Paradoxes and Contradictions in Halakha, Lesson 3
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- Parallel planes of explanation and one interpretation versus multiple interpretations
- Examples of explanations on different planes
- Consistency, the principle of charity, and the negative connotation of a psychological explanation
- Cause as a sufficient condition and the difficulty of two independent explanations
- Correlation between systems of laws, Godel, Escher, Bach, and a topological defect
- Free choice, knowledge and choice, and miracles
- Psychology and judgment as a combined explanation
- Harmonization between plain meaning and homiletic interpretation
- The distinction between facts and norms, and an argument for changing Jewish law
Summary
General overview
The speaker deals with dissolving dichotomies and adds techniques beyond what he presented earlier, moving from literary and philosophical examples to a logical discussion of what an “explanation” is and what is required of it as a sufficient cause. He presents the idea of parallel planes of explanation through Oscar Wilde’s The Happy Prince, the myth of Newton and the apple, and different explanations for becoming religious and for leaving religion, and then qualifies the point by saying that the parallel between explanations becomes problematic when an explanation is required to be a sufficient condition; in such cases it may be better to see it as a single combined, complex explanation rather than two independent explanations. He then examines the possibility of a “global” correlation between systems of laws, such as theology and physics, and explains how breaks in such correlations appear as exceptions like miracles or as a “topological defect.” Finally, he adds two methodological points: harmonization between plain meaning and homiletic interpretation, and the fallacy of inferring a norm from a fact without a bridging assumption.
Parallel planes of explanation and one interpretation versus multiple interpretations
The speaker argues that there is sometimes a tendency to assume that a phenomenon has only one explanation, and he cites Maimonides in the second root, where he writes that homiletic interpretation cannot be the interpretation of a verse because a verse has only one interpretation, namely its plain meaning. He presents Nachmanides as wondering at Maimonides and arguing that there can be several interpretations of the same verse, by virtue of PaRDeS and the idea that the Torah has seventy faces. He sharpens the point that according to Maimonides, homiletic readings such as “apples of gold in settings of silver” are an expansion and the spirit of the matter, not interpretation. He places under examination the tendency to think that one explanation excludes another, and marks a distinction between one correct interpretation and the fact that in practice there are many interpretations.
Examples of explanations on different planes
The speaker brings the story of Oscar Wilde’s The Happy Prince and describes how the lead heart of the statue cracks in two at the very moment when the heart “breaks” over the death of the swallow, so that the breaking receives both a physical explanation, namely changes in temperature, and a psychological explanation, namely pain. He brings the myth of Newton and the apple and asks why a physical explanation is needed if one can give a theological explanation in terms of sin or “afflictions of love,” and he presents the possibility of holding both a theological explanation for the apple’s fall and a physical explanation in terms of the law of gravity. He describes the case of someone becoming religious, whose secular friends explain it psychologically while his religious friends explain it philosophically, and then shows that someone leaving religion receives the reverse treatment, where the religious explain it psychologically and the secular philosophically. He concludes that significant life moves can be analyzed both on the psychological plane and on the plane of judgment and deliberation.
Consistency, the principle of charity, and the negative connotation of a psychological explanation
The speaker presents an initial claim that switching planes according to convenience may look like intellectual dishonesty because of inconsistency, and then adds a qualification: sometimes this is not dishonesty at all but a consistent conclusion that follows from each side’s worldview. He uses the principle of charity to argue that if a person assumes that the philosophical truth is belief in God, then someone who reaches the opposite conclusion will be seen as someone who did not complete the philosophical deliberation but was influenced psychologically, and the same in reverse from the secular point of view. He sharpens the point that a psychological explanation is perceived negatively when the decision belongs to the domain of truth and falsehood or of judgment, because it portrays the act as impulse rather than decision, and he distinguishes between acknowledging psychological influences and completely canceling the role of judgment.
Cause as a sufficient condition and the difficulty of two independent explanations
The speaker defines a cause in terms of a sufficient condition for the effect, and explains that a necessary condition by itself is not enough; therefore two different “sufficient conditions” cannot coexist as independent causes of the same event without undermining the concept of explanation. He uses the example of Newton to show that if the physical explanation is sufficient, then the apple would have fallen even without sin; and if the theological explanation is sufficient, then the apple should fall even without the physical conditions. From this arises a tension between accepting physics as an ever-binding lawful system and introducing theological exceptions. He presents the possibility that the true explanation is a combined complex explanation whose components join together, but emphasizes that then it is already one complex explanation and not two parallel explanations each of which “stands on its own.”
Correlation between systems of laws, Godel, Escher, Bach, and a topological defect
The speaker proposes a model in which two different systems of laws can yield the same results without direct law-to-law translation, and he distinguishes between local correspondence, which is trivial translation, and global correspondence, in which the outputs are identical even though the rules do not correspond one-to-one. He uses the example from Hofstadter’s book Godel, Escher, Bach, with a system of letter strings, the axiom MI, and inference rules that generate a set of “legal words,” to show that the same set can be generated by a completely different system of rules. He applies this to theology and physics as a global correspondence between two systems of explanation, each of which “explains” the whole, though they are not identical, and then argues that it is very difficult for a global correspondence to hold without breaking points.
The speaker explains the idea of “topological defects” through the transition between Cartesian and polar descriptions of the plane, and demonstrates that at the origin there is a breakdown of one-to-one correspondence, because r=0 corresponds to every angle. He connects such breakdowns to a breakdown of correlation between physics and theology and identifies them as miracles, arguing that since ordinary faith also accepts miracles, this indicates that there is no full correlation between the laws of nature and theological considerations. He adds that in the realm of interpretation one can see a parallel break between the revealed and the hidden in the notion of “a scriptural decree,” which marks a point where the correlation between hidden explanation and visible explanation breaks down.
Free choice, knowledge and choice, and miracles
The speaker argues that perfect prior correlation between systems of laws becomes problematic if one accepts free choice, because the laws of nature cannot be fixed in a way that will simultaneously fit every future choice. He notes that one could suggest that God “looks” at what a person will choose and plans accordingly, but connects this to the issue of knowledge and choice and states that he does not agree that the Holy One, blessed be He, can know in advance what will be chosen, without entering into the discussion. He emphasizes that within faith itself, the very need for miracles shows that the Holy One, blessed be He, does not see the laws of nature as fully carrying out His will, and therefore the proposal of two parallel planes of explanation remains problematic.
Psychology and judgment as a combined explanation
The speaker argues that in the example of becoming religious and leaving religion there is no way out except to see the psychological explanation and the philosophical explanation as a combined explanation rather than as two independent parallel explanations. He presents human action as the sum of psychological influences and judgment, where each component by itself may be a necessary condition but not a sufficient one, and the weighting of them together is what explains the act. He notes that in such a case there is no room for “topological defects”; rather, there is a structure in which elements combine to produce a complex explanation.
Harmonization between plain meaning and homiletic interpretation
The speaker adds a technique of harmonization and presents Henshke’s article on plain meaning and homiletic interpretation as a way of resolving tensions through a synthesis that yields a third result. He gives the example of “an eye for an eye,” where the plain meaning is interpreted as literally taking out an eye and the homiletic interpretation as monetary compensation, and suggests that through harmonization one takes “the value of the damager’s eye” rather than his eye itself and not the value of the injured party’s eye. He describes this as a synthesis of the plain meaning and the homiletic interpretation, and as a combination of interpretations similar to the logic of combining explanations.
The distinction between facts and norms, and an argument for changing Jewish law
The speaker emphasizes that one must distinguish between values and norms on the one hand and facts on the other, and that deriving a norm from a merely factual system is considered a fallacy. He gives the example of an argument in favor of changing Jewish law that relies on a change in reality, such as the claim that women today should be valid for testimony or for judging because women in the days of the Sages were uneducated or not familiar with the ways of the world, whereas today the situation has changed. He states that the argument as such is fallacious because it infers a normative change from a factual change, and explains that to make it valid one must add the assumption that the disqualification for testimony stemmed from lack of education or lack of social involvement. He concludes by saying that next time he will apply these methods to additional examples and then move on to paradoxes and loops.
Full Transcript
[Rabbi Michael Abraham] We’re dealing with Hanukkah matters. Well, yes, matters of dichotomies, not matters of Hanukkah. Matters of dichotomies and dissolving them. Today I hope I’ll finish with this part, and then I’ll move on. I said there would also be paradoxes and loops, so that’ll be in the next sessions. I spoke about a few basic techniques with which one can dissolve dichotomies, and today I want to add another two or three and then move on to a few examples to demonstrate it. One of them, really, is what we can call parallel planes of explanation. A lot of times we—it’s somewhat connected to the apparent correlations I talked about—a lot of times when we relate to some phenomenon and try to explain it, there’s an assumption that explanations—an explanation can only be one thing. Maimonides, for example, in the second root writes in passing that homiletic interpretation cannot be the interpretation of a verse, because a verse has only one interpretation. Every verse has only one interpretation, what is called the plain meaning. And therefore the homiletic interpretation cannot also be the interpretation of the verse, but must be something else. And Nachmanides is puzzled by him. He says: what’s the problem? Why can’t there be several interpretations of the same verse? PaRDeS, seventy faces to the Torah, and so on. So in general—not only in interpretation, but in explanations generally—there is a tendency to think that one explanation excludes another explanation. I’m going to argue that this tendency is not entirely mistaken, but at this stage I’m presenting it as a tendency that requires examination. The first story I want to bring—I want to bring two or three examples to demonstrate this point. There’s a story by Oscar Wilde, The Happy Prince, a well-known children’s story, I assume. Meaning, the prince dies, so they set up a large statue on a tall pedestal, a high column, in his memory, made of gold and precious stones. And from there he looked beyond the wall of the palace and saw the whole city—which of course while he was alive he saw none of, because he was closed up in the palace and lived his life in merriment and joy without noticing all the suffering around him. Oscar Wilde, obviously. So the statue looks around and sees everything that’s going on. Finally he’s high enough, above the wall. At some point a swallow arrives there—or a little bird, that’s how it was translated in what I saw—whose friends had already flown off to warmer lands. In winter, after all, swallows fly to Egypt, and he was a bit late, so in the cold he got stuck in Europe. Then one night he lands on the statue of the Happy Prince and decides to sleep there and continue on the next day, and during the night all kinds of drops of water fall on him. He doesn’t understand what’s going on, until he sees that the prince is crying. So he asks him what’s happening, and he tells him, look, there’s this poor woman here and this poor man there, and he starts sending him on errands, little by little. Take some of my gold leaves and give them to that poor woman, take out my eye—which is of course a precious stone—and give it to that poor man, and my sword that’s inlaid with precious stones, and so on. In short, he strips him little by little and distributes everything to all the miserable people around. And at a certain point the cold intensifies, time passes and they’re deeper into winter, and then the swallow feels he’s about to die, and there’s some heartbreaking farewell scene there with the prince, and he says goodbye to him—I’m about to finish my career, I don’t remember the exact quote—he explains to him that he’s about to die, and that’s it, he dies. And then it says there: then a dull cracking sound was heard from inside the Happy Prince. His lead heart split in two. Oh, how terrible the cold had been. The lead heart split in two because it couldn’t withstand the changes in temperature; the lead simply cracked because the cold was too intense—while of course this happens at the perfect moment, when his heart breaks over the death of the swallow. And the question is: what actually caused the breaking of the heart? The changes in temperature, or the heartbreak over the swallow’s death? In the story, of course, it’s both. That’s the physical mechanism, and that’s the emotional explanation. Two parallel planes—not necessarily a need to choose one and abandon the other.
[Speaker D] But either one of them was enough, or both together?
[Rabbi Michael Abraham] Yes, I said I’d qualify that later, in just a moment. There’s, for example, Newton and the apple that fell on his head according to the well-known myth, and then he discovered the law of gravity. And the question, of course, is why Newton, as a believing Christian, needed a physical explanation. Basically it’s obvious that apparently yesterday he committed some sin, and as a result they dropped an apple on his head as punishment. What exactly here needed explanation? Why search?
[Speaker E] It could be—
[Rabbi Michael Abraham] —that these are afflictions of love? What? Afflictions of love. Maybe he rules like the Talmudic text there, that there are afflictions of love too, even though Maimonides doesn’t rule that way. I assume he doesn’t either. What does it say there? Afflictions of love. Afflictions that come without sin. Maimonides says there’s no such thing, more or less. The Talmudic text says there are afflictions of love, and Maimonides argues there aren’t; it goes against the Talmudic text. There’s a lot written about that. In any case, clearly what he thought on the theological plane did not prevent him from searching for the physical explanation. Even though on the theological plane he explained the fall of the apple through some sin he committed yesterday—say, he didn’t turn the other cheek or something like that—and in parallel he also needs to offer a physical explanation for why the apple falls. And these are two planes of explanation, each of which in principle stands on its own. The plain meaning and the homiletic interpretation that I mentioned earlier from Maimonides and Nachmanides. A third example is a story about—I think I mentioned this in the past—the person who becomes religious, whose secular friends don’t understand what happened to him, what kind of crisis he went through that he decided to take such a step, and they find all sorts of emotional, psychological explanations for why he did it. His new religious friends, of course, explain it on the philosophical plane: the guy discovered the truth. Finally he understood that he’d been living in error until now, and finally he arrived at the truth. They are philosophers and the secular ones are psychologists. Now when we look at someone who leaves religion, as it’s called, then the religious explain that he wanted to permit forbidden sexual relations to himself, right? Meaning, the opposite: they become psychologists, and the secular say that finally he understood the nonsense he had believed until now and abandoned it.
[Speaker E] Today it seems to me that it’s already openly accepted to present it on both sides as things that have nothing to do with philosophical arguments.
[Rabbi Michael Abraham] Okay, yes, you’re saying there’s an even greater deterioration. Could be.
[Speaker E] Not always, but often.
[Rabbi Michael Abraham] In any case, yes—there is a tendency to attribute everything to psychological and emotional matters. That’s part of the same outlook of determinism and neuroscience and things of that sort, according to which everything is basically products.
[Speaker E] I don’t think from that direction, but simply from the direction that there’s less appreciation, as it were, for the idea that this was done out of philosophical considerations and all that.
[Rabbi Michael Abraham] It’s the same thing. It all comes from the same place. So with the one who leaves religion, suddenly everyone switches roles: the religious become psychologists and the secular become philosophers. Now what exactly does this tell us, beyond intellectual dishonesty? Why is it dishonest?
[Speaker C] Because it’s inconsistent? Why is it dishonesty? Because it’s inconsistent.
[Rabbi Michael Abraham] Yes, because when something happens that fits your position, you explain it philosophically, and if it doesn’t fit your position, you explain it psychologically. Anything that doesn’t fit your position happens on the higher plane, and what—
[Speaker D] —does fit, it’s just not necessarily that. They’re giving the person the benefit of the doubt, so they say that when he did it, he was using his mind.
[Rabbi Michael Abraham] Right. In that context too, in one second I’ll also qualify this—just a moment. It’s not the same qualification as before; this is a qualification specific to this example. I accept these comments about this example, but I’ll get to it in a second. So who’s right here? Both of them, of course. Meaning, it’s clear that any person who takes some step can be analyzed on the psychological plane, and you can offer explanations on the philosophical plane. None of us is free of psychological influences, but I assume that most of us—certainly in very significant steps in life—also exercise some judgment, whatever that means in each case. And even if not, we also operate at the higher cognitive level, not only on the unconscious psychological planes. And therefore, in principle, both are right. So why does each side choose the plane that suits it? Seemingly, both planes are valid—or both are planes of explanation. Fine, so as I said earlier, maybe it’s intellectual dishonesty. You choose what’s convenient for you so you don’t have to deal with it. When you see someone leave religion, it’s convenient to attribute it to psychology, because you can’t deal with the philosophical questions he raises. And the reverse. Now here, in this specific example, I really do accept the comments that were raised here, because here that’s not precise. Because if I truly assume that the correct conclusion on the philosophical level is belief in God, then someone who reaches the opposite conclusion—the principle of charity itself says that if so, then apparently he didn’t make the philosophical judgment, because otherwise he wouldn’t have reached that conclusion. He apparently made the psychological calculation. And the reverse from the secular point of view. Meaning, it’s just a consistent conclusion from my worldview, so that’s fine. In that sense there isn’t necessarily intellectual dishonesty here, at least not necessarily. Rather, it’s a result of my worldview. If, for me, the philosophical truth is faith, then whoever leaves it, whoever goes in the opposite direction, is apparently under psychological influences. And conversely, if my truth is disbelief, that there is no God, then whoever reaches the conclusion that there is, is apparently driven by psychology. So here it isn’t necessarily intellectual dishonesty. A bit similar to the apparent correlations with Rabin—whether Rabin had a mandate to return the Golan—we talked about that, the apparent correlations.
[Speaker F] But doesn’t the psychological reason carry a negative connotation?
[Rabbi Michael Abraham] It comes to say there isn’t a philosophical explanation—it’s just psychology. That’s really the claim.
[Speaker F] Negative psychology, because psychology—
[Rabbi Michael Abraham] No, psychology is by definition negative. When you make decisions that also belong to the plane of truth and falsehood or to the plane of judgment, then saying that you made them on the psychological plane or under psychological influences is always a negative statement.
[Speaker F] It’s impulses?
[Rabbi Michael Abraham] Yes, impulses rather than decisions.
[Speaker B] And also not by your own judgment.
[Rabbi Michael Abraham] It seems simple. I don’t know.
[Speaker G] Is that lack of differentiation?
[Rabbi Michael Abraham] Yes. You didn’t really make a decision; you were simply driven there by all sorts of factors that don’t depend on you, that don’t depend on your judgment. In any case, whether or not this is dishonesty doesn’t matter right now, but one thing is important to me in this example: that both planes of explanation are correct. Meaning, what these three examples basically show is that many times, when we offer an explanation on one plane, that does not contradict the fact that on another plane of reference we will also offer an explanation. There’s an explanation on the psychological plane and an explanation on the philosophical plane. With Newton there is an explanation on the theological plane for why the apple fell, and there is an explanation on the physical plane for why it fell. In The Happy Prince, that bird there, the swallow, there is an explanation on the emotional plane for why his heart broke, and there is an explanation on the metallurgical plane—strength of materials—for why his heart broke. So these are really parallel planes of explanation, and usually we use them in parallel. Meaning, we don’t need to assume that if one of them is true then we have to throw out the other, and vice versa.
[Speaker G] With Newton it was probably in order to discover the law, the law of attraction. Or else it was a sin for—
[Rabbi Michael Abraham] Or if it was in order to discover the law, then indeed that doesn’t contradict. But it still does contradict.
[Speaker D] Why in order to discover the law? Someone caused it to fall? Then it didn’t happen because it was a physical explanation.
[Rabbi Michael Abraham] No, someone caused him to be there under the apple so that he would discover the law. But even that is still a physical event, so it doesn’t really solve the problem.
[Speaker B] Even Maimonides there, that there’s only one explanation—does he accept the—
[Rabbi Michael Abraham] —metaphorical plane? What is “apples of gold in settings of silver”? The introduction to Guide of the Perplexed. So Maimonides says—Nachmanides brings “apples of gold in settings of silver”; that’s one of Nachmanides’ arguments—and Maimonides apparently understands that this is only homiletic interpretation. It’s an expansion of the verse, but it isn’t interpretation of the verse itself. From the way Maimonides writes there, there is no more than one correct interpretation of a verse. That’s what he says. And all those homiletic readings of “apples of gold in settings of silver,” with multiplicity, with things hidden behind it, with many deeper and other hidden interpretations—Maimonides will explain that as not interpretation, but expansion, the spirit of the matter, but not interpretation. Interpretation there is only one. And Nachmanides attacks him precisely on the basis of—
[Speaker D] But one can be complex. I mean, what does one mean?
[Rabbi Michael Abraham] Complex is fine, but it means one thing.
[Speaker D] Several things that are the interpretation.
[Rabbi Michael Abraham] Fine, but that’s still—not, “both this and that” is not a complex interpretation. A complex interpretation means that you need two elements that together create the interpretation. That’s something else. Here, neither of the elements needs the other. No, these are two interpretations. A complex interpretation is one interpretation that is composed of several things, each of which is necessary; without it there would be no interpretation.
[Speaker D] Why not? Because that’s how he argues it.
[Rabbi Michael Abraham] No, that’s what he claims.
[Speaker H] But there’s something very confusing here. Interpretation is subjective. Everyone has his own interpretation.
[Rabbi Michael Abraham] No, Maimonides claims it isn’t.
[Speaker H] Wait, so if Maimonides is talking about interpretation, then no—he has to talk about facts. A fact is only one thing.
[Rabbi Michael Abraham] Interpretation—what do you mean, fact? The meaning of the verse. What is interpretation? The meaning of the verse has only one meaning.
[Speaker H] Meaning is something subjective, and therefore there are many.
[Rabbi Michael Abraham] That’s what you say. He says not. What? He says not.
[Speaker D] No, there can be a thousand interpretations. What is the correct interpretation?
[Rabbi Michael Abraham] No, of course, the correct interpretation is one. The factual point that there are several interpretations—even Maimonides agrees to that.
[Speaker H] Yes, but one can’t speak of one interpretation when one is talking about interpretation. No, why? When you talk about facts, there is one fact. What did the text intend? Basically, what did the verse intend? What did the verse intend? You take a text and ask what the interpretation is. Someone wrote this text—what did he mean? There is only one intention.
[Rabbi Michael Abraham] No, obviously. That’s what Nachmanides argues. But Maimonides says no, there is only one answer here.
[Speaker H] No, no, he intended—there too he put in also—
[Rabbi Michael Abraham] No, Nachmanides really does argue that the Holy One, blessed be He, intended all of them. Yes, clearly you can say that. But Maimonides argues not—that as to what the intention of the Holy One, blessed be He, is, there is one answer to that. Everything else is expansions and other matters, but it is not the same interpretation.
[Speaker G] Sometimes it’s worth—
[Rabbi Michael Abraham] —preferring Nachmanides to Maimonides.
[Speaker G] What? That maybe shows—what? That sometimes it’s worth preferring Nachmanides to Maimonides.
[Rabbi Michael Abraham] Very often, I think.
[Speaker H] In any case, there can be several reasons that motivate a person to do something. Now I’m not talking about a verse, where we don’t know what the Holy One, blessed be He, intended, so it’s easy to say there’s only one interpretation and that’s it, even though we don’t know anything. Okay. But let’s talk about human behavior: why did so-and-so hide when he heard a noise? Okay? Fine? There can be several interpretations of why he hid. One possibility is that in his childhood he went through a similar event, and I don’t know what—
[Speaker D] But why did he really hide? What? Why, really?
[Speaker H] So that’s it—there are several reasons.
[Speaker D] The question is whether these reasons together caused it, or—
[Speaker H] —whether each one separately also was— It could be that one is enough, but it could also be that each of them is correct in its own right.
[Rabbi Michael Abraham] Wait, so that’s exactly what I’m talking about.
[Speaker H] What? So that’s exactly what I’m talking about now—
[Rabbi Michael Abraham] —that there can be several interpretations. No—Maimonides says regarding interpretation, Maimonides regarding interpretations says that there can only be one interpretation of a verse. Nachmanides disagrees with him even on that. But are you only talking about verses? No, no, I’m talking about planes of reference or parallel planes of explanation. Quite the opposite—that’s my claim: that there can be several parallel explanations. Do you want to refute what?
[Speaker H] You said from the start that you want to refute the—
[Rabbi Michael Abraham] No, in a moment I’ll qualify it. If you want to argue then, we’ll argue then. But first let me say what it is you want to argue with. Okay? You want to spare them this mistake. Okay. In any case, the fact is that many times we relate to events or things on several planes, where on each plane we offer an explanation, a cause, an interpretation—it doesn’t matter right now—and that does not necessarily have to cause us to abandon the parallel explanations. It may be that all of them are true simultaneously. But in truth it’s hard to accept this logically. Logically? Why? Because usually when we talk about a cause—let’s talk about a cause—then a cause is supposed to be a sufficient condition for the effect. There are those who want to claim that it is necessary and sufficient for the effect, but at least a sufficient condition it has to be—that is agreed by everyone. Something merely necessary is not a cause, meaning merely necessary. Either a sufficient condition, or a necessary and sufficient condition, but in any case it has to be a sufficient condition for it to be sufficient—such that given the condition, the effect occurs. That is a sufficient condition. Okay? The effect necessarily occurs—that is, it cannot be that the condition is present and the effect does not occur. A necessary condition is not like that.
[Speaker H] Could it be several—could it require several things?
[Rabbi Michael Abraham] Yes, or no—not several things. It could be one out of several.
[Speaker H] Each one—
[Rabbi Michael Abraham] A necessary condition is a condition that does have to hold for the effect to occur—sorry, actually I need to phrase this differently. Problematic. It doesn’t have to yield the effect. If the effect occurred, then certainly the necessary condition was there, if it is necessary for that effect. But if the condition occurs, the effect does not necessarily follow. Okay? That is called a necessary condition.
[Speaker E] That sounds a bit odd. Why? If I put several things on a weight until it tears, then it’s not—so the cause is only—
[Rabbi Michael Abraham] So the combination of all of them?
[Speaker E] The combination of all of them. Fine, okay.
[Rabbi Michael Abraham] And you could also put no weight on it at all, but cut it with scissors, and then it tears too. So that means that the combination of all of them may be a sufficient condition. What kind of necessity? What do you mean?
[Speaker G] Logical or physical—what?
[Rabbi Michael Abraham] No, physical necessity, certainly. Cause belongs to physics. In any case, once we grasp cause as a condition that has to be sufficient, then that means that say Newton sat under the tree, and the physical conditions for the apple to fall were present. Now if Newton had not sinned, and I accept the physical explanation, then the apple still would have fallen. Because the physical explanation says that the physical conditions are sufficient for the apple to fall. Right? Otherwise it’s not an explanation. It has to be sufficient. So if that’s so, then even if sitting there had been a perfectly righteous man who committed no sins, once the physical conditions are present, the effect must occur: the apple falls. If the force is strong enough compared to the strength of the apple’s attachment to the tree or branch, then the apple falls—if I accept physics as the explanation. But if so, then even without Newton sinning, the apple would have fallen on his head. And conversely, if I take the theological explanation as an explanation, then it too is supposed to be sufficient.
[Speaker H] No, but without his sinning it wouldn’t have fallen.
[Rabbi Michael Abraham] Wait a second, just a second—but it has to be sufficient. Now once it has to be sufficient, that means that if he sinned, the apple ought to fall on his head regardless of whether the physical conditions are present or not present. Because that is what a sufficient condition means.
[Speaker E] And the explanation would change. If he sinned, then it’s because he sinned, and if he didn’t sin, then it would be afflictions of love.
[Rabbi Michael Abraham] Yes, but then you understand that the apple falls on his head because of the afflictions, because of the sin.
[Speaker E] I—
[Rabbi Michael Abraham] I’m saying: but that doesn’t work. Because if you say that an apple falls on his head because of the sin, even though the physical conditions were not met, then you are basically saying that you do not accept physics. Someone who accepts physics says no: the falling of an apple requires certain conditions. There are laws of physics.
[Speaker H] When you speak about cause, that’s completely clear—logically completely clear. But interpretation—no, wait.
[Rabbi Michael Abraham] So I’m starting with cause because there it’s easier. We’ll see in a moment. There it’s easier because with cause—for example in the context of Newton and the apple—I can talk about cause as a sufficient condition, and two sufficient conditions, that can’t be. Two sufficient conditions that are different. But their combination—
[Speaker D] It could be that only the combination of them. Each one by itself is not a sufficient condition. Right, each one separately is not a sufficient condition.
[Rabbi Michael Abraham] Fine, but then that’s something else. Then you are basically saying that there aren’t two explanations here; now we’ve gone back to complexity. Here there is one complex explanation. Certainly. If we say that theology plus physics is really one complex explanation, that’s perfectly fine. But then you have to pay careful attention: if it’s one complex explanation, then first, it is one explanation. Second, if the conditions are not present and he sins, an apple does not fall on his head. And if the conditions are present and he does not sin, it also does not fall on his head. That means that physics is basically not correct.
[Speaker D] It could be that usually He could arrange that if he sins then it will fall on his head, but generally He prefers to combine it with the laws of physics.
[Rabbi Michael Abraham] So generally. Are the laws of physics correct or not correct? That’s what I’m asking. Are the laws of physics generally correct?
[Speaker D] What? The laws of physics are correct.
[Rabbi Michael Abraham] But an apple doesn’t fall if the force holding it to the tree is not weaker than the force of gravity.
[Speaker D] Maybe here it wasn’t supposed to fall—it wasn’t supposed to fall because the physical condition wasn’t there.
[Rabbi Michael Abraham] But if it wasn’t supposed to fall, then physics forbids it from falling. Right. So how did it fall? A miracle.
[Speaker D] So I—
[Rabbi Michael Abraham] I’m saying: then physics is not correct. Physics as something independent. The laws of physics—
[Speaker D] —are not correct.
[Rabbi Michael Abraham] For this to happen, something else has to happen as well in order for this thing to happen. But Newton’s second law says that this can go—
[Speaker D] —also on the basis of the laws of physics.
[Rabbi Michael Abraham] But here the physical condition wasn’t present. But if there wasn’t a physical condition, then how did it fall? A miracle. But physics says that without the physical condition being fulfilled, apples don’t fall. Unless there’s a miracle. No, physics doesn’t say that. You say that. Physics doesn’t say that. You’re explaining Newton. No problem, but I’m saying again—so basically I understand, but then that basically means that you don’t accept physics. Because the laws of physics as they’re usually understood are an exclusive condition. I do accept physics. Fine, then you don’t accept physics. Then you don’t accept physics. Why don’t I accept physics? Because you’re saying that if the force that binds the apple to the tree is stronger than gravity, it still could be that the apple falls. Or the other way around, if the force isn’t stronger… physics doesn’t say that. I’m saying that physics does say that. Fine, then this is wordplay. So you’re saying that physics also includes theology. Fine, that’s just words. It recognizes that there are other forces. It doesn’t recognize that. Newton recognizes that; physics doesn’t recognize that. It could be that only Newton didn’t accept only physics. Fine, that’s words. What’s usually called physics—you don’t accept it, that’s all, there’s no other way. But the event, the event wasn’t, the event wasn’t that an apple fell; the event was that an apple fell on Newton’s head. Right, a physicist. Right. So that means I can accept the physical dynamics and agree with the physical laws, but then I only say: the apple would indeed fall, but it wouldn’t fall on his head. The Holy One, blessed be He, arranged for Newton to be there; He didn’t cause the apple to fall, rather He arranged for Newton to be there. That’s what the Holy One, blessed be He, did. Yes, but the apple fell because of physics, and Newton was arranged to be there because of the sin. Exactly. But then I ask: Newton’s movement toward the tree is also a physical event. A sufficient cause, as you said earlier, a sufficient cause for the apple to fall, but not a sufficient cause for it to fall there. But that also doesn’t work. Because Newton’s movement toward the tree is also a physical event. Newton’s movement toward the tree is also a physical event. Not the combination—Newton’s movement toward the tree itself. You’re saying that it’s not a result of physics but of the decision of the Holy One, blessed be He. What was the event? I’m saying the event was that Newton came under the tree and the apple fell on his head. Now I’m asking: how did Newton come under the tree? Each one separately. So I’m saying: that has a physical explanation; only the synchronization of the two events at that same moment, that same second—there’s something additional here. What? But the synchronization is also physics. If each one separately is physics, then the synchronization too is under the control of physics. No. What do you mean no? If physics dictates that Newton will get there and physics dictates that the apple will fall there, then physics dictates that the apple will fall on his head. But physics didn’t dictate that Newton would arrive at the exact second that the apple… No, but physics dictated Newton’s arrival. Physics dictates that, that’s what you claim. Well then, if so, everything is dictated by physics. There’s no combination. If physics dictates that Newton arrives and physics dictates that the apple falls, then it dictates both of them. Physics doesn’t dictate both; it dictates each event separately. Fine, but each event separately. But this meeting contains nothing beyond the two occurrences of the two events. But the meeting of the two events at the same moment, the same second—there’s something additional here. What? If everything is deterministic, then there’s nothing additional, there can’t be anything additional. No, there can be. What? A theological explanation. Why did Newton get there? So we’re back to the theological explanation, from when? Is everything deterministic? No, physics is deterministic. No, only physics. Only physics is deterministic. What? Not everything. But really, you started with a theological explanation, then moved to a physical explanation, now you’re going back to a theological one, so really the theological one won’t help, because if you give a theological explanation for an event that is a physical event, then once again you’re basically saying that the laws of physics were violated. The physical event is Newton’s arrival under the tree. Yes, I’m saying the laws of physics were not violated here. Yes they were, because he got there even though the laws of physics did not dictate it. Including the timing and everything. Obviously. He got under the tree even though the laws of physics did not dictate it; the Holy One, blessed be He, did it. That’s what you say. So the laws of physics were violated. Not what I say—you say it. Well, I don’t. So it turns out that for everything you have a physical explanation. Yes. So the Holy One, blessed be He, is seemingly unnecessary. Not unnecessary—He just doesn’t have a part in this matter. He doesn’t intervene, there’s no providence. So fine, I said that long ago. Yes, I think you’re right. But that’s not what I said here. In a moment maybe I’ll comment on that too. I think it would have been possible to settle the Newton case—that it’s really circularity because of a mental drag—I think it can be arranged with the brackets of necessity. You have to write it with the necessary and the proven inside all the parentheses and not only at the end. Physically necessary? Or logically? Physically—we’re talking here. Physically. The fact that it has to be, it has to be because such-and-such. I’m almost sure it can be arranged. Like you did there in the article? I’m almost sure it can. Fine, we need to see. I don’t know, I don’t think it can, but maybe—by all means. No, I didn’t agree there either, so if it’s the same thing it won’t convince me. Fine, in any case, that’s why I’m saying that in the end, somewhere, the physical picture was violated. The physicalist picture. That’s the picture that says the laws of physics determine the physical events that occur in the world. That gets violated in any case—if you see physics as a condition that determines the occurrence. If you leave a gap—what? There are also people who want to defend it and don’t require violating the physicalist picture. What do you mean? That I would claim that from the outset God created the world in such a way that the phenomena would occur because of—wait, one second. I’ll get to that in a moment. I don’t think that’s possible, but I’ll get to it in a moment. In principle, when I talk about two parallel explanations or two parallel causes, in the end—even though we do this a lot in life, and I brought a few examples—it’s still something problematic. But one second—in interpretation it isn’t problematic. Why? No, interpretation less so. That’s why I’m focusing on conduct. No, in interpretation it’s something else. No, he meant to convey two messages, both of which you can see at once. So that’s already somewhat equivalent to what Arik wanted to say on the physical plane too. What he really wants to say is that also on the level of physical events, the Holy One, blessed be He, established the theological laws and the physical laws in such a way that they always produce exactly the same results. There is some kind of perfect correlation here; the Holy One, blessed be He, is omnipotent, He can do anything. So He established the theological laws that govern what happens, in parallel to the physical laws, each of which completely governs what happens, but somehow it always comes out matching. Then the theological laws say nothing, because it happens anyway because of the physical laws. No, no, but I’m saying—it’s another description and another legal system that… By the same token you could also say that the physical ones say nothing, because it would happen anyway for theological reasons. Both planes are correct, both planes exist, and there’s a wondrous correlation between them. That’s the claim. Maybe I’ll bring an example that will make this a little clearer—when we do—that will make the idea clearer. I don’t agree with it, by the way, but only in order to clarify it. There are two possibilities for creating a correlation between systems of laws. You can create a correlation—when I say correlation, I mean that the two systems of laws will produce exactly the same phenomena; that’s what I call a correlation. Not the laws themselves—the outputs of the laws. Okay? One possibility, which is the simpler one, is simply to translate one law into another law. Meaning, this law basically does the same thing as that one, it’s just formulated in another language. Essentially it’s like saying the laws of physics in Hebrew and saying the laws of physics in English or in theological language. It doesn’t matter. You’re just translating law X into law Y, okay? From English to Hebrew, doesn’t matter. But it’s the same law itself; it’s just two ways of formulating it. It’s like in quantum mechanics—you have Schrödinger’s description, and you have the description of… Yes, exactly. These are different descriptions of the same thing. Exactly—so you can translate one into the other. But there’s a less trivial correlation, and that’s what I call a local correspondence: every law corresponds to another law. There’s another correspondence, which is a global correspondence. Let me perhaps give you an example. In Hofstadter’s book Gödel, Escher, Bach, he brings there—he asks a riddle. He gives an axiom, MI. That is, let’s first introduce a few preliminaries. They translated it—two people translated it over 16 years. Yes, I know, I saw that it came out in Hebrew. In any case, so it started, the whole business starts—that is, the system deals with strings of letters. There are strings of letters that are legal words in the language, and there are strings of letters that are illegal words in the language. Okay? Like any language, basically. Now we want to produce rules of generation, meaning rules that generate the legal words. Okay? We start with an initial string, say MI. Fine? I have three words, three letters in the alphabet: M, I, and U. Now I build a word, MI. I say the first axiom is: this word is legal. Fine? Now I give several rules for how I move from one legal word to additional words. For example, a word that ends in I—you can add twice U after it. Or a word that begins with M—you can erase the M and write another I in its place. Or something like that. All kinds of such rules; these are called rules of inference. I infer one word from another word. Okay? And then I can describe the whole language in these terms. I have an initial word, a collection of rules of inference, and that gives me a set of words—maybe infinitely many words even, doesn’t matter, it can be infinite, it can be finite—a set of many words that I describe by means of a few simple rules. Now, there’s no obstacle whatsoever to describing that very same language itself by means of a completely different set of rules, such that you cannot translate rule A in this system into… one rule in this system, rule B here into rule 2 there, and so on. No, there’s no such correlation. Again, the rules don’t correspond locally, rule to rule; rather there is a different set of rules here and perhaps a different first word as well. The output, the collection of words, is the same words. The legal words in this language are the same words as in this language, and everything else is illegal. That’s what I call a global correlation. Meaning, there’s no correlation between the laws—otherwise it’s trivial, it’s just different languages, there’s nothing beyond that. But it generates the same results. So now by analogy I do the same thing in our context. I say: there is a collection of laws in theology—what needs to happen in every set of circumstances in the world, considerations of how the Holy One, blessed be He, runs His world toward the goals He wants. Fine? There is a system of physical laws—the laws of physics. Now, assuming there’s no correlation at all between one and the other in terms of a physical law matching a theological law one-to-one, it could still be that the collection of events that will be created by the system of theological laws—or the chain of events created by the system of theological laws—will be exactly the same events as in the physical system, and an event that is not legal from the standpoint of physics, like the illegal word in that language, will be an illegal event also in the theological language. Okay? Even though there’s no one-to-one correlation between theology and physics. Here it’s easier to explain what Shmuel said earlier: that these aren’t two explanations in the sense that one is superfluous. They are two different explanations and there’s a perfect correlation between them, but you can explain it on this plane and you can explain it on that plane, and both explanations are correct. Both explanations are correct. You’re talking about the physical rules as a subset within the theological rules. Everything is theological rules. All of it is theological rules. Part of the theological rules… But that’s just words—what is this, semantics. No, it’s not just words. After all, it explains separately; physics separately explains everything; it doesn’t need the theological addition in order to explain. According to this explanation it doesn’t explain separately. Of course it does, it explains separately. What I’m proposing now is a model for how physics can explain everything separately, theology explain everything separately… I’m going back to Newton. I’m going back to Newton. In order to provide parallel explanatory planes, I’m going back to the complex explanation, but in the form… meaning, everything is theological rules. When I say theological rules, I mean everything that God wanted to happen here. Fine, so that’s words. But that’s only words, because when I say that I want to believe in physics, it means what you call physics I call theology and now everything is fine. No—it’s physics as you call it, just remove the “it’s only physics,” that’s all. Fine, remove the “it’s only physics”—that’s not physics. Why not? Because physics says what will happen given certain circumstances. And if you say that something else also has to occur in order for it to happen, then that’s not physics. That’s not what I’m saying. I’m saying what will happen under given circumstances is part of the rules that the Holy One, blessed be He… that under given circumstances this is what will happen. But given that the theological conditions don’t allow it, then how will it happen? No, except where there’s a clash with other rules. Okay, so when there’s a clash with theological rules, physics doesn’t work. So that means you don’t accept physics. Why should I care whether you call it theology? That doesn’t solve any real problem, it’s words. Why? It leaves you with trust in physics, it leaves you with physics. No, it leaves me with no trust in physics whatsoever. Why not? It leaves me with trust in theology alone, that’s all. Again, just words. No. So I call that physics. What you study in the physics department I call physics, okay? That I call physics. Let’s talk about that; let’s not change the words. And it won’t work. No, it won’t work. It will work. No, because physics says the apple will fall and it won’t fall. Take a case of theology where physics will work. No, but physics says the apple will fall. If the net force on it is downward, it will fall. And Newton—even though Newton did not sin—in physics they don’t study whether Newton sinned or not. This could be a specific case where either there really was a deviation from the physical rules and… It’s a deviation. When there’s a deviation, then the physical rules don’t work. Why can’t there be rules with exceptions? I don’t understand what that means. This is really wordplay. When I speak of trust in physics, it means that the laws of physics always work. Without exception, always. That’s it. That’s what a law in physics means. If you don’t accept it always, then you don’t believe in physics. That’s not a crime—that’s my opinion—just a mistaken definition. No, it’s not a crime. He’s allowed not to believe in physics; I’m only saying that we need to know what we’re talking about. To say there are laws—you can say of any law that it has an exception. I can say whatever I want, but what you study in the physics department—what do you study, what you say or what I say? I study what you say because we deal with laws. Not because we deal… Yes we do. In the lab, if it doesn’t work, nobody will accept that Newton didn’t sin and therefore it didn’t work. Right, because usually… not because usually, but always. Usually—but sometimes… So what, usually but sometimes yes? So what’s the problem—here it happened, what’s the problem? Not likely. It could happen, not likely. They don’t accept that; it’s not lawful. They don’t accept it and say it’s unlikely. No. This is a dispute about words, no. That’s not what’s called physics. You can define physics differently, but then it isn’t physics. A law of physics—if it doesn’t always work, then it’s not a physical law. Yes. Fine, no, I’m saying—I’m not saying you’re wrong, I’m only saying that’s not the definition of physics. And that definition is fine. If physics says that this is physics and not a tautology, that’s obvious—it’s a simple statement. No, and that’s what physics says in the accepted definition. So I’m saying something different from what physics says. No problem, fine. And it seems to me that many people say that too. I can also say that Judaism is Christianity and there’s no contradiction between Judaism and Christianity, because to me Judaism is Christianity. That’s how you solve the problem—that’s my solution—because what I’m saying is both reasonable and, it seems to me, many people would say it: that there are physical laws. No physicist would say that. A physicist who believes in miracles would say that. No, what do you mean believes in miracles? Ordinary occurrences, not miracles. Ordinary occurrences, right—also I say that most occurrences are ordinary occurrences. But ordinary occurrences—no miracle happened in the lab. In the end, when something doesn’t work, the physicist throws the paper in the trash. Right, and justifiably, justifiably. Why? Because presumably… Based on what is that presumed? Based on what? Do you know whether Newton sinned or not? Based on what? What’s probable about that? I don’t know, it seems to me that the world behaves in a way… What, the world behaves in such a way that usually everyone is righteous? I don’t understand what your assumption is. But how? That depends on theology. Because theology is God’s will. More wicked people, more righteous people. What—God’s will is always that things remain according to the physical laws except for exceptions. What do you mean God’s will? I’m asking how it is carried out, not what His will is. So exceptions are a kind of miracle. What’s the problem? From time to time miracles. From time to time miracles, depending on how you define miracle. Fine, so we talked—not last year, maybe the year before, I don’t remember anymore—about the concept of miracle. We talked about it quite a bit. I’m not talking about that; I’m talking right now about occurrence in the ordinary course of the world. Fine, okay, that’s obvious. So I’m saying there are exceptions; to accept that theology says that in certain cases there are exceptions. I’m saying what I study in the physics department does not hold. Fine, let’s agree on that. That’s all. That’s what I’m talking about. You don’t accept that—fine, maybe you’re right, no problem—but that’s not physics. That’s it, unequivocally. A miracle too is not physics in the physics department. In any case, this correlation in principle might perhaps explain the existence of parallel explanations. Right? Because basically it says there is a completely parallel explanation; it exists on its own; they are not combined to form a complex explanation, but rather they are two simple explanations and each of them is fully correct. If there is a one-to-one correspondence, why do I need the second one? You don’t need it—not that you need it—but that’s the truth. Yes, but you don’t need it; but the truth is that the theological considerations are always fulfilled and the physical considerations are always fulfilled. Yes, so in that case, for someone who wants theology in order to explain the world, physics is enough for him. Not true—he doesn’t need it. He doesn’t need it—I’m saying: someone who wants to explain theologically is right; someone who wants to explain physically is right; both are right. But whether you want to accept it or not, you can live with these two planes in parallel. That’s what I want to claim. Now the big problem here is, of course, that if we accept that a person has free choice, then that creates a certain problem, because it would not have been possible to determine the laws of nature in advance in a way that would fit both a choice to the right and a choice to the left, and the laws of nature would completely match what the person… But one can say that from the outset God sees what the person will choose and plans accordingly. That brings us to the issue of knowledge and choice. That brings us to another issue where you know I disagree—that the Holy One, blessed be He, cannot know in advance what we will choose. But fine, I don’t want to get into that discussion now; we already argued about that. In any case, on this plane, the simple fact is that even in conventional faith, the Holy One, blessed be He, needs miracles. Right? That’s the fact. We talked about that when we discussed miracle. Needs what? The Holy One, blessed be He, needs miracles—I’m saying it intentionally with that word. Needs miracles. He was not able to carry out what He wanted to carry out through the laws of nature. He needs the splitting of the Red Sea, He needs all kinds of things that are against the laws of nature. The intention was that there would also be miracles—that was the consideration. Fine, it doesn’t matter. So now the question of whether that detracts from His omnipotence or not—you can say what you’re saying. There was a consideration of its own because that was simply what was needed. I don’t care, I don’t care, but in the end I’m saying the very fact that the Holy One, blessed be He, uses miracles means that the Holy One, blessed be He, does not see the laws of nature as something that completely carries out His will. There is no full correlation between theology and physics, because if there were full correlation there would be no need whatsoever for miracles. Okay? So there is no full correlation. Now you could say He wanted that from the outset—I don’t care, we won’t get into that now—but there is no full correlation, because otherwise there would be no need for miracles. Now what does this actually mean? It means there is a simple thing. Many times when we make correlations—and this is specifically about global correlations, not local correlations—if there is local correspondence, think again about the language example: if there is local correspondence between the two systems of laws, there will be no deviation at all. That’s a mathematical statement. If every such law corresponds to such-and-such a law, they generate exactly the same world, then obviously in Hebrew and in English the same thing will happen; it changes nothing. But if the correspondence is global, then here it can indeed break. It can break from time to time. Meaning, there can be a situation where with this set of laws you cannot carry out exactly what this set of laws carries out. There will be certain cases in which the correlation breaks. Example—now they are not equivalent. Yes. Correct. That’s what I’m saying. As a result of the fact that it’s a correspondence… It could be that you are still in process? No—carry out means a certain local event, not reaching a global purpose in the sense that it’s a result and both will bring about the result. No, I’m talking about a local event. I’m now explaining what happened to some person at a given time on the way to the larger goals. I’m not talking about the larger goals. I’m talking about the everyday occurrence that happens everywhere at every moment. Okay? So now I’m saying: if indeed this global correlation doesn’t work completely, then there has to be some point at which it breaks. And that point is what in mathematics is called a topological defect. Meaning, when you do—for example, think of a description in a polar system of the set of points in the plane, and a Cartesian description. Okay? A description in x-y and a description in distance from the origin and angle from the x-axis. I assume that’s familiar, right? To everyone—isn’t polar familiar? What? Not familiar? I don’t know, I think they teach it in high school, no? Never mind. Every point in the plane can be described in one form, which is called Cartesian, after Descartes—yes—what its x component is and what its y component is. What its projection onto the x-axis is and what its projection onto the y-axis is. That’s called a Cartesian description. In addition, every point in the plane can also be described in another way: what its distance is from the origin of the axes and what the angle is between the line connecting it to the origin and the x-axis. That is called a polar description. Distance and angle, or two components. Okay? Now in principle these two descriptions are equivalent. Every point in the plane can be described this way and can be described that way. In one place it breaks—at the origin. At the origin, when the point is the origin itself, the distance is zero. Once the distance is zero, any angle you put there gives the same thing. Meaning, the point corresponds to an entire polar line, the line of r equals zero with every angle, every theta. It doesn’t matter at all which one. So here it breaks. This thing is basically the basis of what are called topological defects. Topological defects are always breaks or fractures in global correspondences. Meaning, points where the global correspondence breaks. What happens in our contexts is the same thing. A miracle. Sorry, if the distance is zero and at every angle, then why is that bad? Why is that… It’s perfectly fine; there just isn’t a point-to-point correspondence. It’s not point to point; it’s a point to a whole line. It’s an entire line of r equals zero and all the thetas. Okay? No, it stops being one-to-one and onto. Look: r equals zero and all the thetas is still the point, still the same point; it maps to the origin point in Cartesian coordinates. So why—so that gives only one point? Right. So there is a correspondence? No, but r equals zero and all thetas in the polar description is infinitely many points. r equals zero and theta equals this, r equals zero and theta equals that—those are two different points, and all of them map to one point in Cartesian coordinates. I thought they were different points of the polar description. Of course. It’s not one-to-one and onto, the mapping. Two coordinates. So basically what happens in global correspondences—usually, by the way, such defects occur. It’s almost impossible for two systems that have no law-to-law correspondence between them, but are two independent systems—these systems of laws—to produce exactly the same phenomena. Think again about the words; it’s almost impossible. It’s very rare that something like that happens. Therefore… so within the polar definition there’s a problem, not in the correspondence to the other. Why? There is no one-to-one and onto correspondence. Draw r and theta on a Cartesian system. Fine? r here and theta here. Fine? Then that Cartesian point corresponds to the entire x-axis in the polar description. It’s not point to point. One-to-one and onto means every point corresponds to a point and a point here corresponds to a point there. But that’s not the case. When I say a point in polar coordinates, distance zero and a given angle. Distance and angle—that’s a point in polar description. A certain distance and a certain angle. That’s a point. So if it’s a different angle? It’s a different point in polar coordinates, but in Cartesian coordinates it corresponds to the same place. It’s a set of two—you explained that this is the distance from that point. Distance and angle. Distance and angle. When I have distance zero but the angles are all angles. Obviously, it’s the same Cartesian point that has infinitely many polar descriptions. Not only the same point—it’s the same Cartesian point that has infinitely many polar descriptions. Think of it as that set being much larger than this one. That Cartesian point has infinitely many polar descriptions, not just one. That’s a waste of a lot of rules over… In any case, in a place where there is a global correspondence, many times there is one point—there are many points that correspond to one point in Cartesian coordinates. The mapping… the mapping is not point to point, not one-to-one. Yes, so in polar coordinates it’s simply an insufficient definition, that’s all. What do you mean an insufficient definition? That’s the definition of the… there are many points that have the same… There is no other polar definition; that is the polar definition. That is the polar definition—there isn’t another one—every r and every theta. Now true, the definition is allowed not to be one-to-one and onto; you just need to know that this can create all kinds of problems. No problem, that’s allowed, it’s perfectly fine. There are descriptions that are not one-to-one and onto; that’s what creates the problems. So it’s not like what you said earlier, that the correspondence between them is one-to-one and onto—it’s not point to point. Right, that’s why I’m bringing this. You said that two maps that happen to a point, that gives the result you said. Right, because every point in the two-dimensional space has a Cartesian description and has a polar description. A point that does not have such a description is not in the two-dimensional space. The words here are points in the two-dimensional plane. That’s called—that’s the analogue of the words. Now I have two systems of rules that can describe the set of all legal words. The illegal words are what is found in the space, not in the two-dimensional plane. Fine? So the illegal words will receive neither a polar nor a Cartesian description. And the legal words—each of them has a Cartesian description and a polar description. So in that sense they are parallel systems according to the definition I gave earlier. But between them there is no one-to-one and onto correspondence, there isn’t; not every point corresponds to a point. In laws that are to be parallel, then I say, by analogy to laws, I say as follows: if every law corresponds to every… say, if I were defining r as something specific and theta as something specific one-to-one—for example if I rotate the system of Cartesian axes, this is already too much mathematics, but when I rotate the Cartesian axis system, that is of course completely one-to-one. Because every x-prime is defined by x and y and y-prime is defined by x and y linearly, so it is one-to-one in an obvious way. Okay? So there are transformations that are and transformations that are not. But never mind, let’s get back to our matter—leave the mathematics. For our purposes, I’m talking about a correlation, say, between theology and physics. When this correlation breaks, that’s the topological defect in this global correspondence; that is a miracle. If there were local correspondence, there would be no need whatsoever for miracles. Because every physical phenomenon would correspond to the theological goals and vice versa, right? If the correspondence is local, then all the phenomena match perfectly; there’s no need at all to resort to a breaking of the laws of physics. If there is a need to resort to a breaking, that means the correlation is global and not local. And that’s what I said earlier: the moment the Holy One, blessed be He, needs miracles, it means there is some sort of break in the correspondence between physics and theology. By the way, in interpretation—if I return to interpretation, to what Shmuel asked earlier—there is a correlation according to Nachmanides, say, between levels of interpretation: peshat, remez, derash, and sod; say peshat and derash for the sake of discussion. Okay? There too there are topological defects. Or peshat and sod if you prefer, not peshat and derash; let’s speak about peshat and sod, where there are topological defects called a scriptural decree. A scriptural decree is a topological defect in the correspondence between peshat and sod. Why? Because the assumption is that behind the matter sits an explanation in the esoteric level, but when it’s a scriptural decree, I don’t know how to explain it in the revealed level. So the correlation between the esoteric explanation and the revealed explanation breaks. And again this means that the correlation between the revealed and the esoteric is a global correlation and not a local one, because otherwise it couldn’t break; it would have to be one-to-one. Okay? So I’m showing you that many times these global correlations, which could have justified double explanations, usually cannot really provide the explanation, at least not fully, except for exceptional cases. And here we arrive at the exceptional cases. If I say there are no miracles and you solve the whole problem… If I say there are none, then there are none, but the Torah says there were. I don’t know. You can say there weren’t, but then you don’t accept what the Torah says. The Torah says there were miracles. You know the Torah better than I do? Do you know where you stand? But now we are on the philosophical plane. On the philosophical plane every religion has its miracles and its beliefs and so on and so on. Don’t get into what you—stand outside it. Wait—from the outside I would come to the conclusion that there are no miracles, everything is fine. But choice also creates a problem for you even without miracles. What? From the outside I’m not in the dilemma at all; I don’t need to look for the solution. After all, the whole dilemma is that there is a mismatch between theology and physics. If I’m outside, there is no theology; there is only physics. But choice also creates for you the same problem without miracles. Huh? Fine, those who stand outside may also give up free choice for the same reason; they also give up free choice. Yes, the same thing, exactly. But our topic is not Judaism—you are now talking about dichotomies and the possibility of solving them. You brought an example from the Jewish world, you said interpretations; suddenly you go down to beliefs. The moment it goes down to beliefs, there’s no end to it. What do you mean there’s no end to it? But I’m saying, within the faith… Stay on the philosophical plane. Why should I stay there? I want to bring an example from here. Why go there when it doesn’t illustrate? I’m looking for where it does illustrate. So within the plane of beliefs, there you can see an illustration of two parallel systems of explanation whose correlation breaks. If you don’t… I didn’t solve anything—I’m saying that you need to resort to miracles if you accept that there are two parallel systems here. Fine, that’s a consequence, there’s no other way. You can say there were no miracles and not accept parallel systems and live with physics in peace and quiet; you have no problem, you don’t need to solve anything, so there’s no need to make correspondences. Okay, so here—I’m not making them. Great. So if that’s the case, does that say something about the Mishnah of the ten things that were created on the eve of the Sabbath at twilight? What do you mean? They were apparently something fixed, maybe, I don’t know, or something, I don’t know. Maimonides really speaks about that; he explains all the miracles that way. Right, and we discussed that when we talked this year about miracles. In that case you have to give up free choice if you go in that direction. In short, parallel explanations—parallel explanations are a problematic thesis. Where will the point be between the psychological? Ah. So psychology and judgment—what I said earlier about returning to repentance and leaving religion—there, in my opinion, there is no escape but to understand that we are dealing with combined explanations. A complex explanation composed of the two elements. When a person does something and psychology comes and explains what he did, my assumption is that this explanation is not complete. It gives a condition that may be necessary but not sufficient. Sometimes it can be both. And also the philosophical explanation. It can’t be, because then it’s an uncontrollable impulse; it’s something not subject to judgment. I’m talking about the ordinary actions of human beings where there is also judgment. We say, right, there are also psychological influences. In the end, what a person does is the sum of psychological influences plus his judgment; the weighing of both together gives you what the person does. There, for example, I don’t think there is room for topological defects. There it does seem to me that it is supposed to be combined. Meaning, it is the sum of the two. What about psychology and the physical? Just as a point—that’s the explanation. So if you’re a reductionist, then it’s a mapping. If you’re not, then you need to choose: either they combine, or one has to choose. Or there’s that global explanation—maybe the sensitive point? A global correlation. Fine, but then again the question is where the places of mismatch will be. Fine, if psychology—since psychology… why assume there must be places of mismatch for everything? No, I’m saying maybe there aren’t. If it always matches, then fine. But if it always matches, that also raises the suspicion of reduction. If we’re not reductionists, usually the motivation not to be reductionist is to say that there is something in psychology that you cannot predict by means of physics. Fine, otherwise what’s the point of being a reductionist when you are essentially saying that in any case they correspond—or vice versa? Biology and quantum mechanics are difficult. Okay, there? You can describe the biological processes, all the biological processes, using mechanics, right? But still. That’s the common belief; I wouldn’t stake my life on it. There is no such description. Of course, because either it is difficult or it still eludes us. The description is complex; the accepted excuse is that the description is too complex because biological systems are many-particle systems, and try now to calculate the whole set of particles that compose a biological system. But the accepted assumption among reductionists is that there is reduction, except that it is so complex that we cannot present it. Right, but even in physics before biology, statistical mechanics is exactly that. Well, statistical mechanics is exactly that. You don’t calculate every particle in a pit. You do statistics. Temperature—but temperature is exactly all of thermodynamics, all of thermodynamics. Obviously, temperature is an additional factor that you introduce from outside. No, you make a canonical ensemble, a microcanonical ensemble, you make various decisions about your distribution, and then you can derive the macro from the micro. And you don’t calculate every particle. But those are assumptions; you can’t do it without the assumptions. Wait, weren’t those assumptions measured on individual particles? Can’t you sample this in some way to test those assumptions? I don’t think so. How do you directly measure the velocity of a particle? No, you can observe some physical properties that are some sum over all these things, but you can’t measure the velocity of a particle—it’s impossible to measure, even from the standpoint of quantum theory, because you need to know where it is in order to measure the velocity. You work with a distribution. You don’t know where it is when you measure only the velocity. So how do you know it’s that particle? You don’t. You can approximately measure the velocity. I don’t think so—for a gas of particles there’s no chance. How would you measure 10 to the 21 particles? Not all of them. Measure a hundred. Who says those hundred are a representative sample? The locations are not the relevant distribution. Who says it’s a representative sample? I don’t know. And particles—that’s a gas? What? How many particles make a gas? Yes. Infinite, you know. Thermodynamics is only infinite. But we know that large numbers are similar. If I want to… fine, that’s no longer connected. Fine, in any case, for our purposes, I’m saying that parallel planes of explanation are very attractive, but they are still problematic. Meaning, it is the sum of the two. Unless one sees them as summed, as a complex explanation that is the sum of both. So when someone gives a psychological explanation and someone else gives a philosophical explanation, we treat these as explanations, as parallel explanations. Exactly, even though they’re not really explanations. You have to understand—they’re not really explanations, because an explanation is supposed to be sufficient. Exactly. Also, how do you normally arrive at it? You’ll have to arrive at some explanation. Why did you arrive at that explanation? You analyze certain phenomena, so if you could, you wouldn’t arrive at two explanations that are identical just as a theory you develop. Why would you arrive at both? Suppose theology is given to me from above—I don’t arrive at it, but rather the Holy One, blessed be He, delivered it to me. Suppose; theoretically that could be. Fine, that’s only a theoretical issue. Okay, this really took me much longer than I thought. That’s because of us, right? Fine. Two more points that I’ll insert in the two minutes that remain. One of them is harmonization, and that’s a bit similar to cumulative explanations. Meaning, sometimes there are two things that compete, but you can harmonize them. I think I mentioned not long ago Henshke’s article, right, on peshat and derash? I thought I mentioned it, no? This year, I hope. I remember it as really not long ago. So he, for example, gives—he creates some harmonization between peshat and derash in very beautiful ways, I think. Many times you think—for example, “an eye for an eye”—so the peshat says to take out the eye, the derash says monetary payment. Henshke comes and says: you can harmonize the two, and basically say that you extract from him the value of his own eye, not the value of the injured party’s eye. What is that? It’s basically some kind of summation of peshat and derash together. Because the peshat says take out his eye, and the derash says no, no, don’t take out an eye, instead take money. If there were only the derash, I would take the value of the injured party’s eye. If there were only the peshat, I would take the eye of the damager. But when there is peshat and derash, then I take the value of the damager’s eye. That, for example, is a combination; he makes several combinations there, several examples of this matter. So that’s the matter of harmonization, but it is completely parallel to the combining of explanations that I mentioned earlier, or the combining of interpretations in this case. Interpretations and explanations have a fairly similar logic, although you are right, as Nachmanides says, and there is no obstacle in that the Holy One, blessed be He, intended several explanations in parallel. And the reason for that is that it doesn’t happen by itself; the Holy One, blessed be He, did it. So He can—even a human being can make a sentence that can be interpreted in two… yes, can convey two messages in the same sentence. What’s the problem? In principle it can be done. In natural events, where it happens as though in a natural process and not synchronously or something else, then it’s a different story. That’s one point. The second point is the naturalistic fallacy context. It’s also very important to distinguish between values and facts. Meaning, when we derive a value or a norm from a factual system, this is usually regarded as a fallacy. Because facts alone cannot provide an explanation for a value or a norm. Let me maybe give just one example to clarify this, because I still want to finish the methods this time. Suppose there is an argument in favor of changes in Jewish law. Arguments in favor of changes in Jewish law often hang on changes in reality. For example, there are people who want to argue that today a woman should be valid as a witness or as a judge, because women in the days of the Sages were uneducated or unfamiliar with the ways of the world, they sat at home, and therefore the Sages said that they are disqualified; the Torah, the Sages, the midrash said they are disqualified. But today, since the situation has changed, they should be validated. That argument in itself is a fallacious argument. What is the logic here? It is a fallacious argument because the change you point to is a factual change, and you want to infer from it a normative change—in this case, a halakhic one—namely that a woman was once invalid for testimony and now a woman should be valid for testimony. In order for the argument to become valid, you need to add another assumption here: that the invalidity of a woman for testimony stemmed from the fact that she was uneducated or not involved in social life. Yes? If you add that, the argument becomes valid. So here too, many times there are parallel planes that people raise, but one needs to know that these planes are not parallel—they are different. It’s not parallel. Meaning, the facts do not determine the norms or the judgments. Okay? So we need some additional assumption that connects the planes in order to derive the judgments or the norms from the facts. Okay, next time I’ll use all the things I listed here on a few specific examples—that I didn’t get to now, though I also intended to do that today—and then we’ll move a bit to paradoxes and loops and all kinds of things of that sort.