Free Will and Choice – Lesson 5

Table of Contents

• The framework of the discussion: determinism, libertarianism, and the three planes
• The contradiction between the principle of causality and free will
• Defining causality: time, logic, and causation
• Attacks on the time component: time travel and paradoxes
• The dispute over the logical component: necessary and sufficient condition versus sufficient condition
• Steinitz’s argument and the lecturer’s response: mixing up logic and causality
• David Hume: causation is not observable and the principle of causality is not empirical
• Causality in physics: symmetry of equations and external causal interpretation
• Correlation is not causality: Raymond Smullyan and Leibniz’s clock parable
• Halakhic examples from tort law: necessary condition, sufficient condition, and “it began with negligence and ended in an unavoidable accident”
• Implications for free will: even “Humean” causality remains deterministic
• Closing questions and additional remarks

Summary

General overview

The lecturer tries to formulate a position in the dispute between determinism and libertarianism on three planes: the a priori philosophical plane, the scientific plane, and the diagnostic plane. He now begins the scientific plane through an examination of the principle of causality. He argues that the central tension arises because acts of choice are also physical events, and if every physical event is dictated by physical causality, then there is no real possibility of diverging into two different outcomes from the same given state. He defines causality as a combination of a temporal component, a logical component, and a component of causation, and shows how each of them has been attacked philosophically and how science tends to make do with the first two. He concludes that even adopting causality in the style of David Hume, without the causation component, still leads to determinism and therefore still creates a difficulty for free will.

The framework of the discussion: determinism, libertarianism, and the three planes

The lecturer states that one can try to decide the dispute between determinism and libertarianism on three planes: a priori philosophical arguments, scientific findings, and finally a diagnostic plane of examining one’s internal stance if the first two do not decide the issue. He says that today there are claims that science has already settled the question of free will, to the point that some think it is no longer even a question. He presents the current discussion as a transition between the philosophical and the scientific, because causality is a foundation of science but does not arise from empirical experience.

The contradiction between the principle of causality and free will

The lecturer describes causality as the view that everything that happens has a prior cause, and when a person chooses, that is expressed in an act that is a physical event involving movement of body and brain. He argues that if every physical event has a physical cause that dictates the outcome, then given a particular physical state, the next moment is determined and there is no possibility of branching from it in two different directions. He presents free will as the demand that even in that very same state one could choose this way on one occasion and that way on another, and therefore he sees here a fundamental contradiction between a causal worldview and libertarianism.

Defining causality: time, logic, and causation

The lecturer defines a causal relation as including three components, and he says that if one of them is missing, we are generally not inclined to regard it as causality. He states that the temporal component requires the cause to appear before the effect, that the logical component requires an if-then relation in which, given the cause, the effect always appears, and that a component of causation is also required, one that is not reducible to constant succession in time. He illustrates that temporality alone is not causality through the example of the sunrise occurring before the fan is switched on, and that even temporality together with if-then is not enough through the example of three o’clock and three-oh-one, where there is constant succession but no causation. He adds that the third component does not have to be narrow physical causation דווקא; psychological or spiritual causation also counts as causation in his view, so long as all three components are present.

Attacks on the time component: time travel and paradoxes

The lecturer says that the temporal component is challenged by ideas of traveling backward in time, which lead to paradoxes, and he describes the problematic nature of the very claim that one returns to the same time when one’s very presence there changes the situation. He brings up the grandfather paradox to illustrate loops and problems of identity and causality. He argues that causality does not operate backward in time, and distinguishes this from determining the truth-value of a statement, which can be interpreted as “operating” backward in time because it is not a physical event.

The dispute over the logical component: necessary and sufficient condition versus sufficient condition

The lecturer presents a philosophical dispute over whether a cause must be a necessary and sufficient condition for the effect, or whether it is enough that it be only a sufficient condition. He gives an example in which paper catches fire either by a match or by the focusing of the sun’s rays, and concludes that everyday life supports the idea that a cause need not be unique and therefore need not be both necessary and sufficient. He remarks that trying to unify the causes under a more general cause, such as an increase in temperature, only pushes the question one step back, because the increase in temperature itself can also come about through different routes.

Steinitz’s argument and the lecturer’s response: mixing up logic and causality

The lecturer attributes to Minister Steinitz, in the book Etz HaDa’at, an argument according to which if causality is a necessary and sufficient condition, then it has two characteristics: uniqueness and symmetry, and therefore supposedly there cannot be causal chains longer than two links. He explains Steinitz’s claim that in a chain A→B→C, the symmetry also turns C into the cause of B, and thus uniqueness is violated. He rejects the argument and says it is a mistake because it mixes up logical implication with a full causal relation, and that in order to be a cause it is not enough to be necessary and sufficient; the event must also precede in time and include a component of causation. He adds that on the logical plane one can say that the necessary and sufficient condition for the existence of B includes the whole chain before and after it, without thereby turning future events into causes, because logic is not subject to time.

David Hume: causation is not observable and the principle of causality is not empirical

The lecturer presents David Hume as claiming that there is no way to learn from observation the relation of causation itself, but only at most to see constant succession in time, which establishes a temporal and logical relation. He says that according to Hume, the general principle of causality—that everything has a cause—is not learned from experience but is posited a priori, and that it is precisely this general principle that leads us to interpret pairs of events as causal. He notes that Hume, as an empiricist, concludes that what is not learned from observation does not exist, but the lecturer himself accepts the principle of causality even though he agrees with Hume that it is not a result of observation. He emphasizes that the physical relation of causation is exactly the component that is not observational, and he points to the absurdity of giving it up when one wants to preserve the intuitive distinction between causality and correlation.

Causality in physics: symmetry of equations and external causal interpretation

The lecturer uses Newton’s second law, F=ma, to argue that the equation itself does not contain a causal direction, because it can be written in equivalent ways and gives no hint as to which side is the “cause” and which is the “effect.” He says that physicists’ tendency to assign force the role of cause and acceleration the role of effect is a philosophical interpretation added to the equations, not something that follows from them. He argues that in practice physicists tend to define causality in terms of temporal priority or the light cone—that is, in terms of the temporal and logical components—because only those can be inserted into equations, whereas the component of causation does not enter directly into mathematical formulation.

Correlation is not causality: Raymond Smullyan and Leibniz’s clock parable

The lecturer brings, in the name of Raymond Smullyan, the possibility of understanding astrology not as the stars causing what happens on earth, but as a correlation and synchronization between two domains. He uses Leibniz’s parable of the clocks to show that two clocks showing the same time do not cause one another, but are synchronized by a third factor or a shared mechanism. He uses these examples to sharpen the distinction between a temporal-logical relation and the existence of influence or causation.

Halakhic examples from tort law: necessary condition, sufficient condition, and “it began with negligence and ended in an unavoidable accident”

The lecturer brings examples from the laws of bailees to illustrate a hierarchy among the components of causality. He describes a case in which a bailee opened a door and an animal went out and was lost, and he states that this counts as causation that obligates payment. He describes a case of placing money in a forest and it being burned in a fire, and explains that this creates liability because a person knows that fires are common in a forest, even though the act is not, factually speaking, a sufficient condition. He describes a case in which money was placed in a forest and was stolen, and identifies this as “it began with negligence and ended in an unavoidable accident,” with reference to Bava Metzia 42 and the halakhic ruling that in such a case one is liable. Alongside this he mentions a case in which the animal went out to the marsh and died in its normal way, where one is exempt according to almost all views, except for Abaye’s position according to the Rif in Bava Metzia 36. He concludes that in the case of death in the ordinary course there is only a temporal relation; in the case of “it began with negligence and ended in an unavoidable accident” there is a temporal and logical relation without full causation; and in the case of ordinary loss there is also a component of causation that establishes full causality, at least on the legal level of assigning responsibility.

Implications for free will: even “Humean” causality remains deterministic

The lecturer returns to the principle of causality and formulates it as follows: a cause is an event that comes first in time, constitutes a sufficient condition, and brings about the next event. He argues that when a person stands at an intersection and goes right or left, this is a physical event of a body with mass, and therefore according to the principle of causality it must have a physical cause that dictates the outcome. He considers the possibility of adopting Hume’s interpretation, according to which there is only time and logic without causation, and argues that even then the problem of free will is not solved, because given state A, physics still determines that B will occur and not C, even if one says that the state merely “predicts” rather than “causes.” He concludes that determinism remains a result of the laws of physics even without the component of causation, and therefore the problem vis-à-vis libertarianism remains.

Closing questions and additional remarks

The lecturer answers a question about “seeing relations” and distinguishes between visual relations such as big/small or right/left, and relations such as father and son, a causal relation, or love, which are not seen with the eyes. He responds to a request about managing mute and explains that he used mute-for-all in order to deal with random noise created when there are many participants. He responds to the remark, “The Hasidim always claim that no apple falls unless the Holy One, blessed be He, decrees it,” and says that this does not solve the problem and that he spoke about this last time; in his view, it is nonsense.

All right, I’m starting again. I’m muting microphones, with your permission. Okay, let me remind you where we are. We’re trying to see whether it’s possible to decide, yes, to formulate a position in the dispute between determinism and libertarianism. And I said that we can try to do this on three planes. The first plane is the a priori philosophical plane: logical arguments for and against. We went through some of them, to see whether by such means one can show that one side is not coherent, or that the other side is coherent. That’s one plane. The second plane is the scientific plane: do we have scientific findings that can show us who is right, or at least point in one direction or the other? I mentioned that in recent years there have been claims of this kind, that science can actually decide this question. The question has ceased to be a philosophical question and has become a scientific question. Many will tell you it’s not even a question anymore—meaning, science has already decided it, so it’s not just that it became a scientific question; it has ceased to be a question at all. And the third plane is the diagnostic plane, where we try to see how to form a position if we didn’t reach a conclusion on the first two planes—that is, to try to look within ourselves and ask: so what do we nevertheless think? To try to make some kind of diagnosis for ourselves. I’ll get to that at the end. Right now I’m at the beginning of the second plane, the scientific plane. I really only began it in the last few minutes of the previous session, in a short and schematic discussion about causality. Because what stands at the center of the scientific discussion, and also the philosophical one—I said this is on the seam between them—is the contradiction, or clash—really I’d say contradiction, not clash—the apparent contradiction between the principle of causality, or the causal picture, and libertarianism, and the assumption that we have free will. I described this very schematically last time. I said that in principle, according to the causal picture, everything that happens has some cause—at least everything physical that happens has a prior cause. In the end, when a person chooses, the thing expresses itself in some act he performs. An act a person performs is also, among other things, a physical act: his body moves, his hand moves, even the brain that thinks, the head that thinks, is basically moving electrons. So almost—well, not almost—everything we do, even if it is the result of a choice, is a physical event. And if that is so, then according to the causal view it should have a physical cause. And if it has a physical cause, then that cause dictates the result. Therefore I have no possibility of deciding whether to do this or that, because given the present physical state of affairs, the result of the next moment is determined. We have no way, from within that same state, to go in two different directions—at least according to the causal outlook. And that basically contradicts free will, because free will says that even if I am in that very same state itself, I can once choose this way and another time choose that way. If my choice one way or the other is always affected by a difference in the prior state, then that’s not a choice. It just means I am not in the same state. So a different state causes a different result, and therefore I still remain within the causal physical world, yes, within a world where my physical state determines what I will think or what I will do, and not my free decision. So that, in a nutshell, is the contradiction between the causal picture and the conception of free will, of free choice. I’ll spell this out more later and try to see whether there are nevertheless degrees of freedom within physical causality—quanta, chaos, things of that kind. I’ll do that very briefly later. But for the moment I’m just laying out the basic picture. Now why do I say that this chapter, or this argument, lies on the seam between the philosophical plane and the scientific plane? I’m really right at the transition between concluding the philosophical examination of the question of free will and beginning the scientific examination of it. Because the concept of causality is indeed foundational in scientific thinking, but it has no empirical source. That is, it is basically an a priori principle; it is not a principle we drew from experience. And therefore one can see the claim I just raised as a philosophical claim and not a scientific claim, even though of course it is also a scientific claim. Science posits certain causal laws—good question why, but that’s what it does—and then if I adopt them, that basically means I have no free choice, because physical causes and effects generate everything that happens. So in order to understand this seam better, I want to dig a little into the guts of causality. This concept is a somewhat elusive one, and I want to talk about it a bit. I mentioned earlier that the concept of causality is not drawn from experience. So in order to see that better, I’ll first define what causality is. Causality is made up of three components. When I say that there is a causal relation between event A and event B, I am saying three things. If one of them is missing, it seems that this is not a causal relation. The first component is the temporal component. That is, the cause is supposed to appear before the effect. Okay? If something appears after something else, it is not reasonable to see it as its cause; we do not see it as its cause. Therefore the first component is the temporal component. The second component is the logical component. The logical component means: if A, then B. When I say that A is the cause of B, I am saying that if A happened, then B will happen. And if I also use the temporal component, then B will happen afterward, meaning as a consequence of it. Why am I distinguishing between these two things? Because there are many pairs of events where event A precedes event B, but we would not define them as cause and effect. For example, the sun rose in the morning, and therefore this fan is operating. The sun rose before the fan started operating, but nobody would say that sunrise is the reason this fan is working. Why not? Because there is no if-then relation. That is, it’s not that if the sun rises then the fan works. In our case that’s what happened. In our case it is true that first the sun rose and afterward the fan started working, but there is no logical connection between them. The connection between them is only temporal: A appeared before B. There is no logical connection between them of the form if A, then B. Meaning the logical connection basically dictates that it always happens. Meaning that if A, the cause, is present, then the effect B will always appear. But here it’s not always so. In this case it was so, but not always. Therefore here the temporal relation holds, but the logical relation does not. But the logical relation also doesn’t give us a complete answer. For example, after three o’clock there will always be three-oh-one. So is three o’clock the cause of three-oh-one? I think the answer is no. Even though here both the temporal relation and the logical relation hold. Three-oh-one always appears after three, and also—sorry—it appears after three, and it always appears after three. Meaning this is both temporal and logical. I can always say that if it is now three, then in a minute it will be three-oh-one. The if-then also holds here. So why don’t I see this as a causal relation? Because I do not see a relation of production, of bringing about, between three o’clock and three-oh-one. This is a constant temporal succession, but it is not causation. Causation has to tell me that three o’clock itself, in some sense, generates three-oh-one. It’s not enough that it always precedes it; it also has to bring it about. Say that every day after sunrise so-and-so goes to work, okay? And let’s say this happens every morning. Does that mean that sunrise is the reason he goes to work? No. It appears before, it always appears before, but there is no causal relation. The fact that the sun rose does not cause me to go to work. What causes me to go to work is my decision to go to work, my desire to earn money—everyone with his own reasons. Therefore we need to add a third component to the causal relation, and I call it the physical component. That is—physical here meaning that there is causality here. In other words, physical here means there is causality in the sense of bringing about. I physically cause the event that comes afterward. When I say “physically” here I do not mean specifically physics. One can also speak of psychological causation. A person went through some crisis and therefore behaved in such-and-such a way. That too is a causal relation. Even though I don’t necessarily need to invoke physical causation between those two things. Materialists will say that there too it is physical causation, but I don’t need that. Meaning: mental or spiritual causation, for me, is also causation, so long as these three components are present. Without one of them we generally will not tend to see the relation between two events as causal. If one of the things is missing—if the cause appears after the effect, or it appears before the effect but not always, or it appears before the effect always but does not generate the effect—then in all these cases we will not see it as a cause. Okay? A cause requires all three things. This is an important point. Now let’s take a look at these three components, because all three have come under attack. Okay? For example, the temporal component has undergone various attacks. The temporal component has undergone, for example—yes, many physicists in recent decades, like science fiction people even earlier, have toyed with going back in time. Going back in time is really a notion that in principle involves a logical paradox, in my opinion. That is, not physical impossibility, but a logical paradox, in my opinion, to speak of time travel. Yes, killing your grandfather and all sorts of paradoxes arise there. Killing your grandfather is just one example. Suppose I go back five hundred years in time. But five hundred years ago I wasn’t there. And now that I’ve gone back five hundred years, I am there. So did I really return to that time? Or did I simply create something like that time today? Because I didn’t really restore the state that was there. When it was there, when that was then, I was not there. So if I returned there, then something changed; I didn’t return to the same time. So in what sense am I in the same time? Okay, in short—it doesn’t even have to reach the paradox; the grandfather paradox only sharpens the problematic nature of the matter. But the problem exists even without it. The grandfather paradox is that I kill my grandfather, so who killed him? If my grandfather died, then my father was not born, so I too was not born. So who is it that went back in time and killed my grandfather? These loops in time lead to many problems. In any case, the temporal component of the causal relation is challenged by these games of going back in time. Meaning: you go back in time, and then the fact that you were born causes your grandfather to die, if you killed him. So the cause appears after the effect in time. Fine. But as we see, this leads to all sorts of paradoxes, and therefore it is not reasonable to accept the idea that there can be a cause that appears after the effect. It seems to me that last time, when I spoke about logical determinism, I also dealt with this issue a bit and said that causality cannot operate backward in time. The determination of the truth value of a proposition can operate backward in time. Again, because that is not a physical event. But physics does not work backward in time. And again, I know there are physicists who play around with backward influences in time. Also, the definition of the notion “backward in time” in physics is not so simple. It has to do with some kind of cone in spacetime; it’s not simply “backward in time.” So I’m not going into that here. That was the temporal component. As for the logical component—just a second, yes—the logical component also needs to be defined. Because the logical relation between cause and effect is disputed among philosophers. There are philosophers who argue that the cause must be a necessary and sufficient condition for the effect. That is the logical relation, the logical component of the causal relation: that it is a necessary and sufficient condition, right? The character of the condition belongs to the logical component of causality. What does “necessary and sufficient condition” mean? It means that whenever the cause is present, the effect occurs. In other words, the cause is a sufficient condition for the effect. And whenever the effect occurred, before it there was the cause. That is also a necessary condition. The effect cannot exist unless before it there was the cause. Other philosophers argue that the cause is a sufficient condition for the effect—not necessary and sufficient, just sufficient. It need not be necessary and sufficient. In other words, every time the cause occurs, the effect occurs. It need not be that only this cause can produce the effect. Maybe other causes can also produce the effect, and then I would see the effect without this specific cause having preceded it; some other cause preceded it. So therefore, I don’t know, paper catches fire. It could be because I lit a match there and burned the paper. Another cause: I focused the sun’s rays there with a magnifying glass, and therefore the paper burned. So do I call setting the paper on fire with a match a cause? It is not a necessary and sufficient condition; it is a sufficient condition. If you light it with a match it will burn, but it is not necessary and sufficient, because in fact I can also get the paper to burn without lighting a match, by focusing the sun’s rays. So that condition is not unique, and therefore it is not necessary; it is only sufficient. Seemingly, in our everyday life, it seems to me that the sufficient-condition view is the correct one; it need not be necessary and sufficient. Now one can get a bit casuistic here, because one could say that both lighting the fire with a match and focusing the sun’s rays actually raise the temperature of the paper very, very, very high, and then it burns, so in the end there is only one cause that always burns it; it’s just that there are several channels for creating that cause. But that won’t solve the problem either, because then the question becomes: how do you raise the temperature? What is the cause of the rise in temperature? And the cause of the rise in temperature can be one of several things. So again we have gained nothing; we have only retreated one step backward. The question whether the cause must be unique remains. Well, the accepted view is that it is a sufficient condition and need not be necessary and sufficient. On this point there is an argument of Steinitz—Minister Steinitz, I no longer keep track of which minister; probably finance, I don’t know, I don’t follow. Today it’s hard to keep track in general; you need a registry. But in one of his books—if I remember correctly, The Tree of Knowledge, yes, The Tree of Knowledge is divided into three essays, really an assemblage of three essays, and the middle one deals with causality—there he brings a proof that a cause is a sufficient condition and not a necessary and sufficient one. What is his proof? He says as follows: a necessary and sufficient condition has two properties. Suppose I say that A is a necessary and sufficient condition for B. That has two properties. One property is that if A is the cause of B, then there cannot be another cause of B. A necessary and sufficient condition is unique. How do I know that? Suppose A is the cause of B. Now I ask whether C can also be the cause of B. Under the assumption that the definition of cause is “necessary and sufficient condition,” it cannot be. Why? Because to say that C is the cause of B means that given C, B occurs. But A is necessary, so if A did not occur, how did B occur? After all, B cannot occur unless A preceded it. Therefore a necessary and sufficient condition is always unique. There cannot be two necessary and sufficient conditions for the same effect. Necessary and sufficient—the first characteristic of this relation, of a necessary and sufficient condition, is that the condition is unique. If and only if. What? If and only if. Yes, exactly. Necessary and sufficient is what mathematicians call “if and only if,” equivalence for logicians, and “necessary and sufficient” for philosophers. Fine, it’s the same thing, all the same old stuff. In any case, necessary and sufficient has a second characteristic, and that is symmetry. That is, if A is a necessary and sufficient condition for B, then B is also a necessary and sufficient condition for A. How do we know that? How do we see it? Simple. What does it mean that A is a sufficient condition for B? It means that given A, B certainly occurs, right? If so, then B is a necessary condition for A, right? Because it cannot be that there was A—because it’s only A. What? Yes. Because it’s only A. I’m saying: if A is sufficient for B, that means that given that A occurred, then B occurs. No, if A is necessary, only if A is necessary then B is sufficient. If A is necessary then B is sufficient; if A is sufficient then B is necessary. In other words, if one is a necessary condition for the other, then the other is a sufficient condition for the first. Fine. That’s the direction; it is true in that direction. So those are the two directions, that’s the relation. It’s implication, for those who want it in logic, yes? If A, then B. No, if it is sufficient, that doesn’t mean it is necessary in reverse. If it is sufficient, there could be another condition that is sufficient. Right. If it is only sufficient. So that means B is not necessary. There may be another condition that is sufficient, there may be another condition that is sufficient, but both of those conditions will be necessary for the result. The result is necessary for each of them—sorry. The result is necessary for each of them. Think about it: if one of them occurred, then the result necessarily occurs. So can I exist without the result occurring? No. So that means the result is necessary for me. Right? The other way around. Yes, it always flips. That is, if A is sufficient for B, then B is necessary for A, and vice versa. That is the relation. Now if that is indeed so, then it says that when A is a necessary and sufficient condition for B, then B is necessary and sufficient for A. The necessity of A gives rise to the sufficiency of B, and the sufficiency of A gives rise to the necessity of B. Right? So if A is both necessary and sufficient for B, then it is unavoidable, clearly B is also both necessary and sufficient for A. Fine? So that means a necessary and sufficient condition has two characteristics: first, it is unique, and second, it is symmetric. If A is necessary and sufficient for B, then B is necessary and sufficient for A. Now if we use these two characteristics, says Steinitz, we reach a paradox. Let us try to think of a causal chain longer than two links. Say A is the cause of B, and B is the cause of C. Okay? Say I lit a match; as a result the match burns with fire. I brought it near paper, or it was already near the paper; as a result the paper burns with fire. Then afterward the whole forest catches fire. So here we have one event bringing about another, right? A causal relation is by its nature chains—usually perhaps even infinite ones; it doesn’t have to be, but it can be infinite. So let us take a causal chain of length three. Event A leads to event B, is the cause of event B, and event B is the cause of event C. Now look: under the assumption that the interpretation of the causal relation, the logical component of the causal relation, is that it is a necessary and sufficient condition, then such a chain cannot exist. Because if A is a necessary and sufficient condition for B, then there cannot be another necessary and sufficient condition for B. It’s unique. Right? But it is also symmetric. So if B is the cause of C, then C is also the cause of B. Right? If there is a necessary-and-sufficient relation between them. And then it turns out that B has two causes, both A before it and C after it. The symmetry between B and C dictates that just as B is the cause of C, so too C is the cause of B. It is a necessary and sufficient condition. A necessary and sufficient condition is symmetric, right? But then it turns out that just as A is a necessary and sufficient condition for B, so too C is a necessary and sufficient condition for B. So it turns out that the cause is not unique. The symmetry causes the cause not to be unique. It could be, because if C is a necessary and sufficient condition for B, then that means A is also there, and then A and C are there together. No, wait, those are already explanations. I’m first presenting what Steinitz said. So Steinitz argues that according to this conception, that the cause is a necessary and sufficient condition for the effect, there cannot be causal chains of more than two links. Okay? That is, every causal chain has at most two links. That is his argument. And therefore he says: since we know that causes roll forward, meaning there are causal chains longer than two links—cause and effect only—this is a sign that the causal relation is not a necessary and sufficient condition. Wait, I’m muting again. This argument is not correct. Why is it not correct? Exactly because of what Ze’ev said earlier. If A is the cause of B, and B is the cause of C, then when I look at the logical conditioning and only at the logical component—not the causal component, and that is exactly the point—causality is not logical conditioning. Logical conditioning is only one component within the causal process. But let us focus on that component for a moment. If I focus on that component, then clearly both A is necessary and sufficient for B, and C is necessary and sufficient for B. That does not mean that both A and C are causes, because in order to be causes it is not enough that you are necessary and sufficient for the result; you also have to precede the result. And C appears after B, not before it. So first of all, remove causality from here; you are only talking to me about logic. And if you are looking on the logical plane, then I no longer have a problem with the time axis, because logic is not subject to time, as we discussed last time regarding logical determinism. And therefore I am really saying the following. On the logical plane—again, not the causal one—on the logical plane, the necessary and sufficient condition for the existence of B is that A be before it and C after it. And if you like, also D, E, F, the whole chain to infinity. This whole thing together is the necessary and sufficient condition for B. Now this already doesn’t sound so surprising, because I’m not saying that all of this is a cause of B. To say that it is a cause of B would be strange, since there are things here that appeared after it, so the temporal component does not hold. How can future events be the cause of a present event? Therefore I say: I’m not talking about the causal relation, I’m talking only about the logical component within it. And I ask: what is the condition for the existence of B, the logical condition? And the answer is: the logical condition is A before it and C, D, E, F after it. And that condition really is unique. It is unique and symmetric. B is a necessary and sufficient condition for the entire chain before and after it, and the whole chain is necessary and sufficient for B. And there is also no other necessary and sufficient condition for either of them. Everything holds and everything is fine. Steinitz is simply conflating logical conditioning with causal relation, and that is a mistake. The causal relation contains three components, not only the logical one, but also the temporal one and the physical one. But as for the matter itself, as I said earlier, the accepted conception—and I think it is fairly clear that this is right—is that a cause is not a necessary and sufficient condition. Even though I just defended that thesis tooth and nail against Steinitz’s attacks, I don’t accept it. I think it is incorrect. It is incorrect because it simply does not fit how we understand causality. As I said before, I can light the paper either with a match or by focusing the sun’s rays. Both will count as causes of the burning of the paper. So there is no problem with that at all. Each of them is a cause; it does not have to be unique. Therefore the cause—the logical component of the cause—is not that the cause is a necessary and sufficient condition for the effect, but rather that it is a sufficient condition for the effect. That I do need. There is no philosophical view in the world according to which a cause is only a necessary condition and not sufficient. That does not exist. It is either necessary and sufficient or sufficient. Fine? Why? Because when I talk about causes, I am among other things saying that once the cause occurred, the effect must also occur. That is what “sufficient condition” means. In other words, the effect must occur. It cannot be that the cause occurred and the effect did not occur. If it is possible that the cause occurred and the effect did not occur, then I do not call it a cause, right? The sun rose in the morning, and I can still decide not to turn on the fan. Right? So you cannot say that sunrise is the cause of the fan’s operating. Because the fan can operate without the sun, and the sun can rise and I still won’t turn on the fan. There is no logical relation between them—not necessity, not sufficiency, nothing. Without a logical relation there are no causes. Therefore, the temporal component—we said the effect always occurs after the cause. The logical component is that the cause is a sufficient condition for the effect. Meaning, given the cause, the effect necessarily occurs. There is no other option. But if the effect occurred, it may have had several causes—that is possible. But if one of them occurred, then the effect necessarily also appears. That is the meaning of saying that the cause is a sufficient condition for the effect. The third component is the physical component, and that too has been challenged. The challenge there is David Hume’s challenge. David Hume argued that we cannot learn the relation of causation between events from observation. We cannot, and we did not, learn it from observation. When I see a person kick a ball and then the ball flies away, I say that because he kicked it, the ball flew away. How do you know? All you know is that whenever one kicks the ball, the ball flies. So you know that the temporal relation holds: first one kicks, and then immediately the ball flies. You know that this temporal relation always holds, and therefore there is also a logical relation. The kick is a sufficient condition for the flight of the ball. Whenever one kicks the ball, it flies—unless it is an iron ball. Okay, so the ball flies. Thus the temporal relation holds and the logical relation holds. But how do you know that the physical relation holds? How do you know that the ball flies because of the kick? You cannot know that. All you see is that whenever you kick it, it flies. But that too could be only a temporal and logical component. How do you know that the physical component is also present? So the answer is that we assume it. We do not observe it, we do not infer it from observation; we assume it. It makes sense. That is, it seems reasonable to us that when a person kicks, because of the kick the ball flies. But if so, then that claim is not something drawn from observation. And what is more, David Hume asked not only about a causal interpretation of a specific pair of events—kicking the ball and the ball flying, therefore the kick was the cause of the ball’s flight. Who says? says David Hume. Maybe it is only temporal succession and a logical relation, but no causation between those two things. You cannot see causation with your eyes. By the way, no relation can be seen with the eyes. You cannot see with your eyes that so-and-so is the father of so-and-so. A relation between two things—I’m not talking about a spatial relation—a relation between two things is not seen with the eyes. You see the thing; you do not see the relation between that thing and other things. It is always an interpretation, okay, or other knowledge, or whatever it may be. But it is not vision; you do not see relations between things. So you also do not see the causal relation. But more than that, even the principle of causality—the principle of causality that says everything must have a cause—not just an interpretation of a specific pair of events, but the general principle of causality that says that everything that happens must have a cause, things do not happen by chance—that too we did not learn from observation. We assume it a priori. It is embedded in our thinking, but this thing is not drawn from observation. How could one even see that from observation? Do we know that everything had a cause? We cannot decipher even a causal relation between two specific events. So how can we determine that every single event always had a cause? We have not seen this even once. Therefore the general principle too, the general principle of causality, is not the result of observation. In fact it works in exactly the opposite direction. The general principle of causality is an a priori assumption of ours, that everything that happens has a cause, and because of that we also give a causal interpretation to specific pairs of events. If someone kicks a ball and it flies, I say: obviously everything must have a cause—that’s the assumption I come with. And here, apparently the kick, which always leads to the ball’s flying, is probably the reason it flies. It goes from the general principle to the examples, not that we learned the general principle from the examples. That is what David Hume argues. As a result, you have two possible responses. David Hume, being an empiricist, says that if something was not learned from observation, it does not exist. He sticks to observation. Whatever does not arise from observation does not exist. Yes, like the teacher’s brain in the famous joke about the student—sorry, in the famous joke about the teacher’s brain. That’s what David Hume said. But of course, that conclusion does not follow from his argument. All that follows from his argument is that the principle of causality and the causal interpretation of events are not the result of observation. From that point on, now decide whether you accept only things that are the result of observation or not. He decided to be an empiricist. He accepts only things that are the result of observation. But I am not an empiricist. I think the principle of causality is true, even though I agree with David Hume that it is not the result of observation. But this sharpens very much what I said before: David Hume leaves in the causal relation, because of this consideration, only two components: only the temporal component and the logical one. He is unwilling to accept the physical component. And I argue that there is also the physical component; without it we would not call things a cause. Even David Hume would not say that sunrise in the morning is the cause of my going to work. Because I could have chosen not to go to work. Right, I always go to work—so what? But it is not because of sunrise; it is because I decided. So it is not a cause. David Hume, according to his own definition—if he wanted to be consistent—would have called that a cause. Because the temporal relation is present and the logical relation is present, and he does not care about the physical relation. Do you see the absurdity here? What I call the physical component of causality is exactly that component that is not observational, that does not emerge from observation. That is the physical relation. The logical relation and the temporal relation do emerge from observation. The physical relation does not emerge from observation. And in fact, think about, say, the equations of physics. Newton’s second law says that force equals mass times acceleration. Yes? If I apply a force F to a body of mass m, then its acceleration will be force divided by mass. Okay? That is a principle Newton established. So I write F = ma. Force equals mass—F is force, m is mass, and a is acceleration. F = ma. Which is the cause and which is the effect? When you look at the equation itself, you have no way to know. Right? It could be that acceleration is the cause of the force; it could be that force is the cause of the acceleration. Since it is an equality, the equation can be written with the force on the right or on the left. It makes no difference which side of the equation you write things on. And yet I have never seen a physicist in the world write ma = F. Everyone writes F = ma. Why? Because it is obvious to everyone that when I apply force to a body and as a result the body accelerates, the force is the cause and the acceleration is the effect, not the other way around. It is not that the body accelerated and therefore a force acted on it. The force acted on it, and therefore it accelerates. And this happens at the same moment, not afterward. In ordinary mechanics, yes, not in field theory. So it happens at the same moment. So how can you determine that the force is the cause and the acceleration is the effect, and not the reverse? Look at the equation. In the equation it is completely equivalent. F = ma. Is there any hint in the equation who is the cause and who is the effect? No hint. There is no way to know that from the equation. Or in other words, absurd as it may be, physics adopts David Hume’s causal principle—only David Hume’s causal principle. That is, only the temporal and logical components, without the physical components. The physical components are the physicist’s interpretation. They are not the physics. That is really philosophy. I look at the equation. What physics says is that when there is force, there is acceleration. That is what physics says. I, as an interpreter, say: yes, but it is logically obvious to me that the force is the cause of the acceleration, not the reverse. That is an interpretation I give to the equations. It sounds of course very reasonable, but it is an interpretation that I give to the equations. It does not emerge from the equations. In the equations the status of force and acceleration is the same. They appear in a completely symmetrical way. And therefore in the world of physics, David Hume’s definition of causality is indeed the accepted one. But it is accepted because only it can be inserted into equations. The physical component—yes, of course, ironically—cannot be inserted into equations. And therefore physicists somehow do not take it into account in defining causality. Those who know, know that when physicists speak of a causal relation between events, they mean that the first event was before the second event, or that the second event is inside the first event’s light cone. That is only the temporal and logical constraint. That is all. Not the physical constraint. And the result is that because physics focuses only on things that are observational, and only on things that equations can describe—and both of those conditions fail in relation to the physical component—yet every rational person understands, every physicist is also a bit of a philosopher, and every person in the street is also a bit of a philosopher, so we all understand that there is something more in the causal component, in the causal relation. Beyond time and logic there is also causation itself: that A causes B, not merely that A always appears before B, but that A must cause B for me to say that A is the cause of B. Okay? Let me perhaps give you another example. Raymond Smullyan used to be—maybe he still is, I don’t even know—he lived a long life, by now he’d have to be well over a hundred, I don’t know whether he’s still with us. He was a Jewish-American logician who did logical stand-up comedy and wrote all sorts of amusing texts. A very interesting and very clever man. And once he argued that there is some kind of point regarding astrology. Yes, he says astrology cannot be true, because how can something that happens in the stars influence immediately what happens on earth? According to relativity, the influence can travel at most at the speed of light. So how can what happens up there affect immediately what happens down here? It contradicts the laws of physics. I never understood this question, because what we now see happening up there is of course what happened up there many years ago. The information simply reached us at the speed of light, and that is what affects things. Fine, but never mind, let’s say the question is a good one, because I’m bringing it for the sake of the answer. So what Raymond Smullyan says is that in fact you don’t need to assume, in order to believe in astrology, that the stars are the cause of what happens down here. What you need to assume is that there is a correlation between the two things. Whatever happens in the stars, the same thing happens down below in parallel. That does not mean that there is a causal relation, that what happens in the stars causes what will happen below. It means they are synchronized. Meaning that if you look at what happens in the stars, you can know what happens below—not because one is the cause of the other, but because such things happen in parallel. So this nicely illustrates the difference between a situation where there is a temporal and logical relation—that’s astrology—and the question whether there is also influence, the physical component. Right? I have two clocks, Leibniz’s parable, Leibniz’s parable of the clocks. I have two clocks that always show the same time. So what is the conclusion—that clock A is the cause of clock B, or that clock B is the cause of clock A? No. The conclusion is that apparently there is a third factor that synchronized the two clocks. Their mechanism was built so that they come out synchronized. Right? That is, when I see that something is correlated with something else, it does not mean that one of them is the cause of the other. Not necessarily, at least. So therefore, therefore—I see that he died in 2017, so may these words be for the elevation of his soul. In any case, the claim is that all three components are needed to constitute a causal relation: the temporal component, the logical component, and the physical component. Let me perhaps give a halakhic example. In Jewish law we speak about the laws of damages. If I caused damage to my fellow, to his property, I have to pay him. For example, if I burned his, I don’t know, grain, I have to pay him. But of course, it need not always be such direct causation in order to count as a cause. Suppose someone deposited an animal with me, okay? And I opened the door and the animal went out and was lost. Legally, this is considered causal responsibility. Meaning I am considered negligent, and I have to pay. Even though the animal could have remained inside. Physically this is not causation. I opened the door; the animal could have stayed. It is not a sufficient condition for the animal’s being lost. It is a necessary condition, but not sufficient. As opposed to the fact that if I had not opened the door, the animal could not have been lost. But the fact that I opened the door does not mean it will be lost. It is a necessary condition, not a sufficient one. Okay? We said: a necessary condition is not a cause. But in the legal world, because I bear responsibility as a guardian, if I created a necessary condition for the loss, then I am considered the cause of the loss. Yes, the legal responsibility makes up for the missing sufficiency. That is one case. Let us look at a similar case. Suppose money or banknotes were deposited with me, and I put that money in a forest. Then a fire came and burned it, a fire broke out in the forest and they were burned. I am considered negligent; I have to pay. Why? Because a person knows that fires break out in a forest. Now again, what I did was not a sufficient condition for what happened, because a fire might also not have broken out. So it could be—I could have put it there and it would not have burned. But clearly if I had not put it there, it would not have burned, right? There is a necessary condition here even if not a sufficient one. But as I already said, because it was deposited with me, even a necessary condition is considered a cause on the legal level. So if I put the money in the forest, that is like leaving the door open before the animal and the animal gets lost. I put the notes in the forest and the notes were burned. The responsibility is on me; I am negligent; I have to pay. What happens if I put the coins, the banknotes, in the forest, hid them there, and thieves came and stole them? There the Talmud in tractate Bava Metzia 42a calls it: “it began in negligence and ended in an unavoidable accident.” What does that mean? After all, hiding it in a forest is considered good hiding from the standpoint of guarding against theft. Thieves can always somehow find it, but all in all it is a good hiding place. I put it in the forest, in a hunters’ hut, in a crevice—no thief would think of it. I hid it well, and thieves came and stole it; I’m under compulsion, I’m exempt. So what happens now if I put the money in the forest and thieves came? It’s a good hiding place against thieves, but it is negligence because a fire could break out. But no fire broke out; thieves came. So there is a dispute in the Talmud, and in Jewish law we rule that if it began in negligence and ended in an unavoidable accident, he is liable. Meaning if I was negligent regarding the fire, even though in the end no fire happened, the forest remained intact, thieves came, and against thieves it was a good hiding place, a reasonable hiding place, and nevertheless they came—I am liable to pay. What if I put the money in the forest and the money disintegrated? It was made of a material that was not durable, but of course it would have disintegrated in my house just the same. It makes no difference, because that is the nature of the material; it has nothing to do with where it was. In that matter, almost all opinions say one is exempt, except for Abaye according to the Rif in Bava Metzia 36. That is what is called “it went out to the meadow and died in its normal way.” Yes, the animal went out to the meadow and then had a heart attack. It could just as well have had the heart attack in my house. So the fact that I was negligent and opened the door did not cause the damage in any way. It was not a necessary condition, not a sufficient condition, not a condition at all. There is no logical component here at all. Okay? According to Abaye as interpreted by the Rif, one is liable in such a case, but the accepted view—and certainly in practical Jewish law, and even the Rif agrees—is that one is exempt. So if I summarize, this is how it works. If I opened the door and the animal was lost, I am liable—that is negligence, pure and simple. If I opened the door, the animal went out to the meadow and was stolen there—wait, and let us say the meadow is considered a place well protected against thieves because it is hidden or something like that—and it was stolen there, all right? There, in practical Jewish law, I am liable; that is “it began in negligence and ended in an unavoidable accident,” a dispute, but practically I am liable. If I opened the door, the animal went out to the meadow, and had a heart attack, there I am exempt. What is the difference between these three cases? These three cases define the three components of causality. When I opened the door, the animal went out to the meadow and had a heart attack, what relation is there between my opening the door and the death of the animal? Only the temporal relation, right? Meaning I opened the door and after that the animal died. There is neither the logical relation—it is not a sufficient condition, not a necessary one, it would have happened anyway, it has nothing to do with opening the door—and certainly there is no physical component, you did not cause it, right? That is only the temporal relation. A temporal relation is not enough to obligate. What happens when I opened the door, the animal went out to the meadow—and I remind you, the meadow is considered a place protected against thieves—and thieves came? The problem was that the animal could have been lost, and therefore I was negligent in opening the door, but in the end what actually happened was that thieves came; the animal was not lost, rather thieves came. In such a situation there is a dispute, so this is a more serious case, and in practical Jewish law we rule that one is liable. What is there? There only the logical relation holds. Why? Because opening the door is not the cause, in the physical sense, of the theft. After all, it is not a sufficient condition; it is only a necessary condition. What I can say is that if I had not opened the door, the animal would not have been stolen. It is not that opening the door caused the theft of the animal, but rather that if I had not opened the door then the animal of course would not have been stolen, because it would not have reached the meadow. Or if I had not put the money in the forest, then the money would not have been stolen, because the thieves would not have found it there, even though placing the money in the forest is good guarding against thieves. But if I had not done it, then it would not have been stolen. So there is only a logical relation, but no relation of physical causality. Okay? That is basically the claim. So the case of “it began in negligence and ended in an unavoidable accident” is a situation where there is both the temporal relation and the logical relation, but not the physical relation. The case of pure negligence—where I open the door and the animal is lost—what does that mean? Here I already see, at least legally—and again, I say, only legally—I see here also a relation of causation. Your act was what caused the animal to be lost. It is not only that if you had not done it, it would not have happened. Why? Because the very reason you are forbidden to open the door is precisely because what is expected is that the animal will go out. Legally we treat it this way: when you open the door and the animal is lost, from our standpoint, even though factually it does not have to happen that way, still for purposes of imposing responsibility on the person, we view it at least legally as though if you opened the door, from our standpoint you lost the animal. Therefore you positively caused the loss of the animal. By contrast, if you opened the door and in the end the animal was not lost at all but was stolen, you cannot be blamed for its being lost, because it was not lost. And regarding the theft, you actually guarded it properly. All that can be said is that if you had not opened the door, the animal would not have been stolen. That is a negative relation; it is a necessary condition but not a sufficient one. But if you opened the door and the animal was lost, that is a sufficient condition. On the legal plane it is a sufficient condition. So these three cases form a hierarchy. The first, according to everyone, one is exempt except for one view according to the Rif. The second is disputed; in practical Jewish law we rule that one is liable. The third, according to all views, one is liable. What is the hierarchy among them? Exactly the three components of the causal relation. In the first case there is only the temporal component. In the second there is also the logical component. And in the third there is also the physical component. Therefore full causality appears only in the third case, not in the second. In the second case we impose liability, but it is not a full causal relation. We impose liability also for the logical condition. Now I want to make one more remark and say this: which of these three components did I identify earlier as the result of observation? Which of these three can be inferred from science? Actually the first two. Right? The temporal component and the logical component. The physical component—as I said earlier—we bring in from home. Whoever brings it in, because David Hume does not bring it in from home, or he claims he does not; I don’t believe him. But he says, no, as far as I’m concerned that is not part of the causal relation. But the first two components are components that are the result of observation. Now let us return to the question I described at the end of the previous class. Now we are equipped with a better understanding of what a causal relation is. Let us say we accept the principle of causality. If we accept the principle of causality, that means every event must have a cause. A cause means that the event which is the cause of the event I am discussing must satisfy three things. It must appear before my event, it must be a sufficient condition for my event, and it must cause it, produce it. Okay? And the principle of causality says that there is always some such event, or something like it, that constitutes the cause of the event under discussion. If I adopt the principle of causality, that means—suppose I say that if I burn the paper, then the paper burns. So I lit a match and burned the paper. Is there any possibility that the paper will not burn? No, because the causal principle says the cause is a sufficient condition for the effect. If the cause occurred, then the effect necessarily also occurs. Now let us return to the conception of free choice. Free choice essentially says this: a person stands at a crossroads and has to decide which way to turn—right or left. The libertarian claims that this is in his hands. He can turn right and he can turn left. Now turning right and turning left is a physical event. A body with mass goes right or goes left. That is a physical event. A physical event, according to the principle of causality, must have a cause, one that is a sufficient condition, prior in time, and that causes or generates it. Right? What is that cause? That cause is presumably certain currents in the brain that cause this decision, like I described last time. They travel through the nerves, stretch the muscles or contract the muscles, and the muscles move and that is how I begin to move, begin to go. Okay? So there is some very long causal chain here, of course, with thousands and thousands of stages. I’m only describing it schematically here. But all of it is a relation of physical cause and effect. So basically the claim is that if the state of affairs when I stand at the crossroads physically dictates going right, then it cannot be that I have the choice to go left. But “cannot” here is in a much deeper sense than what we discussed in the previous class concerning God’s knowledge, because it is impossible not only in the logical sense or the temporal sense. It is impossible also in the physical sense. That is, the present state of affairs—first of all, I can know what will happen after it because there is a logical connection: if the state is such-and-such, then the result is such-and-such. And more than that, the principle of causality says that the present state also generates the next state, not only that I know what the next state will be. But notice: this is according to the accepted conception of the principle of causality. Let us take the principle of causality in Hume’s interpretation. Hume basically says: it is only time and logic without physics. All I can say when I say A is the cause of B is that if A occurred, B will always follow it. I am not saying that A generates B—that I cannot say. I can say that if A occurred, B will always follow it. That is what I can say: the temporal and the logical. Does that solve the problem of free will for me, if I adopt the principle of causality in Hume’s interpretation? Because then I am really saying the present state does not generate the result; it only predicts it. That is, if the present state is such-and-such, I know what will happen next, but that does not mean the present state generates what happens next. I argue that this does not solve the problem of free will. Because in order to define my action as a freely chosen action, both possibilities have to be able to be realized. But even if Hume is right in his interpretation, physics does not allow the second possibility to be realized. Because physics says that if the circumstances are A, the next state will be B. True, the circumstances do not generate the next state, let us say according to Hume’s interpretation. I think they do; every normal person thinks they do. But let us adopt Hume’s interpretation for the sake of the discussion. I only want to argue that it won’t help us, it won’t solve the problem. Because still, given circumstances A, it cannot be that B will not happen. And therefore even if circumstances A do not generate B but only predict the existence of B, that is enough to make it impossible for me to do C after A. Because this violates the laws of physics. Although I give up the relation of production between cause and effect, determinism still comes out of physics. Physics is deterministic even if we adopt the Humean interpretation of physics, of the laws of physics. Physics is still deterministic, and therefore there is a serious problem here. If we accept the principle of causality, then it cannot be that I stand at the same crossroads, with the same state of affairs in the world, and be able to do either B or C. If the state is A—and I mean the state of all affairs in the world, from all the—whatever you want; let us say I know everything, okay?—I ask what will happen in the next moment. The libertarian says: it’s open, it depends what I decide. If I decide to do B, there will be B; if I decide to do C, there will be C. The determinist says: what are you talking about? The principle of causality says that if right now the state is A, the next state will be B. Whether A generates B or A merely predicts B does not matter. But the next state must be B. You cannot do C. And if so, then there is no possibility here for free choice. That is essentially the claim. And it is very important to understand that giving up Hume’s interpretation does not solve the problem. It does not solve the problem. All right, I’ll stop here. Basically what I did today was describe the concept of causality in order to sharpen the difficulty vis-à-vis the libertarian conception. And next time I will try to propose a solution, or a decision, or some way in which libertarianism can nevertheless be reconciled with the principle of causality. Okay, I’m done here. I’ll open the microphones if anyone wants to respond, if anyone wants to comment or ask or something like that. I’ve opened them. I want to ask: you said that the relation between two things is something we understand, not something we see with our eyes. When I see a cat and a mouse, don’t I see that the cat is bigger than the mouse? I said visual relations I obviously do see. I also see that one thing is to the right of another thing. But relations like father and son, relations like a causal relation, relations like so-and-so loves so-and-so—you don’t see those things. First of all I wanted to make a general comment, sort of. About the fact that you mute everyone. I understand that sometimes there’s noise, but if possible, maybe mute in a way that doesn’t lock everyone out; this is a class here. I muted everyone without taking control of the microphones, and that’s how the noise came out. So I simply had no choice. Because people somehow randomly open the mute, I don’t know how else to explain it. When there are many participants apparently there’s no choice; that’s from accumulated experience. The Hasidim always argue that not even an apple falls unless the Holy One, blessed be He, decrees it. Yes. Which is kind of like Hume or something, but then they say that the Holy One, blessed be He, gives free choice, which is supposedly above that. That doesn’t solve anything. But that’s what I talked about last time. In my view that’s nonsense. Is that it? Anyone else? Thank you very much. Shabbat shalom. Okay, Shabbat shalom. Thank you, Shabbat shalom, thank you very much.