardrum, then they produce sound. And if there is no eardrum there, then there are pressure waves, but there is no sound. Therefore, when a tree falls in the forest and no one is there, it does not make a sound. That is the correct answer. What does this really mean? Does it mean the concept of sound reflects nothing that happens in the world? No. It does reflect something. It reflects the pressure wave, the acoustic wave that occurs in the world. But the phenomenon of sound itself is indeed a phenomenon of consciousness. It exists only in my consciousness; it does not exist in the world itself. My consciousness colors the acoustic waves in terms of sound—high-pitched sound, low-pitched sound, this frequency, that frequency, sound intensity, and so on. All these things are really phenomena of consciousness, but they reflect something happening in the world itself. The language I use to describe what happens in the world itself is of course the language of my own consciousness. But it is only a language for describing what happens in the world itself; in the world itself something is happening. Therefore Kant wants to say this: if I accept the distinction between phenomenon and noumenon, and I say that all scientific claims are claims that concern the phenomena, that is, the world as it appears to me, then now I no longer need to be so surprised that there are things I can know about the world a priori, without observing it. Why? Because if I refer only to the facts as they appear in my consciousness, then clearly my consciousness itself already dictates certain things about the facts I will see. For example, I can tell you in advance that light at a certain frequency that is not in the visible spectrum—I will not see it. I won’t see that light. I see that people from Ra’anana are joining now—wasn’t it announced that this was at eight-thirty? Maybe I didn’t see that it was at eight-thirty. No, the email said nine. Really? Yes, I checked, and that’s what the email says. A relaxed person beyond the usual. Fine, anyway, I had arranged with him that he would send a message saying it’s at eight-thirty, because on my WhatsApp too I wrote eight-thirty. He asked because today is Friday and it’s short, so we’re doing it earlier. So apparently there was some misunderstanding there; I apologize. Anyway, there’s a recording here, so anyone who wants can make up what they missed. So let me continue for a moment. We are dealing with Platonism on the scientific plane. I talked about the dispute between informativism and actualism that we discussed last time. I said that the dispute is a philosophical dispute and not a scientific one. It is rooted in the question whether I trust phenomena I have not observed directly—the scientific entities, gravitational force, the electron, all kinds of such entities that I arrive at through scientific abduction—and the question is to what extent I regard these things as claims about reality or as claims about me. That is the dispute between informativism and actualism. This dispute is basically philosophical, and therefore the question is how one can decide it. So right now I’m in the philosophical discussion of this dispute. And this dispute is basically translated by Kant into the question of how I can trust processes that are processes of thought and not of observation. Right? That is basically the question of rationalism. Because when I arrive at a scientific law, I do not arrive at it only by observation. The observations give me a collection of facts, and after that I make some generalization on the basis of those facts and arrive at the scientific law. But the generalization is a thought-process. Right? The world does not have to behave the way I think. And since that is so, the actualist says: so why should I take it seriously? In other words, that is only a claim about me; it is convenient for me to think this way. Fine, but that isn’t the world. The informativist, by contrast, puts trust in intellectual tools as tools for knowing the world, and therefore for him the scientific law is a claim about the world. And then, in order to explain this, I said that basically the big question we have to decide, if we want to know who is right, the actualist or the informativist, is the question of whether and how we can trust thought-processes as a tool for knowing the world. Is observation not the only tool for knowing the world? That is really the question. Kant formulated this in the language of synthetic a priori judgments—I won’t now go back through all the details. But basically Kant says: synthetic judgments are judgments that contain information beyond what is found in the definitions of the concepts. On the other hand they are a priori—they are not the result of observation, or not only of observation. And therefore we have here some judgment expressing information that I arrived at through a thought-process and not through an observational process. And the question is how such a claim can be accepted. And Kant says: all the laws of nature are really this kind of claim. The laws of nature are synthetic claims. What does that mean? That when I state the law of gravitation, that is not a law that follows from analysis of the concepts involved in it. There is some claim here that adds information about the concepts—say, objects with mass. So someone who knows what mass is will not thereby arrive at the law of gravitation. The law of gravitation claims something more beyond what is embedded in the definition of the concept of mass. On the other hand, it is impossible to arrive at the law of gravitation by observation. Observation gives me the facts I observed, but after that I have to make a generalization and an abduction to arrive at the general law. Therefore, the law of gravitation is really a judgment containing information—I called that a synthetic judgment—but on the other hand it is a priori. In other words, observation alone does not do the job; there are thought-processes here. And the question is how such a thing can be, and so it is with all the laws of nature. I said that all the proposals throughout history that were offered to explain this problem failed. Now I was in the middle of presenting the Kantian proposal. And Kant basically wanted to claim that the propositions of science, the laws of science, deal not with the world itself but with the world as I perceive it, with the phenomena and not the noumena. And since that is so, then it could be that I can say something about the world even without observation. Why? Because after all I know my own tools of thought; I can know what they will show me. For example, I don’t know whether I’ll see the next object as yellow or red. But one thing is clear—I won’t see it in a color outside my color spectrum. That I can tell you without having looked at it. Why? Because I know my own color spectrum, because I know the limits of my vision. So therefore, because I am relating not to the object itself but to the object as it appears to my eyes or my consciousness, then the limits of my consciousness are tools that can give me claims about the world—in the sense of the phenomenal world, the world as it appears to my eyes. Therefore, Kant says, that is the explanation. That is why we can make claims that are on the one hand synthetic, claims about the facts, about the world, and on the other hand a priori—they do not require observation, because I know that anything that does not fit my cognitive apparatus simply will not appear in my consciousness. And therefore I can… So is Kant an actualist? That’s an interesting question—how to define him. In a certain sense yes, because with respect to the facts of the world itself he is an actualist. He is not willing to recognize facts about the world itself; these are facts of consciousness. But when you treat consciousness as the facts themselves, then no, he is not an actualist. He claims that scientific theory is a theory that is a claim about the world, not about me. But of course, what is “the world”? The world is the way it is reflected in my consciousness, not the objective world out there. So where to place him on this map is a somewhat tricky question. In any case—Rabbi, Rabbi, just one small question—also the actualist and also the Kantian, according to this explanation, if, say, there were a practical difference regarding betrothal of a woman: someone says, I betroth the woman on condition that this really exists in the world too, not only in my consciousness and not only in my conceptual tools; it really exists in the world. So really the actualist would say she is not betrothed, because we basically have no idea—or maybe doubtfully betrothed. Like betrothing with a date, lest it be worth a perutah in Media. Yes, we have some kind of Platonic science according to which perhaps the date is worth a perutah there, so she is doubtfully betrothed. In this case science is that Platonic world—the world of Platonic ideas. The question is whether there is something real there, a Platonic world of ideas or not, so she is doubtfully betrothed. Anyway, the claim in the end is that in order to justify synthetic a priori claims, or the trust we place in the laws of science, we are in a certain sense giving up their objectivity. We are basically saying that science does not deal with the world; science deals with the world as it appears to our eyes. But Kant did not go all the way; he did not make science completely subjective. He made science inter-subjective. What does inter-subjective mean? It means it exists within every subject. It is not that my science and your science are two completely different things because this is subjective. He assumed that all human beings share the same science; after all, we have a scientific community and we all reach the same conclusions. But these are claims that are ultimately about the world as it appears in human consciousness, not about the world as it is in itself. And indeed, he was criticized already on this point: if so, why don’t you take the next step and say, wait a second, why inter-subjective? You can’t even know what is in someone else’s consciousness. All you can know at most is what happens in your own consciousness, and then you’ve already completely emptied science of its objective dimensions. So there are various criticisms of Kant. I think the strongest criticism—Zeitlin, for example, presents a criticism of Kant; he has an article on Lev Shestov, some Russian philosopher, I don’t know exactly, I had never heard of him before then. You know, once I had someone—when I was doing my post-doc, I worked with a Russian physicist, an immigrant from Russia; now he’s in the United States, but he was in Israel and we worked together. I once asked him—a cultured, intelligent fellow and so on—I asked him, tell me, why do the Russians have so many first-rate poets and writers, but not a single first-rate philosopher? There aren’t any. None of the first-rate philosophers were Russian. So he said to me, what do you mean? There was, say, Tolstoy for example, or others. You understand that the examples he gave me were writers. Writers with some philosophical temperament, but they are writers, not philosophers. And it’s a very interesting point. I think the Russians have some kind of character—so it seems to me, this was the explanation I suggested to him, and he said I might be right—they have some sort of character that does not deal with abstract things as such, but with their realization on the ground. Not for nothing did communism break out in Russia. It wasn’t born in Russia, it was born in Germany, but it burst out in Russia because the Russians take philosophy and apply it in the world. Others can remain in the philosopher’s armchair. Yes, so Tolstoy too is their philosopher, but he is a philosopher who described things through situations that happen in the world. Not in the real world, but in concrete situations in the world—through books and stories. He does not speak about philosophy in its abstract sense. Somehow—I don’t know—maybe that’s right, maybe not. In any case, there was one Lev Shestov who apparently really was a philosopher, I don’t know exactly what kind, and he attacked Kant on the very distinction between phenomenon and noumenon. He said: who says the distinction between phenomenon and noumenon is not itself a phenomenon? And how do you know there is a noumenon? You can say: I deal with the things in my consciousness, period. You can’t say that there are things beyond it but I don’t deal with them. Who says there are things beyond? But that’s not so terrible, because fine, then you’ve turned Kant into a solipsist in a certain sense, into someone who does not accept the existence of an external world but speaks only about the world as he perceives it—and from there on everything continues as usual. But I think there’s a stronger claim. Let’s think for a moment. Say Newton’s second law says that force equals mass times acceleration, yes? F equals ma. Not “say”—that’s what Newton’s second law says. Now suppose the true second law of Newton were F equals ma squared. All right? In other words, force equals mass times acceleration squared. So what would that mean? Let’s say we take an object weighing one kilogram and one newton of force acts on it, then it will move with acceleration… no, here that won’t work. Say instead an object has a force of two newtons acting on it, and its mass is one kilogram. All right? Then what is its acceleration? Two, right? The mass is one, the force is two, so force divided by mass is two over one, which is the acceleration, so that’s two. By contrast, if the law were F equals ma squared—if we ignore the units problem, never mind—F equals ma squared. Then F is two, if m is one, then a squared equals two, meaning the acceleration is the square root of two, 1.4, not 2, right? Now suppose the correct law were F equals ma squared. So what do you, Kant, want to say? That if a body with mass were moving at an acceleration of 1.4 I would not see it? I only see it if it moves at acceleration 2? Why? I can see bodies at acceleration 1.4 that weigh one kilogram. The only difference is: if the force acting on them is 1.4. But if the force is two and the acceleration is 1.4, then suddenly I won’t see them? How does this affect my vision, this different relation between force and acceleration? You understand that we are dealing here with some crazy speculation. In other words, you are coming to explain one thing that is not understood and not explained by means of something else that is even less understood and less explained. And this reminds me of an English-English dictionary. An English-English dictionary is a dictionary that takes one word you don’t understand and explains it by means of ten other words that you understand even less. That’s what you’re doing here. In other words, Kant is offering here some utterly implausible speculation to explain something that I merely don’t understand—not that it is illogical, I just don’t understand it. In other words, you have only retreated backward. You made the problem harder, not easier. Yes, so the Kantian solution is not a solution either. And then the question really remains: so how can one trust the laws of science, the laws of nature? The actualist is right: the fact that I think in a certain way is all very nice, but the world owes me nothing. Who says the world operates in the way I think? Now that is really the question, and the question is what to do with it. Now I want first of all to show you—and this may come as a surprise—I am going to prove to you that actualism is wrong and informativism is right. Now pay attention: before I go into the proof, I want to explain what this means. Up to now we have understood that this is a philosophical dispute; there is no way to decide it by scientific tools because… But it can be decided empirically. In other words, this is a scientific dispute and not a philosophical one. Not only is it a dispute that can be decided—I claim that it is not a philosophical dispute at all, but a scientific dispute. And it can be decided, and I can prove to you that informativism is right and actualism is nonsense. So let me show you. I’ll ask the following question. Look at this graph. All right? This graph describes a relation between force—F means force—and acceleration. Okay. In the scientific context, what do I do? I measure. You see? The hollow circles—one, two, three, four, five—those are the points I observed. You see, when the acceleration was one, the force was this; when the acceleration is two, the force is this; when the acceleration is three, the force is this; and so on. So the hollow circles are the results of the experiment. Now this is what I measured. I now ask myself: what is the general law? You see that this is basically the problem of scientific generalization. I measured five observations; I don’t yet know Newton’s second law, that F equals ma. Okay? But I measured the relation between F and a for five different values of force and found that this is the relation between force and acceleration. Now I ask myself what the general law is. The question what the general law is is really the question of what the graph is, right? Which graph fits the points I observed? And here, notice, the graph every beginning physicist will tell you, everyone who ever copied a physics lab report will tell you, is this straight line. Right? It fits all the points I observed, and therefore every student in the lab knows that you need to draw the straight line, and that’s the result. Or in other words, the general law says there is a linear relation between force and acceleration. F equals ma, Newton’s second law. That’s how we arrived at Newton’s second law. Now the actualist, or someone else, will come and say: wait, wait, who said so? There is also another possibility. Look at the dashed line. You see the dashed line? It also passes through every point I measured. You see, every hollow-circle point lies both on the dashed line and on the straight line. So the dashed line too is a possible explanation, and of course there are infinitely many such curves. So why do you choose the straight line? The actualist tells you: because it is the simplest. True, you’re right. It may be that the right curve is the dashed one and not the solid one. But the solid one is simpler. Yes, a linear line has one parameter, or two parameters—it’s simpler. Therefore I choose that line because of Ockham’s razor. I choose it, but I’m not claiming it is the correct line. I’m only claiming it is the simplest line, therefore I choose it. Right? That is actualism. What does the informativist say? The informativist says no: if it is the simplest line, then in my opinion it is probably also the correct line. Not certain, but fairly likely it is the correct line. So the actualist asks him: who told you? Maybe it’s the dashed line. So the informativist says: maybe, but I think not. I think the simpler line is the correct line. Now notice, up to this point I haven’t said anything. They both accept the straight line. Their dispute is only over how to regard the straight line. Is it a claim about the world, as the informativist says, or is it only my convenience choice, as the actualist says? Now I will ask a different question. I want to settle the dispute between the dashed line and the straight line. What will I do? I’ll do experiment six or seven. You see, these are experiments I have not yet performed, and I’ll check. If the result falls here, then I have corroborated the hypothesis that it is the straight line, right? The solid line. Or here, yes, in case seven. But if it comes out here or here, then I have refuted the straight line, right? So I can do an experiment and decide between the two theories. Will that experiment help me distinguish between actualism and informativism? No. Obviously not, right? The actualist too will say that I will abandon the theory because it no longer serves me, but not because I discovered the truth; it just no longer serves me, so I need to choose another theory. And the informativist will say I need to abandon it because I discovered the theory is incorrect. In this case the simple theory is not correct. So up to this point we still haven’t managed to distinguish between actualism and informativism. Now I’ll ask a different question. I have not yet done the experiment. What is the probability that this experiment will succeed—that is, that the result for six will be here and the result for seven will be here? Pay attention to this answer: actualist and informativist will give totally different answers, right? The actualist will say: what probability? Zero. After all, there are infinitely many possible lines. The solid line is not necessarily the correct one; it is simply the most convenient for me, so I use it. But any line could be the case, right? Simplicity is not a criterion. Therefore, from his perspective, the probability that the next point will also fall on the straight line is zero—one over the number of possible lines. Not exactly, but I’m saying this just illustratively. The probability is zero, okay? Assuming perfect precision, of course, and all that. What will the informativist say? What is the probability that the next experiment will succeed? I don’t know, but not zero. Forty, fifty, seventy percent—depends how much confidence you have in the law. Say, if I were asking you about the law of gravitation or Newton’s second law, I assume you would say ninety-nine percent, right? Because we have good confidence in that law; that confidence is clear. Now notice: I have asked a question that is in a certain sense scientific, factual. What is the probability that the next experiment will succeed? The actualist will answer zero, and the informativist will answer 0.9—ninety percent, say, or I don’t know, sixty percent, but not zero. Okay? Now notice, I now have a way to decide. Let’s look at all the scientific experiments that have been performed throughout the history of science: how many of them corroborated the theory and how many refuted the theory? If it turns out that almost none of them corroborated the theory, then apparently the actualist is right. If it turns out that a substantial percentage did corroborate it—thirty percent is enough; thirty percent is a very high percentage compared to zero, right? I don’t need ninety percent for this. I need a significant, statistically meaningful percentage that is not zero. Okay? Then the informativist is right. Now if we leave aside all the people who copy lab reports from Newton—the students studying physics or engineering—and look at people who do experiments seriously, you understand that the percentage of experiments that succeeded is not zero. I don’t know what it is, but it isn’t zero. I assume it’s something like ninety, ninety-five percent, even more. The experiments in which we replaced a scientific theory are very rare in human history. The overwhelming majority of experiments corroborate the existing theory. Some will say maybe that’s dishonesty, but no: if we take the measurements seriously, it corroborates the existing theory. That means that the history of science proves informativism empirically, because according to the actualist, what should have happened? I construct the hypothesis—say the straight line—perform the next experiment, and of course the result should come out here, because there’s no reason it should fall on the straight line, and then I would have to adopt the dashed line. Then I would do the next experiment, but it wouldn’t fall there—it would fall here. Then I would throw out the dashed line. In other words, I would be constantly chasing my own tail and I would make no scientific progress at all. I should still have today the scientific knowledge of Adam. Yes, there’s a difficulty in what… you took the example of Newton’s law, which we know works in the ordinary world, let’s say, but today we know that if you go to small things there is quantum, or large things there is Einstein’s theory. It’s some kind of generalization, let’s say, of Newton, so in principle Newton isn’t true, but it works. It doesn’t matter what “isn’t true” means—at low speeds it is true. Again, I’m not claiming Newton is true. I’m claiming Newton is not arbitrary. It is not a shot in the dark. It is not that whatever experiment you perform, you can never have the slightest idea what will come out. According to the actualist, you need to understand, according to the actualist I should have no clue whatsoever what the next experiment will yield. If the experiment succeeds, the actualist ought to faint from astonishment because there is almost no chance that would happen. But the actualist is not astonished, and neither is the informativist. Experiments sometimes fail—in the case of high speeds Newton indeed doesn’t work so well—but usually it works. And even when it doesn’t work, we know that he is right at low speeds; we just need to make some generalization. It’s not that we threw Newton into the trash. So that means that, basically, the history of science constitutes an empirical decision in favor of informativism. People don’t notice this point. This dispute goes on as though it were a philosophical dispute with no way to settle it. This dispute was settled long ago. The whole history of science proves that informativism is right. If actualism were right, today we would not have scientific knowledge any greater than Adam’s. Adam’s theories would be exactly like ours; there would be no difference. His theory isn’t true any more than ours is true; it predicts nothing, just as ours predicts nothing. Ours is built on twenty experiments and his on one or two. So what? But the probability that the next experiment will succeed is zero in both cases. I would say more: in the world there really are no actualists. I’m going to medicine; I don’t think anyone would go into surgery saying, well, it worked many times, but who knows about the next time? The probability is zero that next time he’ll do what he’s supposed to. Exactly. That’s saying the same thing I said. Basically what you’re saying is that anyone who is an actualist would never board an airplane. Because the fact that airplanes worked until now doesn’t mean it won’t crash on this flight. On the contrary, nearly all the probabilities are that it will crash. Therefore you should not do anything, rely on any induction you’ve made, because every induction you make, you use it to predict future events. And if you think it is a poor predictor of future events, then as a predictor it is worthless. So when you ask this actualist or skeptic, he says yes, I don’t have anything better, so that’s what I do. But that’s nonsense of the highest order. He ought to be trembling with fear when he boards a plane. Because there is a 99.99 percent chance the plane will crash. 99.9999. And he is not trembling with fear, no more than I am or you are. Therefore I claim that actualism is nothing but a colossal philosophical mistake. A scientific mistake, not a philosophical mistake. The first mistake is the thought that this is a philosophical dispute. It isn’t a philosophical dispute. To say it is a philosophical dispute—that itself is mistaken. It is a scientific dispute, not a philosophical one. The second mistake is that this dispute was settled long ago. This dispute was settled long ago. And what does it really mean, if I summarize? I hope they didn’t hear those. What? What this really means is that when we build a scientific theory, it is not true that the theory is a statement about us. The theory is actually a claim about the world, not about us. And when I reach the point that the theory leads to the conclusion that there is a certain scientific theory, I assert that as a claim about the world. There is in the world a gravitational force, not just a law of gravitation. There are electrons in the world, not just some images of them in an electron microscope. Rather, there really are electrons in the world. And the actualist claim—which is basically extreme empiricism—that only what I observed directly is true simply gets hit by scientific facts. The whole history of science denies it. Therefore I think this is just philosophical pilpul that has no substance at all. It was refuted long ago on the scientific level. But notice the conclusion: the conclusion in the end is that science basically rests on a Platonic rather than Aristotelian foundation, and it has also proved itself. And if it has proved itself, that really means Plato was right and Aristotle was wrong. In other words, we have a scientific decision regarding this ancient philosophical dispute between Plato and Aristotle. And in the end the claim is that when we arrive at scientific theory, at least in this sense, in the scientific sense—I’m not talking right now about the Platonic world of ideas in the sense of the idea of a democratic state; I’m talking now about scientific Platonism—scientific Platonism means that the theoretical entities I arrive at by means of my theoretical tools, yes, by means of my theoretical generalizations, are real entities. They exist in the world—not in the world of ideas, but in our world. But they exist even though I do not observe them directly; that is why it is called Platonism. So the conclusion is that at least on the scientific plane, Platonism is a fact. Platonism is correct, and Aristotle is wrong in his philosophy. So that is the conclusion on the scientific plane. Next time, in one minute or two, I will try to explain a bit more the significance of this and what it means for philosophical Platonism, and then finish with mathematical Platonism. And with that we will finish this series. I just want to remind you again: we are moving to eight-thirty during daylight saving time. In other words, the Friday classes will be at eight-thirty. I hope the… mix-up that happened today won’t happen again. Rabbi, Rabbi, at the beginning of the class you said that the actualist also accepts abduction, he also accepts scientific theory, he also accepts the law of gravitation, so he also boards a plane exactly like we do. Right, of course. That’s why he’s inconsistent. But the law—does he accept its validity? No, no, he does not accept it. He says that this principle is simply the most efficient way to describe the facts, that’s all. And despite that, he boards the plane—absolutely. That is exactly the problem: he is inconsistent. He simply does not notice that there is an inconsistency here. And the Kantian says fine, I board the plane because again, that’s within my cognitive apparatus. No, there is no problem with the Kantian. The Kantian basically says: what matters to me is that I won’t experience a crash. I don’t know whether in the real world itself there will be a crash. As far as I’m concerned I’ll remain alive. That’s what matters to me; I don’t know what happens in the world itself. Okay, a distinction that seems simple enough to me, but in principle the Kantian doesn’t run into a problem here. There is a completely different question here. There is a dispute between what we may call determinism and free choice. In my opinion everyone in the world behaves as though he has free choice. Someone who gives a one-hour lecture on determinism worked all night on it and so on. He doesn’t really say: well, that’s just how I’m built. Does that mean the same thing—that because everyone behaves as though he has free choice, therefore there really is determinism? I have written more than once: when you ask a person who believes in determinism, he will tell you, yes, I am also compelled to do that. But the experience—if he is honest—he will say that my experience is the experience of a free chooser; I only claim that this is an illusion. So here too. What do you mean, here too? Here, with boarding the plane. Yes—here it is dangerous. He experiences free choice, he invests energy in preparing the lecture, when in fact maybe he didn’t have to do it—that too is not exact, but never mind. But there is no risk in it, okay? Because that’s how he lives, that’s what he’s used to, that’s his consciousness, so he goes with it. But you board a plane when there is a 99.99 percent chance you’ll crash and you aren’t even afraid? That’s something else. The illusion is the same illusion, but the difficulty here is much stronger, because here I don’t believe you that you think it’s an illusion—otherwise you wouldn’t board a plane. And it’s not only planes; it’s also buildings made of concrete and steel, and cars, and trains. And of course medicines. Yes, right. Surgery, yes, everything—everything you do. Also what you don’t do, by the way—you should also be afraid not to do it, because if you don’t do it you may die, and if you do do it you may die. You have no way of knowing. You live in a completely Kafkaesque world. You cannot predict anything. Anything you do could lead to your death within a second. No one lives that way; no one really believes this. The question is still why not. Good question, but first of all I have proven to you that they don’t. Now the question is why not, and about that we’ll speak more. Fine. Rabbi, could it be that the actualist simply never thought of this argument? They sound like serious people. I’ve spoken with quite a few such people, and I asked this question in the plainest possible terms. And from all of them I got the answer: look, I do it because that’s what I’m used to, because I go with what is there. What can I do— not do it? That too is equally dangerous. I said yes, but I don’t see your legs trembling with fear. And by the way, I also don’t see you crashing. Usually you really don’t crash, so everything is fine. Seemingly you should have crashed long ago in practice too, beyond the fear. It doesn’t hold water. It is a relatively simple mistake, but the fact is yes, people do fall into these simple mistakes because they are captive to philosophical arguments. They are captive to that assumption that only observations can teach me about the world. Everything else is speculation. You are so convinced of that that you don’t notice that you yourself do not really think that way. Okay, fine, Sabbath שלום. Sabbath שלום.