Artificial Intelligence – Lesson 14 – Rabbi Michael Abraham

[Rabbi Michael Abraham] Okay, so a recap of the previous chapters. What we saw, really — let’s just talk about the end, okay? We basically saw a bit of the rationale of how a computer is built. We started from simple electrical circuits, where the states of the switches represent the input and the bulb represents the output. With such a circuit you can build what’s called a logic gate — that is, “and,” “or,” that’s a series connection, a parallel connection, XOR, and all sorts of more complicated things. And then with that we built several circuits — connecting several such circuits or several such gates — and basically built a calculator that adds numbers, in principle, which is already really a computer in the sense we’re talking about. But later I said that clearly, if we want to create a machine, that’s what I called an analog computer. An analog computer is basically a computer that simulates the phenomenon. In other words, the phenomenon that takes place in the analog computer is described mathematically in the same way as the problem I want to solve. Say I want to find the derivative of a function, so I take something into which I feed, say, a voltage, and it differentiates the voltage and the current that comes out is the derivative of the voltage. So if I measure the current, I’ve essentially computed it. I feed in a voltage according to a given function, and then I measure the current that is produced, and what I’ve really done is differentiate the given function. Okay? So therefore all those things are analog computers. But the disadvantage of analog computers is that they are computers for one operation. That is, you have to create a separate computer for every operation, for every problem, that you want to solve. If you have a problem, I don’t know, some differential equation or something else you want to solve, you have to build a circuit that exactly imitates the mathematical problem you want to solve. And that’s obviously not efficient, not practical. If we want a system that will solve many problems for us, then what we do — and here we move to the digital computer — what we do is basically take a computing unit that contains many logic gates and combinations of them and so on, which knows how to perform certain basic logical operations, and then I basically try to break every problem I have down into the basic logical operations. And then I give the computer instructions through software. That’s what a programmer actually does. He writes — software is basically a collection of instructions for the computer, which part to activate, when, and what to do with the result. Okay? That’s a simplified description, but that’s really the basic rationale. And then what happens is that this same system of basic logical units can solve lots of problems. For each problem you need to write software. Each such program tells the system which parts to activate and in what order, and for another problem we’ll activate different parts in a different order, we’ll do different things with the output, but we keep using the same machine, the same set of tools or logic gates, and the program is written each time to solve a different problem. So you don’t need to build a computer every time in order to solve a problem; rather, we can write a program for a given computer, one computer, we write a program for it, and the program solves the problem. Okay? That’s basically what’s called a digital computer, and therefore it is much more efficient than an analog computer, because one device, yes, one machine can solve a great many problems. Of course, that shifts the work from the hardware realm to the software realm. Why is it called digital? Hardware is the — yes — the physical stuff, the devices themselves, the electrical circuits, the physical structure of the computer, and the software is basically what the programmer writes in order to activate the various electrical circuits. So now we have a system with one hardware setup, and it can solve many problems. For each problem you have to write a program for what the hardware is supposed to do in order to solve that problem, okay? That’s basically how a digital computer is built.

[Speaker B] Why is it called digital? And how does the software work? I mean, how does it physically operate?

[Rabbi Michael Abraham] The combination — the combination of basic logical units in order to produce more complex operations is basically done with logical tools. We break the complex operations down into basic operations, and then that combination is a logical combination of different logic gates in order to produce the complex problem. Now, logic gates that output one or zero are basically the basic element of a digital system. A digital system — say when I want, I don’t know, when I want for example to calculate x squared, okay? I want a computer that will calculate the function x squared for me. Say when it receives 1 it will give me the result 1; when it receives 2 it will give me 4; when it receives minus 3 it will give me 9, and so on, okay? So in principle you can do that in an analog computer in some way if we have a physical system where there is some relation, say, between voltage and current such that the current is the square of the voltage or something like that, and then I can do it with an analog computer. But if I want to do it with a digital system, then I have to break this operation down into a collection of logical operations and try to build the complex operation through all sorts of basic logical components, okay? And that’s what’s called a digital system, meaning digital, yes? Digital means it works with digits, with something discrete, not something continuous like an analog computer. Fine, but that’s really all… how does the software do the work? What?

[Speaker B] How does the software — how does the software do that work of taking the logical commands?

[Rabbi Michael Abraham] That’s us. That’s the programmer.

[Speaker B] No, physically, how does it work? I’m not talking about how to do it — what does the software, in principle, do?

[Rabbi Michael Abraham] What happens is, you feed the software into the computer, and now you enter an input, okay? Now, once you’ve fed the software into the computer, you’ve basically built a computer for solving that particular problem.

[Speaker B] Fine, I’m asking how the software takes the logical commands like the Rabbi demonstrated to us from the beginning and arranges them. How does it physically do that?

[Rabbi Michael Abraham] No, it doesn’t arrange them; they’re already there. Software can’t move anything in the structure of the computer. Obviously, I understand. The structure of the computer is given. Right. The software says — the software gives a command: this logical unit should now start operating, take this input, do to it what you know how to do, and pass the result to that other unit. How does it tell it?

[Speaker B] What? How does it talk to it? What does it mean, “tell it”?

[Rabbi Michael Abraham] We translate the programmer’s software instructions into electrical signals. Say I tell it — those electrical signals basically activate the switches of the electrical circuit. So when I write in software, I’m telling it: take the elements you have, put them together, activate two switches, a bulb, and a power source. Of course that’s not what actually happens there, but just to translate it into the terms I was speaking in. If the software tells it to put the two switches in parallel — sorry, in series — then what it’s doing is a logical “and.” If the software tells it to put the two switches in parallel, then it’s doing an “or” operation. Now, of course the software doesn’t move the switches; it only gives instructions on how to activate them and in what order. But the moment it says activate this as if it were parallel, or activate this as if it were series, it’s basically telling it which operation to perform in order to produce the desired result.

[Speaker B] And somehow it gets translated into electrical signals…

[Rabbi Michael Abraham] …that will carry it out. How does that actually happen? Right, I spoke about interfaces. Interfaces are very important. There is an interface before the input and an interface after the output — sorry, before the output and after the input. That is, you enter some input into the computer, and that input is translated by an electrical system into voltages. Say the digit 1 goes in — that gets translated into five volts, okay? Five volts. Now those five volts — the software tells them: take those five volts and send them into this circuit where the two switches are in series, okay? And then that’s what the software instructs it to do. Now it sends it there, and the result that comes out — say if both inputs were 1, the result that comes out is 1. Then there is another interface, an interface before the output, which says: ah, if you got a 1, turn on the bulb. Then I’m outside, I see that the bulb is on, and I understand that the answer is 1.

[Speaker C] Rabbi, how do you say ALU in Hebrew?

[Rabbi Michael Abraham] Arithmetic Logic Unit.

[Speaker C] Yes, how do you say it in Hebrew?

[Rabbi Michael Abraham] An arithmetic-logical unit.

[Speaker C] Isn’t that called input?

[Rabbi Michael Abraham] What? No, no, of course not. That’s the… that’s the core of the computer.

[Speaker C] Is that the CU? CPU. Yes. But if you’re speaking in terms that — if you can translate them from English.

[Rabbi Michael Abraham] Input and output. Yes, okay. Input is what you take in — that’s the input — and output is what you emit, what comes out…

[Speaker C] That’s what connects with the ALU?

[Rabbi Michael Abraham] No, the ALU creates it; it takes the input, computes, and produces the output.

[Speaker C] Ah, now I understand.

[Rabbi Michael Abraham] That’s the heart of the computer, where the calculation is done.

[Speaker C] I know it in English, I just don’t know it in Hebrew, okay.

[Rabbi Michael Abraham] In any case, this idea is what really paved the way for the computers we know, or knew until ten years ago — basically one machine that can solve many different kinds of problems. But again, for each type of problem you need to write a program. In other words, it’s not that the machine now receives a problem and spits out the solution — no, you have to feed a program into the machine, and in that program the programmer thinks through how to solve that kind of problem correctly, and then gives the computer instructions about what to do. That is, instead of building many computers, one for each problem, as in analog computers, I build one computer but have one program for each problem. In other words, each program adapts the computer to solve a certain type of problem, okay? Now this — I’m already saying this ahead of time, we’ll get to it later — but unlike artificial intelligence, for example, where you don’t need any such thing. I mean, it’s one program, one hardware system, everything is one — you don’t need to do anything, you just ask what you want and it gives you the answer. You understand that this is progress, the next step after the digital computer. In other words, if we progressed — the analog computer is one computer for each problem; the digital computer is one computer for all problems, but each problem needs its own program. That is, for every problem you have to write software to solve it. Fine, and that’s complicated; you need talent to write efficient software, good software, accurate software, and so on. The next stage is a computer that solves all problems as it is. You don’t need to write a separate program for every problem, and certainly not build a separate machine for every problem. No — it’s the same machine that solves all problems. Which really sounds like hocus-pocus, and that’s what I want to get to in a moment. But before we move on to artificial intelligence — up to here this is an ordinary computer — now we’ll move to artificial intelligence, not large language models, which are only, I don’t know, five years old, something like that, maybe not even, but I mean artificial intelligence in the sense of neural networks, something that has already existed for, I don’t know, thirty years I think or even more. When I was doing my doctorate, it already existed, so I think that’s roughly when it started. In any case, I want first to summarize what we see up to the stage of the digital computer — what exactly have we learned for our purposes? So I want us to notice two properties of computers as I described them. One property is that the computer solves no problem. The one who solves the problem, in an analog computer, is the one who built the computer, and in a digital computer it’s the one who wrote the software, okay? But the one who solves the problem is always the human being. In other words, both in an analog computer and in a digital computer, the one who solves the problem is the human being. In an analog computer, I literally build the computer so that it will solve the problem. I put in a capacitor because I know it differentiates, or I put in two switches because I know they’re in series and that they do “and”; I simply build the circuit so that it gives me the answer I want, okay? So there it’s obvious that I am the one solving the problem and not the electrical circuit. Now in a digital computer, the computer is one; I don’t build a computer to solve every problem, but I do write a program to solve every type of problem, and therefore the one who solved the problem here is still the human being, not the machine — only this time it’s done with one machine, and the human solves the problem through software, each time a different program written to solve a particular problem, okay? But still, notice, the one solving the problem all the time is the human being, not the computer. The computer merely gives us some operation that we use in order to solve the problem. It’s like taking pen and paper and solving a mathematical equation on them. No one would say that the pen and paper solve the problem, right? I use pen and paper to solve the problem. Computers too, as I’ve described them so far: the programmer or whoever built the hardware, it doesn’t matter, are the ones who use this golem in order to solve the problem. But the one who solved the problem is the human being, not the machine.

[Speaker D] Can you remind me what exactly you mean by solving the problem? Yes, I remember you talked about it, but I forgot.

[Rabbi Michael Abraham] Say, a machine that adds two numbers. All right? It gives me x plus y. I give it x, give it y, and the output is x plus y. Okay? Now I write a program that tells the machine what to do. Take x, see how many units it contains.

[Speaker D] I remember what you said about a deterministic process, yes, that in the end the machine just acts deterministically and… yes, that’s clear, all of it is reason, right?

[Rabbi Michael Abraham] So far, everything is deterministic.

[Speaker D] Yes, and human intelligence is what created the process, what programmed it, right. But in what sense — that’s why I’m asking — in what sense is it not solving it? In the end it brings you the correct answer.

[Rabbi Michael Abraham] Right, just like pen and paper — the pen writes the correct answer on the paper.

[Speaker D] I’m the motor in that case, my hand is…

[Rabbi Michael Abraham] …the thing that moves it, right, you are the motor.

[Speaker D] Not the motor — the computer works by itself, automatically.

[Rabbi Michael Abraham] No, the computer does not work by itself. The computer works according to my instructions; I’m the motor. I move the pen over the paper. I move the units of the computer so that they will build exactly what I want.

[Speaker D] I’m not saying…

[Rabbi Michael Abraham] Exactly like pen and paper.

[Speaker D] I just ask, say, I assume this is syntax, so apparently an ordinary computer can do this — that is, diagonalize a matrix. The computer does that without me.

[Rabbi Michael Abraham] I’m not saying it — no, it doesn’t do it without you, no.

[Speaker D] I give it a matrix, I say, diagonalize it.

[Rabbi Michael Abraham] No, you don’t say “diagonalize it.” You are relying on the fact that inside there is a subroutine that diagonalizes matrices. Someone wrote that subroutine. Okay. Fine, thank you very much. So he solved the problem, not you. Fine, but it doesn’t matter — it’s still a human being.

[Speaker D] So by intelligence you mean that in solving the answer it’s the intelligence that created the path to the solution?

[Rabbi Michael Abraham] No — the software that is inside the computer, yes, the subroutine. Okay, I understand, fine.

[Speaker D] So in the end…

[Rabbi Michael Abraham] In the end, this is really just like water. Water does not solve the Navier-Stokes equations, even though its motion describes the solution. Here too, this is some kind of golem that runs and moves electrical currents according to physical nature and the laws of physics, that’s all. I use this thing to solve the problem, and the one who solved the problem is me. The computer is my pen, that’s all. Now of course it’s a more sophisticated pen, but conceptually it’s still a pen. It’s a pen that I move and with which I write the solution. Now, a second property of computers as we’ve seen them is that the computer of course doesn’t solve a problem not only in the sense that the intelligence needed for it is human intelligence, but also after the human has already fed the program in, what the computer does is not solve a problem. What the computer does is route electrical currents, turn lights on and off, that’s all. What does solving the problem mean here? It’s me as a human being — and this time not the one who wrote the software, but the user of the computer. I look when the bulb lights up, I give it meaning, I call it “one” when the bulb is on. So for me the result of the problem was one. But the computer didn’t do zero plus one equals one. The computer routed electrical currents and acted according to the laws of nature. I give meaning to the output that the computer produced, and for me that means one. So the computer — I’m saying something beyond that. The first characteristic I said was that the intelligence that created the solution was human intelligence and not the golem’s. But now I’m saying: leave that aside. Even after I’ve already loaded the software into the computer, that’s it, the human has finished the work and gone home. Now there is already software inside the computer, it is already a computer that knows how to solve problems — knows how after I loaded the software into it. That was the first point. Now I have a second point. Even after the software is inside it, it doesn’t really solve problems. The software tells it: raise this switch, lower that switch, turn this bulb on; if that bulb is on, turn off that switch; connect these two currents here; and in the end turn a bulb on or don’t turn it on. Okay? That’s all. Now, what the computer does is route electrical currents and turn on bulbs, that’s all. We, when we look at the bulbs, give them meaning. Say, imagine there’s a series of bulbs: one is on, one is on, and one is off, and we say, ah, that’s 110 — one, one, and zero, yes? A lit bulb is one, an unlit bulb is zero. So here there is one, one, zero. Ah, so the result of the calculation is one, one, zero. That’s the result of the… But the computer didn’t do a calculation and didn’t solve anything; it simply lit three bulbs according to what resulted from the electrical currents. Therefore, beyond the fact that the intelligence that created the solution is human intelligence, even after that there is not really any process here of solving a problem. There is a process of routing electrical currents, that’s all. The problem is solved only in the mind of the user. Now I’m not talking about the programmer, but the user. Even in a computer that already has a screen, not lit bulbs like the primitive thing I described — think of a screen. I already spoke about this, that on a screen, say, you see “one plus one equals two” written on the screen. How is that produced? When I type 1 on the keyboard, okay, what I’m really doing is activating a system that lights up the screen in such a way that it displays 1. It simply causes many tiny lights on the screen to light up precisely in the shape of the digit 1. The computer of course has no idea that a 1 is written there; it lights bulbs according to instructions. I light them in such a way that for me the digit 1 is written there. Okay? Same thing when I say plus, so I also light bulbs in such a way that there is a plus sign there. And then again bulbs so that another 1 appears. But all of that is representation, and only for me does it become an addition problem: one plus one. In the computer itself it’s a collection of electrical currents that in the end light up certain points on the screen, and that’s all. The computer deals neither with addition exercises nor with anything else; it simply routes currents. According to its structure, that’s all. We, as those who built the computer and the software and the interfaces and everything, build it so that it lights up the bulbs in such a way that it will tell us, will look to us like, an exercise of one plus one. Okay? But that’s just it — we simply arranged the representation of the electrical currents in this way so that we would understand that that’s what it’s doing right now. Then I say equals, yes? Equals is the symbol that the computer writes there, and here I tell it: light up the bulbs for me on the other side in a way that matches the result of the problem. Okay? So if the result of the problem is one, light up the bulbs for me in such a way that something appears in the shape of the digit 1. Okay? So again, “one plus one,” “zero plus one equals one” is written on the screen. But nowhere in the computer was that calculation performed. Nowhere — not on the screen, not inside the computer, nowhere. I simply build a system such that when I write to it one plus zero, it lights up bulbs on the screen in the form of the exercise one plus zero, and then inside it performs all sorts of operations, routes currents, lights bulbs, and everything exactly as we described in the circuits I presented, and what comes out in the end is the result of the sum of the two numbers that were entered there. And if the result is something, the electrical currents flow in some pattern — and for me those electrical currents are one — I instruct the computer: light up bulbs for me in the form of one. Equals one. Okay? That’s it. So the calculation takes place only in the mind of the user. There is no calculation. Inside the computer no calculation is taking place. Nothing. Electrical currents are just flowing, that’s all. There is nothing there inside the computer — it’s a collection of electrons flowing to various places with voltages and all that. Nothing there has any connection at all to an addition exercise or anything of the sort. We, as those who use the computer, know how to build it in such a way that those meaningless things it does — once this is one plus zero, the result will be translated into one — and then we will see here a calculation: one plus zero equals one. So this is a very important point to understand, that the two characteristics of computers as we have seen them so far are: first, the intelligence used to solve the problem is always human intelligence. Second, the one who actually performs the calculation is the user, not the computer. What does it mean that the user performs the calculation? The user doesn’t perform the calculation; rather, the user gives what happens in the computer the meaning as if a calculation were being performed. It’s not that the user performs the calculation. The computer performs the calculation, but the computer routes currents. I give meaning to what happens in the computer as if there were some addition exercise here, that’s all. This is a very important point, because once you understand these two things, then you understand that Turing’s claim is nonsense. I mean, that claim that says that if a computer knows how to do many terribly sophisticated things, then it really is a person. It’s not a person at all. The one who built it is a genius, and he knows how to make a system such that, in the end, once we give meaning to what it does, it will look to us like solving problems, or answering questions, or things of that kind. No answer to a question and no solution to an exercise takes place inside the computer. A computer does none of that. A computer routes currents and lights bulbs, that’s all it does, according to the instructions I gave it: when and in what order, and which currents to send, and which switches to open, and which bulbs to light. That’s all. So it really could be that the Rabbi can be…

[Speaker D] More precise, and exactly what is it that the computer lacks? Because that’s not clear to me. If what you mean is that it has no reflection, or that it doesn’t understand semantics, then I think that’s what you’re talking about.

[Rabbi Michael Abraham] That it has no reflection is obvious, but I think what I’ve just said goes further than saying it has no reflection.

[Speaker D] Yes, it’s like you’re saying it has no semantics at all; it works entirely on syntax.

[Rabbi Michael Abraham] Exactly. It has no semantics — that’s the definition.

[Speaker D] But then I compare this, say, to the way I always learned mathematics — that you don’t define the concepts; you take them as semantic primitives, yes? As some sort of foundation, and then build concepts on them. So also when human beings build concepts, our most basic concepts, we don’t really — don’t really under-, don’t really understand…

[Rabbi Michael Abraham] …them beyond their use inside the axioms. No, clearly we do understand them. That’s simply not true. In set theory — obviously we understand them. We simply can’t define them, because a definition always uses concepts. So if you define a concept by means of other concepts, there will always be an initial substrate of concepts that you will not be able to define by means of a more fundamental substrate. So how do we understand them? But that does not mean we don’t understand them. In what sense do you understand them, then?

[Speaker D] I don’t understand. I mean, in what sense, say, do you understand the…

[Rabbi Michael Abraham] …element, the word “element” in set theory? If you don’t understand the concept of element, then you won’t understand the concept of set either.

[Speaker D] I understand the concept of element within an axiomatic system in which the concept of element satisfies the assumptions.

[Rabbi Michael Abraham] But that axiomatic system itself uses a conceptual system that it does not define.

[Speaker D] Yes, primitives, you take them…

[Rabbi Michael Abraham] …as primitives, and then I understand those concepts through the axioms. Okay, but those primitives — those primitives you do understand. Because if you didn’t understand them, then the more complex things that are built…

[Speaker D] …from those primitives, you wouldn’t understand them either. I don’t think they have meaning. I think that’s the whole idea of mathematics — to strip them of all meaning beyond their use in the axioms.

[Rabbi Michael Abraham] No, no, no. That’s a mistaken view of mathematics. A mistaken view of mathematics — and of axioms too, by the way. There too — it’s even more common among mathematicians to think that axioms are arbitrary. Axioms are not arbitrary. Axioms are self-evident — at least in some contexts. I mean, the point is that if you use one conceptual system in order to define a higher-order conceptual system, and you don’t understand the basic concepts, then you don’t understand the higher concepts either. Therefore it’s obvious that you do understand the basic concepts. In what sense do you understand them? You understand them, but you don’t know how to ground them in a more basic conceptual framework. That doesn’t mean you don’t understand them.

[Speaker D] But in what sense do you understand them?

[Rabbi Michael Abraham] I mean, when I say that I understand something, that’s when I know how to explain it, when I know that… No, no — not true! Big mistake! That’s a very big philosophical mistake. There is no necessity at all to identify understanding with the ability to explain. Not at all. Even though — yes — there are the famous sayings of Rabbi Chaim, that the quality of explanation depends on the quality of understanding. So yes, the quality of explanation depends on the quality of understanding — that’s true — but the reverse is not true. The quality of understanding does not depend on the quality of explanation. In other words, you can understand primitive things like these, you understand what they mean, you don’t know how to define them by means of other concepts, but you do understand them.

[Speaker D] No, I would argue something like this: I don’t think — maybe here we have an even more fundamental disagreement — I don’t think there is cognitive content apart from language. And if I don’t have the ability to formulate…

[Speaker B] …an idea clearly — Rabbi, Rabbi, can I jump in for a second? Maybe I don’t know the fellow’s name — can you explain to me what the color red is? What does it mean to experience the color red? In clear language so we can understand?

[Rabbi Michael Abraham] There, exactly — that’s what primitives are like.

[Speaker B] But no — does he really not know what the color red is?

[Rabbi Michael Abraham] Exactly, that’s it. It’s obvious that’s not true. Yes, right. You understand what…? There’s no such thing — that assumption, that you think only through language, is ridiculous.

[Speaker D] There is content to cognition, it’s…

[Rabbi Michael Abraham] That… that…

[Speaker D] The fact that the cognitive content in this case is phenomenal observation doesn’t mean it lacks content. Here, here, here content — here, here content I’m talking about…

[Speaker B] …understanding, I’m not talking about linguistic content.

[Rabbi Michael Abraham] I’m talking about understanding, not content. Understanding, not content.

[Speaker D] Yes, but here it’s linguistic content.

[Rabbi Michael Abraham] Well, so the content… you know, there was once — I once wrote a response about this. There was an article in Nature, I think, or Science, I don’t remember, about some tribe in Brazil, the Pirahã tribe, who count according to a one-two-many system. Yes, I heard about that. There are several such tribes around the world. They have one, two, and many, okay? Now this researcher came there and started trying with them. He showed them, say, two batteries and 20 batteries. He asked them where there were more, and they knew: 20 is more than two. Even though they have no concept for 20, but it’s many. But even three and 20 they could compare, although three and 20 are already the same concept — both are “many,” okay? They don’t have a concept for that. And nevertheless they could compare them. Afterward he taught them these things, and once he had taught them that, then they could also compare four and five. Because they’re not stupider than we are; their language simply wasn’t fully developed yet. So after he taught them all these numbers, then they also knew how to tell him which was greater, five or four. Five is more than four. Now I ask: do you really think that when he taught them the numbers four and five, by means of that he implanted understanding into them? I don’t think that can be. Because if they had not already had the understanding, he would not have been able to explain the numbers to them.

[Speaker D] Well, that already gets into — the last part of the Rabbi’s words reminds me of a sophistic paradox: if you don’t know what something is, how do you know to learn about it, and if you don’t know what it is, how do you even go looking for it at all?

[Rabbi Michael Abraham] No, that’s exactly the point. Yes, but it’s not a paradox. There’s no paradox here. You understand it, and afterward you receive language to express what you understand.

[Speaker D] Yes, so that’s the second thing I wanted. By language I didn’t mean natural language, I meant —

[Rabbi Michael Abraham] What difference does it make? Mathematical language is the same thing.

[Speaker D] Yes, exactly. So say in the example of red, the language in this case is… but no, there is no difference between natural language and mathematical language in this sense. No difference at all. It’s a specialized language, but apart from that, yes, I agree that in that respect — only I would say that… how can I give an example? Say, I’ll take another example: the concept of a norm. That… okay? How was it built? They took the concept of distance and stripped it of… other meanings. Once it loses…

[Rabbi Michael Abraham] …it loses from its meaning beyond — no, no, you’re doing it again. You’re doing that fashion again. There is a difference between how one learns something and the question of what — what is the basic understanding that you have? It may be that pedagogically I teach someone what a norm is by saying, look, you understand that murder is forbidden and theft is forbidden too; let’s see what those two have in common — the concept of forbidden. Or the concept of obligation. And then he understands a bit more the meanings of norms in an abstract sense. No, I mean norm in mathematics, like the product — the square root of the inner product. Ah, that doesn’t matter — okay, but it’s the same thing, it doesn’t matter. It’s the same thing. And then I say to him: yes, but obviously inside him there was already that grasp of what a norm is; he just didn’t have the word that expresses it. Because if that grasp had not already been in him, there would have been no way to teach it to him. No way. Fine, but really we’ve drifted here. Yes. So what I actually want to say is that these two characteristics, as we’ll soon see, become somewhat blurred as we now continue up the mountain. We’re now moving on. And what I want to do now is indeed move to neural networks. And what I want to say is this. I’ll perhaps present it like this. Look — our brain is built in a way — this has been understood for quite a while — built in some way as a collection of nerve cells, the main parts of the brain, a collection of nerve cells with connections between them, yes? Various electrical or biochemical connections that conduct electricity. And this is a very, very large network of such nerve cells with connections between them. That is the structure of the brain, okay? In broad terms. There are regions and parts — I won’t go into the details now — but in broad terms this is what’s called a neural network. Now it turns out, or it emerged, that you can build systems that are structured in a fairly similar way to the brain — we’ll still talk about the differences, there are differences — but fairly similar to the brain. And… basically, artificial neural networks, and through them perform all sorts of operations. Okay? And over the years it emerged that this is a way to perform various operations that would be very difficult to do with an ordinary digital computer, okay? If it’s even possible at all. Now, how is the rationale of this built? Look, I’m showing you here, for example, some schematic picture. Okay? Look at this. Do you see? Here there are five nerve cells. Each of them can be on or off, okay? For our purposes that’s one or zero. It’s electrical voltage — either it has no electrical voltage or it has a voltage of a certain level, but for us it’s either one or zero. And you can see that between one cell and another there are various connections. This cell is connected to that cell, this one to that one, and so on — various connections, okay? There are dendrites and synapses and all sorts of things like that, I’m not going into it now, axons. These cells have some output, an axon that comes out, and the dendrites — what? Through a synapse, which is a biochemical connection — that axon carries an electrical signal from the nerve cell, okay? Here an axon comes out, and say here it splits to two cells. Say one dendrite goes here and one goes here, okay? And so on, it can split to more cells. The dendrites are connected to the axon through a synapse — not important right now — but for our purposes there is a connection. I don’t care now how it is built at the biological level, okay? There is a connection between these cells. Now it turns out that a structure of this type is a structure by means of which you can perform all sorts of operations. What happens in such a structure — say for this cell here, for example, look at this cell — this cell has an input from here and an input from here, okay? And maybe from here too, say this is also an input. Fine, there is also an input from here, and this is its output. These are the dendrites, these three, and this is the axon, okay? So here it has one output and three inputs. What this cell does is add together the three inputs that come into it, where on every such connection between cells there is a weight, okay? A certain weight, a number, okay? I’m describing this schematically now. In the brain of course this is implemented electrically and biochemically, but at the abstract level, at the logical level, what we have here are cells that can be either off or on, one or zero; there are connections between the cells, inputs and outputs. A cell has one output and several inputs. Every cell has several inputs, but one output, okay? That output can of course later split and go into several cells, but in principle there is one output. Now, on each such connection there is a number — that’s the weight, okay? Now let’s say this one is on, okay? And this one is also on — say both of these are on. So notice what happens with this fellow here on the far right: from here it’s on, so it sends an electrical signal here; this “on” gets multiplied by the weight of this connection, and this one too, it’s also on, multiplied by the weight of this connection. Here these two inputs are combined. Yes? I sum this weight times the one here, plus this weight times this — depending whether it’s one or zero, whether it’s on or off. That sum determines whether this nerve cell will turn on or off. Once it turns on, it sends signals to the cells to which it is connected, and so on. In other words, this is a process that happens all the time. Cells are constantly sending signals to other cells, turning them off, turning them on, these turn on, they send signals to additional cells, and so on. This is a very complicated process that goes on inside our brain. Now, once they understood this, people began to build artificial systems that are also built this way, where of course we can implement it in software, it doesn’t matter. We say, we give the computer some instruction: know that you have several such cells, each such cell can be either in state one or state zero, there are connections between the cells, and I tell you what the weight of each connection is, and now there is software that tells it: know that if two of these are on and they feed into it, add these two weights and decide whether this one turns on or off, and turn it on, and so on. That is basically a kind of software, okay? I’m running software on a computer so that this is implemented using ordinary computers, of course, but the logic of the matter is different from the logic of an ordinary computer. In a moment I’ll explain this a bit more and it will be clearer. Here for example there is one example, I took it from Wikipedia, doesn’t matter. Here there are three neurons that are the input, here there are two neurons that are the output, okay? And in the middle there are four neurons — that’s called the hidden layer, yes, the concealed layer, the latent one, okay? Which basically performs the calculations. Now what happens here — say I receive as input 1, 0, 0, okay? So now each of these neurons has to decide whether it turns on or not. How does it do that? So say this is zero and this is one and this is also zero, okay? One times this weight reaches here, zero times this weight reaches here, and zero times this weight also reaches here. You see? Three arrows reach here. I sum these three numbers. If it is greater than something, this neuron will turn on. Same thing with this one. You see? It has input from here, input from this one, and input from this one. That sum will determine whether the second neuron turns on. Same for this one and for this one. Once all of these turn on, they in turn activate the output layer. So you see, this goes into both of these, this also goes into both of these, so whether this one turns on will depend on what the states are of all those that feed it, okay? They will determine whether it turns on or not. And now I want to build the system in such a way that it performs some operation, any operation. Say if these three come in — say I want to add three digits: one, zero, zero — I want the result to be one. Fine? Because that’s one plus zero plus zero. So I need to build the weights of this network; I need to place such weights here that for one, zero, zero, the result here will be zero, one. Zero, one is one, yes? If it were one, one, zero, then one plus one is two, and two is ten in binary, so that’s one and zero. In other words, I can turn on these two neurons, remember our bulb, okay? I turn on these two neurons in such a way that that will be the output. And my goal is to build a weight system — every such arrow has a weight on it, both here and here — and with the weights I can play around, and I build the weights in such a way that for every input, yes, every input that comes in here, the result will be exactly the sum. Fine? That’s how I want to build the neural network. Now there are methods for how to arrive at weights that will perform this operation. Let’s take an example of that. I asked our friend Chat a bit to help me with this. Okay, here, look. Let’s look — let’s look at a simple task. I have a formula: y equals 2x plus 1, okay? Now I want to build a neural network that will receive a number as input, the x, and output as output the result of 2x plus 1, yes? For example, if the input is zero, x is zero, then the result will be one, right? If the input is one, the result will be three, okay? Two times one plus one. If the input is two, five. Three, seven, and so on, okay? Now I want to build a network that will do this for me: I feed in that number, it gives me one. Feed in one, it gives three. Feed in two, it gives five, and so on. Fine? I want to build a network that does that, okay? And then I’m basically training it to perform this calculation. Yes? The calculation of that formula, okay? But at no stage do I give it that formula. In an ordinary computer, of the sort I described to you earlier, in the software itself I simply write the formula into it. I literally make it operate according to the formula: take the number, multiply it by two, add one. I’m basically feeding it the formula through the software. Here I simply construct the weights for it, and somehow it turns out that the result is always 2x plus 1. So I want to find which weights do the job. So it starts with a single neuron. It says, let’s say we have a network of a single neuron. So x enters — you see here in the diagram — x enters, it has a weight w, omega, whatever, w, okay? Here some bias, some number b, is added, okay? And it outputs the result. Y-hat is the result, fine? So here is the input and here is the output. And now, look: when the input x enters, I multiply it by omega, the weight of the connection, remember that weights multiply the input, so this is wx. Here there is an addition gate. I add to that some other number, call it b, and that is the result. My goal is actually to ensure that w and b are two and one, because then I get the correct results, okay? But I need to — I don’t know that they are two and one. All I’m given are these data points. Notice that? I’m given these data points: at zero it should give me one, at one it should give me three, at two it should give me five, at three it should give me seven. I don’t know the formula. I want it to give me those outputs — what do I do? So I tell it this: suppose at the beginning we just throw in some w and some b, say b equals zero and w equals 0.5, okay? Now I input x = 2, you see? It should give 5, right? I input x = 2, so what comes out? The y, the output, is a half — omega, the w, is a half times two, plus b which is zero. The result is one. What should the result be? Five, not one. So obviously my w and b are wrong, okay? So what do I do? I basically need to see what to do. I got an error — what do I do with the error? So you define some error function and say, suppose the correct answer is 5 — because I know the answer is 5, I want to get 5 — and the answer I got is 1, that’s y-hat, okay? So the difference between them is basically the error. We square it so that it’s always positive, doesn’t matter, we square it, so the answer is 5 minus 1 squared, which is 16, okay? Now if we want, we do this for all the examples. You see? There are four training examples here. We calculate for each one the error relative to the result that should have been obtained, sum the errors, and that is the error function. Never mind the notation right now; whoever knows, knows. But that’s it — we sum the errors and that is the error function. What do we do with this error function? We want to know what to do now, because we started with omega and b, w — okay, whatever — w = 0.5 and b = 0. Now obviously w = 0.5 is wrong, so I adjust them. I want to know whether to increase, decrease — what to do with w and b. There is a mathematical technique that tells me, based on the error function, what to do in order to reduce the error, to get closer to the correct answer, okay? Steepest descent is the most common method, doesn’t matter. We use certain mathematical properties in order to reduce the error as much as possible. We got some result, a fairly large error, 5 versus 1. We do some calculation, change w and b according to that calculation, okay? And now we get different w and b, okay? We corrected, and get some different w and b. Say after many times — you see? At first it was 0.5 and 0, the next time after the correction w is 0.75 and b is 0.2. Here it understands that w needs to be increased and b needs to be increased. Again increase w and increase b. 0.38, 1.02. Again increase. In the end, after enough times, we will arrive at w = 2 and b = 1, which are the correct answers, and now all the outputs will be correct outputs, okay? Every such step we made — every step here — is basically a training step, okay? We are basically giving it a certain result, correcting, getting another result, correcting again, getting another result, correcting again. In every such step we are continuing to train it, okay? And the assumption is that we have techniques to ensure that as the training progresses, the error relative to the correct result gets smaller, okay? We are constantly moving closer to the correct result. Now of course that was with a single neuron. We basically built the structure by hand, which isn’t very impressive. You see, basically what we did — look at the structure — we had a problem that was x times something plus something, so we simply built a network that adds something and multiplies by something. That’s not especially clever; we already knew that that was what we wanted. We want something more general. Look — suppose I build a network of three neurons. Look at this. x comes in, now here I have three neurons, okay? Now something will happen to each of them after x according to the weights here — there is a weight here, a weight here, and a weight here, okay? Now I say — actually no, the weights are only afterward. It enters those three, from here something comes out multiplied by some weight, from here something comes out multiplied by some weight, from here something comes out multiplied by some weight, I sum all those fellows and some result comes out, okay? Now I already have three numbers to play with. Three numbers to play with: the weight that comes out here, the weight that comes out here, and the weight that comes out here, okay? Now you see here — the schematic description is here — x times w1 gives some result, times w2 gives some result, times w3 gives some result. I add the three together and get some y, something like that. Is the y any good? I check. Say it came out 3 and the correct answer is 1, then I have an error. I correct those w’s again, those weights, so that the answer will be more accurate, and more accurate, and more accurate, until I reach the correct answer. Do you understand the difference here?

[Speaker D] What? What’s the difference here? In both cases it’s linear of degree one, between the first and the second, the first example and the second.

[Rabbi Michael Abraham] In principle there’s no difference here, because you’re just multiplying x by w1 plus w2 plus w3.

[Speaker D] Right, so it’s like a weight of w1…

[Rabbi Michael Abraham] …plus w2 plus w3. Right, right — it’s basically a system equivalent to a single neuron. Yes. Right. I’m just giving simple demonstrations here because I don’t want to get into complications. But in principle, all sorts of inputs can come in and these neurons can activate several output neurons, yes, like we saw earlier, and therefore there can be very, very complicated systems here, and our hope is that we will find a series of such w’s, okay? That will always give us the correct result. Assuming we found such a series of w’s, then every input that comes in will produce exactly 2x plus 1, okay? If we succeed in finding such a set of weights. Now this sounds completely bizarre, illogical, as if why on earth would one proceed in such a way? But it turns out that this is an extremely powerful tool. Look, I’ll tell you how I first encountered it. It was when I was doing my doctorate in physics at Bar-Ilan. I’m not in computers, but I had a friend who was more into computers, and once he showed me — come see some magic. He built a neural network — well, not built physically, it was all in the computer — but he created software with ten such neurons that could receive zero or one, and there were connections between them, from the first to the second, the second to the third, and so on, okay? There were connections between them. And now they wanted — I had to press zero or one, okay? And it was supposed to predict what my next press would be. I tried to confuse it. I typed zero, zero, zero, one, zero, one, one, one, zero, zero, one, zero, one, one, one — as random as I could make it, okay? And it had to guess what my next press would be, okay? Now suppose the system knows nothing and is totally random — what chance does it have of guessing what I do? Fifty percent, right? Either zero or one. That is, I press either zero or one, so if it’s shooting in the dark the chance of guessing is fifty percent, okay? Now it turns out that with an amazingly simple neural network — linear, with ten neurons, where each one only connects to its two nearest neighbors — he managed to predict my next presses with almost 80 percent accuracy. And I tried to confuse it, I tried to kill it, I exhausted myself, it didn’t help at all. Didn’t help at all. It managed to predict my next presses at about 80 percent. And this was the simplest possible neural network. So it turns out — and this is a great surprise — that networks of this kind have abilities to reach results that are very surprising even to those who built them. In other words, this was not foreseeable. Much of it was luck, but somehow people suddenly realized that such networks manage to do all sorts of very, very complicated operations. Now, here I’m not going to get into the non-linear parts, but in fact, when I sum all those outputs from the three neurons here, it’s not just a sum. This sum has to pass some test before deciding whether to turn on this neuron at the end or not. It’s not just the sum. There is some function here that is supposed to ensure that if you pass it, it turns on, and if you don’t pass it, it doesn’t turn on. That introduces a non-linear component that is very important, because otherwise you can’t solve problems that aren’t simple. But in principle, that is the rationale of a neural network. I’ll scroll down a bit maybe, so you can see. Computational problems are relatively simple.

[Speaker G] Rabbi, sorry. Rabbi, sorry.

[Speaker G] Yes. That experiment with your computer friend — doesn’t that apparently lean toward determinism? Is that a deterministic process?

[Rabbi Michael Abraham] Apparently, but it’s not deterministic, because it only predicted me 80 percent of the time.

[Speaker G] But that’s already problematic.

[Rabbi Michael Abraham] It’s not problematic. It just means I’m not completely random.

[Rabbi Michael Abraham] Randomness also isn’t the issue as opposed to determinism. The issue is choice, not randomness. Did you try tossing a coin and acting according to the coin toss? What?

[Speaker D] Did you try tossing a coin and acting according to the coin toss?

[Rabbi Michael Abraham] Ah, no, I didn’t try that.

[Speaker D] It would be interesting to see what would happen then.

[Rabbi Michael Abraham] Yes. The question is whether a coin toss is really… if it really is random, then it wouldn’t predict, I assume.

[Speaker C] The question, the question…

[Rabbi Michael Abraham] …is whether — because you need some system that is responsible, that has some distribution, meaning that it is responsible for those decisions whether to do 1 or 0. With a coin, if it is really random — and the question is whether it is random — but if it really is random, I don’t think it would be able to predict.

[Speaker B] Rabbi, maybe it works only because we are what it simulates? We are built, as the Rabbi said, as neural networks. We created a model that simulates us, so it…

[Rabbi Michael Abraham] Yes, but what was happening there in that network he built for me with those ten neurons — that doesn’t simulate us in any way. It’s just… only the logic is the logic of a neural network, but it doesn’t simulate the brain in any way.

[Speaker B] Why not? At the level of principle, yes?

[Rabbi Michael Abraham] But that’s not — the rationale is like the rationale of the brain. Look, here I’m only giving you an example so you can see how one moves to problems that are not mathematical or arithmetic or computational problems. Here we want to decide, for every point in the plane, whether it is red or blue. Okay? So basically I need to take these points and find the line that separates them, that will determine: everything to its right is red, everything to its left is blue, okay? So you do all sorts of calculations here, you see? You arrive at various intermediate results. In the end you reach some line, some line that really separates — that is, you discover the line that actually divides the reds from the blues. Some kind of line like this or something like it that separates the red points from the blue points. And again, the way you do it is basically by giving it training examples. That is, you say: look, this point is located here, yes, at x1 = 1, x2 = 2, okay? It’s located here and it is red. This point is at x1 = 2 and x2 = 1, and it is also red. This point has its own coordinates and it is blue. These are the training examples, okay? And now it has to understand how this plane is structured, or in what way… how to divide the points between red and blue. Through the training examples it organizes its internal weights, and then it knows that the… that is, what these weights basically do is try to locate the line in the plane that separates the reds from the blues, and then everything to the right of the line is red and everything to the left is blue. So this is basically an attempt to locate a line in the plane through examples, okay? So here too — another problem — in the end we translate it into a mathematical problem, but originally it wasn’t a mathematical problem. So the whole idea in neural networks is ultimately to translate everything into tasks that are numerical tasks. Say a neural network wants to identify a face, wants to identify my grandmother’s face, okay? Now she can be photographed from many angles, in many kinds of weather, lighting conditions, at different ages perhaps, and so on, and I want the system to identify my grandmother, okay? In all those pictures. What do I do? Again I give it examples that train it. To train it means to tune the w’s, yes, the weights that lie on the different connections within the network. And once I arrive at the optimal set of weights, I want to get to a state where it receives a picture of my grandmother and says: yes, 1. It receives a picture of something else and says: 0. That’s my goal, okay? Now to do that I need to translate the image into numbers, because everything works with numbers. So we do that — there are pixels — we translate the intensities into numbers, it doesn’t matter. We translate all problems into problems of numerical input and numerical output, okay? Once that is translated into numerical input and output, all that remains is to find the weights. The weights that will give us the correct result. Now I’m not… I hope that… I skipped a few things here. I didn’t want to make it rigorous, because some people would find it hard to follow. I hope that at least I managed to explain the general idea — that there is here some sort of hocus-pocus of a neural network with various weights, I feed some input into it and it outputs an output. I want the output to be of a certain kind. Say I want to teach it to do addition, like with the computer — perform addition. So I say: if the input is two and three, I want the output to be five, okay? I’m not telling it, now you are performing addition. You don’t talk to a neural network. It’s not like a computer that you program to perform addition. A neural network is trained; you don’t talk to it. I want that if there is two and three, you output five. If there is one and one, output two. If there is minus two and three, output one, and so on. Nowhere do you tell it that this is the operation of addition. You simply give it pairs of input and desired output. And after you train, or organize, the weights of all the connections in the network, your hope is — first of all, you train them so that for all the training examples the correct output comes out — and the hope is that now, for examples not included among the training examples, it will also manage to give the correct result. In other words, suppose my training examples were all the additions of numbers between one and ten — say nine plus three, six plus six, eight plus two, and so on, okay? Various things like that. And suppose I train it — I train it on the examples, this is the computer I want to build — now I train it on, say, only additions of, I don’t know, ten pairs, okay? I give it ten pairs. I say: if you have two and three, the output should be five. If you have one and four, the output should also be five. If you have eight and one, the output should be nine, and that’s it. Now I want it to give me the correct output for all addition problems between one and ten. Also seven plus eight, also six plus three, all of them. I gave it only ten training examples and I want it to produce output for all examples, okay? Now it turns out that if you give it enough training examples, it will produce the correct output for you — and they have to be varied and so on, it doesn’t matter, there are rules for how to do it more efficiently — it gives you the correct results even for examples you didn’t give it. Of course not with certainty, but it can give you a result close to the correct result, a result whose distance from the correct result is relatively small. Because it does not do direct calculation; it does not do x plus y in that sense. This is a completely different mindset from the computers I described earlier. The computers I described earlier, in the end, from our perspective at least, do two plus three equals five. Here it doesn’t do that at all. It simply performs various operations, sums weights and this and that, but somehow, if you train it on enough examples, it can recognize your grandmother’s face. Okay? And that is amazing. I mean, it’s unbelievable. Now what I want — I only want to finish, at least get to some coherent stopping point because we have to finish — what happens with neural networks is that originally neural networks too were a machine whose purpose was to solve one particular kind of problem. So you might take, for example, identifying cats, pictures of cats, okay? So I build a neural network, I give it lots and lots of pictures. On every cat picture I expect it to tell me 1; on pictures of things that are not cats I expect it to output 0. So I train it on lots and lots and lots of pictures, both of cats and of non-cats, and it organizes its internal weights in such a way that on all the examples I gave it it outputs the correct result: 1 for a cat, 0 for what is not a cat, okay? And now I say, I want to take a picture it hasn’t seen, the system, also of a cat, and have it output 1. Or a picture of a soccer ball and have it output 0 because that’s not a cat, and that isn’t included in the examples it saw, okay? Now if I choose enough examples and they are sufficiently varied, it turns out that the systems manage to do that job. But what job are they doing? They identify cats. Now I want another system, a system that differentiates functions or adds two numbers, a different task. Or a system that, I don’t know, identifies chickens, okay? Not cats, okay? Or whatever task it may be. We would need to build another system, train it on the relevant examples, okay? And then after it is trained enough, it will succeed in performing the task for which it was trained, okay? Therefore even in a neural network, which is the next stage, notice: we moved from the analog computer to the digital computer when we introduced software, and that meant that we solve many, many problems with the same device, only each time with different software, okay? Now I have basically gone backward and I’m saying that a neural network knows how to solve a certain kind of problem, the problem for which it was trained. It is better than computers on complicated problems like recognizing a picture of a cat — sorry, a cat image. For an ordinary computer, identifying a cat image is almost impossible; you can’t do it. A neural network does it. Okay? A neural network does do it, so it has an advantage. But it is still in the situation of our original computer, namely a network whose goal is basically to solve one specific problem. If I train it to solve another specific problem, then I change its internal weights, and because I change its internal weights, it will no longer know how to solve the first problem. Do you understand? I don’t know how to make a neural network that solves two different kinds of problems, because once I train it on examples that solve the next problem, the weights reorganize themselves to solve the next problem. That’s it — those are no longer the weights it had before, and it no longer knows how to solve the previous problem. So we are still with the problem of a system that knows how to solve one problem. Now, what happened in 2022 — 2022 or 2023, something like that, I think 2022 — what happened there was that there emerged — this already had earlier roots, people had already thought of this idea several years earlier — but then the ChatGPT model came out, yes? There emerged for the first time a model that succeeds, with the same single network of neurons and weights, in solving all the problems in the universe. It handles all problems with the same neural network. You don’t need to train it each time for a different problem. It goes through some insane training on an impossible quantity of data, and of course it is large — it has very, very many weights because you need to contain all this information within the network. Once you’ve finished that, it knows how to identify my grandmother, it knows how to identify cats versus dogs, it knows how to add numbers — well, actually it’s not so good at adding numbers in particular — or various other things. It knows how to do very many problems without separate training for each type of problem. And the idea that lay at the foundation of this is that basically all problems become textual problems. That is what is called a language model. A language model is the next stage after a neural network. A language model is basically a model that translates all problems into linguistic formulations, and the solution to the problem is to output another linguistic formulation that describes the solution to the question that was the input text. And we train a neural network that receives a set of words and knows how to output another set of words — I remind you of the Chinese room — knows how to output another set of words that will constitute the correct answer to the set of words that came in as a question. Now you understand that all the world’s problems can in principle be described with a set of words. Therefore we have effectively built here a universal machine. It is a brilliant idea to turn the neural network into a language model, because language is the thing through which we express all kinds of problems. And now we are basically using the language model to solve all kinds of problems. Of course, you need to train it also on very, very many — on all types of problems or all types of information there are — and it needs to have very, very many neurons and connections between them. But once we have finished all this madness, we have one universal machine. Of course this is a somewhat simplistic description, but we have one universal machine that solves all problems. And notice: this time it is even without separate software for each problem. Not only do you no longer need to build a separate machine for every problem — you no longer need software. Everything, all the information, is inside the system. The various weights in the network are already organized so that whatever problem it receives, it will output an answer that is the correct answer to the problem we gave it. By the way, this is exactly the person in the Chinese room. We simply built the man in the Chinese room; that is exactly what we did here. And also the way of getting there, by the way — I think John Searle was ahead of his time with this Chinese room example, because the way you build this network is exactly the way you would train the person in the Chinese room — with electric shocks for every wrong answer. He gets an electric shock every time he gives the wrong answer. That’s exactly what we do to the neural network. Now in order to explain this, perhaps next time I’ll go a bit more into the meaning of language in a language model, because I didn’t explain that enough, and also training — the concept of training is a very important concept in this context, so I’ll elaborate on that next time. But that is more or less the end of the road. There are of course many more things — transformers and all sorts of such architectures with which we wrap the neural network — but those are already technical details. In broad terms, my goal was to get as far as a neural network that is a large language model. That is the final station in this journey, at least for now. Okay, sorry that I just… I’m really not sure how clear I was today. And that’s because there — I simply didn’t want to go into all the computational steps. You know what? I’ll send you the chat I used to demonstrate this. Whoever wants can simply read through it in order. It explains the idea, I think, fairly well.

[Speaker F] It would be interesting to see that.

[Rabbi Michael Abraham] The idea.

[Speaker B] But in the end, isn’t it still a statistical matter? When you do the training, in the end the weights are a statistical thing inside it?

[Rabbi Michael Abraham] So I’m getting to the statistical issue. I haven’t gotten there yet.

[Speaker C] Rabbi Mikey, yes.

[Rabbi Michael Abraham] In that…

[Speaker C] In that program your friend made, the one that predicted you with 80 percent — did you try working there not with two numbers but with three?

[Rabbi Michael Abraham] I don’t remember anymore. It was many years ago. As far as I remember, it was two, I think, but I really don’t remember.

[Speaker C] No, my question is this: what do you think — if you ask ChatGPT to predict you in the sequence of numbers, would it be able to do it?

[Rabbi Michael Abraham] I don’t know. We could do an experiment and see; I don’t know. I haven’t done it yet. The first presses I made — you need to understand — in that neural network I described before, the first presses I made were the training examples. Those were the training examples. So it started predicting me well only after five or six presses. At first it didn’t. Because it didn’t know me. But after it saw the first few presses and understood the rationale, or the mechanism, behind my random choices, yes? It basically learned me, and then, after those training examples, it adjusted its weights and began to predict me well.

[Speaker C] No, it’s just — it would be interesting to do.

[Rabbi Michael Abraham] But ChatGPT can’t predict you. I mean, the information inside it does not include how you function randomly. ChatGPT in itself would not be able to predict anything.

[Speaker C] Obviously, yes.

[Rabbi Michael Abraham] No, I’m asking — but if you tell ChatGPT, “Here are my key presses, train on them,” or something like that, “and try to produce an answer from them,” then maybe you would get some good answer, I don’t know. Maybe. But ChatGPT contains information on which it was trained. My random key presses are not information it could have found somewhere. Honorable Rabbi,

[Speaker D] So I asked you about the Euthyphro problem — I can’t hear. I wrote down a few questions, so I asked you in the previous lecture about the problem of Euthyphro and I wrote down several questions on the topic, but before that I wanted to ask: in this approach that sees ChatGPT as a creature like us, if indeed the way it is trained is as you describe, through electrical currents, in their view isn’t that considered some sort of abuse or something?

[Rabbi Michael Abraham] There are such claims today. At Anthropic, I think, there are even some ethical rules about how one treats — because Anthropic are of the more progressive sort — so they have some rules about how one treats ChatGPT. The question whether it is right to shut it down without its permission, or things of that kind — I don’t remember exactly — but they have some such rules because supposedly this is a kind of murder. So I don’t know, there are some weird rules there of that type, and outside Anthropic it’s even worse. I mean, there are all sorts of crazy people. The world is not lacking in crazy people.

[Speaker D] Fine, that’s interesting. But regarding — there is a section where you say in the article about God and the laws of logic that you basically see Him as limited by the laws of logic, and say that, for example, God cannot create a round triangle. So I wanted to ask, from a Kantian perspective — I mean a Kantian epistemology, as I understood that you have one — if logic, if you understand logic as a doctrine of intuition emptied of all empirical content, but not emptied of the rules of thought, as in Kant’s epistemology, how do you… I’ll just read what I wrote down. “I am asking from a Kantian perspective: after all, logic as analytics, a doctrine of intuition emptied of all empirical content of cognition but not emptied of the rules of pure thinking concerning the object, is what you use to infer the contradiction. And therefore it seems there is no basis for such a claim; that is, you are using transcendental rules on a transcendent being. How do you do such a thing?”

[Rabbi Michael Abraham] I don’t understand the question. Maybe I understood — I’ll try to answer and you tell me if I understood you correctly. You assume that the rules of thought too are basically something implanted in us, but I claim not. Those rules of thought are objective. The fact that we know how to use them does not mean they are rules that derive from our structure. I don’t know if I…

[Speaker D] Maybe — maybe I didn’t understand your worldview. Is your epistemology Kantian or…

[Rabbi Michael Abraham] I don’t know what exactly Kant thought about the laws of logic, so I don’t know how to answer that, but I would guess that he thinks like I do.

[Speaker D] I don’t think he thinks like you, because…

[Rabbi Michael Abraham] Okay, if not then I disagree with him. But it doesn’t matter, I…

[Speaker D] So that interests me, because as I understand it, with regard to space and time you do agree with him, in relation to the thing-in-itself. So in relation, in general — no? No. Ah, so you think that… you believe that one grasps things in themselves?

[Rabbi Michael Abraham] No, one does not grasp things in themselves. Space and time are not about things-in-themselves. Yes, but… The question about space and time is whether they are categories of ours or whether they exist in some sense in reality. The question whether I grasp the thing-in-itself or not is another question. Those are two different questions. In other words, space and time — do they really exist, or are they merely forms of our intuition? I’m not sure, but I actually tend to think that yes, they do really exist. It’s hard to give a clear argument for either side here, but my natural inclination is actually to say that they really do exist. They are not transcendental institutions the way Kant sees them.

[Speaker B] Fine, but space and time — one can describe a reality in which there is no space and no time, easily. Easily. We don’t grasp…

[Rabbi Michael Abraham] I didn’t say space and time are logic. But I said that in our reality there is space and time. It may be that there will be another reality in which there is no space and time; that’s something else. But in our reality there is space and time, and that isn’t only with us — it is in reality itself. That doesn’t mean it’s like logic. Two different things. Fine. That is a posteriori — I simply observe reality and see that it has space and time. It might not have had them, okay? So…

[Speaker D] So for you forms of inference are objective matters? Meaning, that is how the Holy One, blessed be He, operates — according to logic? Completely. Yes. So logic…

[Rabbi Michael Abraham] Not that He operates according to logic. That’s exactly it — I wrote there that He is not subject to the laws of logic. Being subject to the laws of logic is simply a construction that is not grammatically correct. We call the laws of logic “laws,” but that is only in an analogical sense.

[Speaker D] They’re not like the laws of physics. Yes, I remember that part, I understand what you mean there. I’ll use it in that same borrowed sense. Fine, so then we have a much more basic disagreement, so I suppose that question has become irrelevant. Regarding the obligation to do good and avoid evil not existing without God: if the argument there is about assuming — then it’s not clear to me what exactly you mean by moral fact. Yes? If I assume a moral fact, it seems to me tautological that if x is not worthy, then it follows from that that one should not do x. That seems true to me as well; I don’t see why that isn’t tautological.

[Rabbi Michael Abraham] No, I didn’t understand the question.

[Speaker D] You claim there that moral facts are laws by which God acts. Right? Now you add and say…

[Rabbi Michael Abraham] What does it mean, acts by them? He perhaps could have acted otherwise, I don’t know, but it’s not that He created them.

[Speaker D] They are imposed on Him.

[Rabbi Michael Abraham] He cannot define murder as good. He could perhaps murder if He were evil, but He cannot define murder as good.

[Speaker D] Yes, yes, that’s why… and that’s what you mean. And now God’s moral intervention is in commanding. That is, the fact that moral facts exist, according to you, does not mean that I am commanded to act according to them. And that is what I don’t understand. It seems tautological to me. If the fact is that x — yes? and x can be a complex claim — x is not worthy, then it seems one cannot act according to x. Why? That’s what it means, “not worthy,” meaning…

[Rabbi Michael Abraham] Who said so? No. Who said that what is worthy — but what do you mean by…

[Speaker D] Or not worthy obligates me? I didn’t understand, what…

[Rabbi Michael Abraham] How do you understand the concept of worthy? When I think of worthy, I…

[Rabbi Michael Abraham] …that if there were a moral obligation, then that is how one should act. And the question whether there is or isn’t a moral obligation is another question, which depends on…

[Speaker D] Can you repeat the definition…

[Rabbi Michael Abraham] …of the concept of worthy? That if there were a moral obligation, then that is how it would be proper to act. But the question whether there is a moral obligation is another question. What I am claiming is that the Holy One, blessed be He, could not have created a world in which murder is good.

[Speaker D] You understand the concept of worthy as a conditional claim? An if-then? That’s how… that’s what it sounds like, as if that’s how you define it.

[Rabbi Michael Abraham] No, it is not a conditional claim, it is a fact.

[Speaker D] Why a conditional claim? Then what do you mean? I mean… you said if, then — if it were such-and-such, then…

[Rabbi Michael Abraham] No, I’m saying that the worthy as such is a fact, but when you ask about its implication for me — how I should behave — that already depends on something else besides that fact. It also depends on whether I am obligated to those facts or not. I understand.

[Speaker D] That’s why I’m trying to understand why it isn’t tautological. That’s why I’m asking what you mean when you say worthy.

[Rabbi Michael Abraham] Exactly — it isn’t tautological. Because there is another step here which says that perhaps I am not obligated to those facts. It is true that murder is evil — but who said I am obligated not to do evil? How…

[Speaker F] All right, happy new year, I just have to leave.

[Rabbi Michael Abraham] Yes, yes, all is fine. We’ve finished the lecture, so now this is just a personal conversation.

[Speaker F] Bye, thank you very much, happy new year.

[Speaker B] Happy…

[Rabbi Michael Abraham] Happy new year, happy new year.

[Speaker B] Happy new year. But how can one impose, Rabbi, some moral norm without the prescriptivity built into it? That’s an empty statement. Say I know that murder is forbidden, but I don’t feel, I don’t recognize the prescriptivity of that, meaning the obligation in it, then it’s an empty statement, just an empty set…

[Rabbi Michael Abraham] It’s not an empty statement. It’s simply a collection of facts, but without obligation to them they are basically descriptive facts and not prescriptive ones. But without prescriptivity there is no content. There is some aspect of reality, but what does that have to do with me? That’s David Hume’s ought-is, basically — it would exist there.

[Speaker D] It doesn’t seem to me like David Hume’s ought-is, because you assume that a moral fact is an is, and that seems to me the issue — I mean, why is a moral fact an is and not an ought?

[Rabbi Michael Abraham] I claim that the difference between descriptive and prescriptive statements comes after the Holy One, blessed be He, has already implanted within us the moral obligation. The moral fact as such is not prescriptive; it is descriptive.

[Speaker D] But now I don’t understand why. That is, a fact — how… I don’t understand how this is not a normative issue. We are claiming here that a is worthy. That is normative, prospective.

[Rabbi Michael Abraham] Normative in the sense that it is a potential for obligation.

[Speaker D] What does potential for obligation mean? I don’t understand.

[Rabbi Michael Abraham] As such it is conditional on another step.

[Speaker D] What does potential for obligation mean? That’s even…

[Rabbi Michael Abraham] Like I said before, there cannot be a world in which there is an obligation to murder.

[Speaker D] There cannot be…

[Rabbi Michael Abraham] But there can be a world with no obligation at all.

[Speaker D] There cannot be a world in which…

[Rabbi Michael Abraham] …murder is good, in which there is an obligation to murder.

[Speaker D] That’s not obligation, that sounds more like… more like fitness, more similar…

[Rabbi Michael Abraham] That murder is good. Forget obligation — that murder is good, leave obligation aside.

[Speaker B] Murder is…

[Speaker D] …good, okay.

[Rabbi Michael Abraham] There cannot be a world in which murder is good. Right?

[Speaker B] Rabbi, why does the Rabbi… why is murder good at all, modally? Let’s suppose a world in which there is no suffering; the creatures in the world were created in such a way that they cannot suffer.

[Rabbi Michael Abraham] Okay. And then…

[Speaker B] So then… and they don’t miss anyone who died, and death has no significance, yes? No, that’s not connected — then it’s not murder. The word sorrow is not grasped; you say it to people, and they don’t understand what…

[Rabbi Michael Abraham] Then it isn’t murder. There is also a value to life. You are translating everything into the suffering of the surroundings, but I’ll go with you for the moment. There is also a value to life, so that’s not the issue.

[Speaker B] No, I don’t think so.

[Rabbi Michael Abraham] But say that it is only a duty not to cause sorrow to those around, fine? Right. So once — once there were no human beings alive, there would also be no prohibition of murder. In a world where there are only sheep and no human beings, there too there is no prohibition of murder. That is obvious. The prohibition of murder is always a function of certain circumstances. If the circumstances are different, then there is no prohibition of murder — but not because of the relativity… not because morality is relative, but because morality speaks about human beings. If there are human beings, you may not murder. If there are no human beings there, then there is no prohibition of murder, but not because morality is different — because reality is different.

[Speaker B] Fine, I just wanted to say… prescriptivity is built into morality. If there were no suffering in the world, if there were no sorrow in the world, there would be no morality. We would not know how to grasp what it is. We would be talking — we would not know what… It would be like talking about the experience of a color that is not within the range of our perception.

[Rabbi Michael Abraham] I can agree with you,

[Speaker B] It would make no sense to speak about morality.

[Rabbi Michael Abraham] No, I can agree with you, but I would agree in the epistemological sense. That is, our ability to distinguish what is moral and what is not. But that is not the source of the validity. Saul Kripke, for example — an American philosopher, an American Jewish philosopher, observant — he wanted to argue that there are analytic a posteriori statements, the one category that according to Kant cannot exist. Why? He basically claims that there are analytic statements — say that seven plus five equals twelve. Kant called that synthetic a priori, and Kripke says: no, it’s analytic a posteriori. What does that mean? It is an analytic statement, but I learn it from experience. They show me with beads, with rods, I don’t know exactly what, and I come to understand that seven plus five equals twelve. And in my opinion he is wrong. He is wrong because he confuses the question of how I learn it — the pedagogical question — with the question of why it is true. Those are two different things. I claim that it is true a priori. I learn it through experience, that’s fine, because that is a pedagogical means. But that is not the reason why it is true. And it is not science.

[Speaker B] How can the Rabbi know that? After all, the Rabbi admits that if from age zero to age one hundred, every time we counted three plus five it always came out ten, then we would be convinced that that is obviously reality and…

[Rabbi Michael Abraham] You are raising a hypothetical situation that cannot exist. What do you mean if every time we counted three plus five it came out ten? It can’t come out ten. Three plus five is always eight.

[Speaker B] But the Rabbi knows that after he experienced it.

[Rabbi Michael Abraham] If we saw round triangles, what would we think — that a triangle can be round or not? The answer is that you cannot see round triangles, because there is no such thing.

[Speaker B] In our categories of perception. Maybe in other categories of perception.

[Rabbi Michael Abraham] Fine, so that’s what I’m claiming — no, it’s not our categories. It is an objective matter. Rabbi Mikey, yes.

[Speaker C] I wanted to ask you — according to Kantian thinking, how does that fit with Rosh Hashanah, for example?

[Rabbi Michael Abraham] I didn’t understand that. We’d be glad…

[Speaker C] I’ll tell you. Because I saw in the Critique of… Kant’s work, Critique of Pure Reason.

[Rabbi Michael Abraham] Yes, Pure Reason, yes. The Copernican revolution, yes.

[Speaker C] He writes that the claim is not that our reason adapts itself to the world around us, but that the world itself — that is, our perception — is organized according to the laws of our consciousness. Right. That is to say, Rosh Hashanah, yes, is not… I mean, there’s no one who says so, it doesn’t even need to be that way. Because if we think positively all the time and see the world differently, then we’ll receive the world in a…

[Rabbi Michael Abraham] First of all, I think that’s not connected. First of all, I don’t agree with him, that’s the first thing.

[Speaker C] So therefore — okay, fine.

[Rabbi Michael Abraham] Because at the root there is no… disagreement. But I’m saying, even if I agreed with him, I think it would be a category mistake. There are certain things that we are built in a certain way and therefore we perceive them that way. We cannot perceive them otherwise, so that is how we are built. Now if you apply that to Rosh Hashanah, then we are built in such a way that for us Rosh Hashanah is the Day of Judgment. We have no other option for seeing Rosh Hashanah. There is no point playing with the question of what would happen if we perceived Rosh Hashanah as just an ordinary weekday, because we are built in such a way that we cannot perceive it that way. For us it is Rosh Hashanah. And more than that — I don’t agree with him, so…

[Speaker C] No, but for the Sages that was really the outlook of all the Jewish people.

[Rabbi Michael Abraham] No, that’s another question. Then you’re simply saying the Sages are wrong. Okay, fine.

[Speaker C] No, I didn’t say they are right or wrong. I’m simply trying to understand how those within the Jewish people — people like you, maybe also like me, maybe many others — who do look at philosophy, at what obligates and so on, yes? And want to understand the world and gain wisdom within the world — how are they supposed to relate to such a day?

[Rabbi Michael Abraham] The way you related to it until now, the way everyone relates to it. I don’t understand what the problem is.

[Speaker C] I’ll tell you, because on the one hand in the Torah…

[Rabbi Michael Abraham] Leave Rosh Hashanah aside. How do you relate to the Holy One, blessed be He? He too doesn’t really exist; He’s only a transcendent idea in your consciousness, no?

[Speaker C] No, here I agree with you completely that the Creator, the philosophical Creator, yes, already exists in my consciousness because I see the world.

[Rabbi Michael Abraham] In your consciousness that doesn’t interest me. But He doesn’t really exist. It’s just that you are built that way. Okay, so take a pill, get over it, and drop this nonsense.

[Speaker C] Fine, maybe that’s an option, yes, but I…

[Rabbi Michael Abraham] So why are you asking me about Rosh Hashanah? Ask me about the Holy One, blessed be He, about the principles of faith, about everything. I mean…

[Speaker C] No, but even Kant has no problem with the Holy One, blessed be He. What? Even Kant has no problem with the Holy One, blessed be He, also with the…

[Rabbi Michael Abraham] Forget Kant — I’m asking you. You asked a question about Rosh Hashanah. I’m saying, what is Rosh Hashanah? Our whole world basically becomes subjective. Forget Rosh Hashanah — what do you want from Rosh Hashanah?

[Speaker C] No, because Rosh Hashanah is supposedly — first of all it’s the eve of Rosh Hashanah, second it’s supposedly the Day of Judgment in our understanding, yes? So I’m asking here, if that’s the case — after all, we’re only receiving it that way, yes? That is, our mind — how many? ten, twenty, thirty…

[Rabbi Michael Abraham] Listen, there is a tradition. I don’t understand the… There is a tradition that this is the Day of Judgment, and that’s all. Either you accept the tradition or you don’t. What does that have to do with transcendental conceptions?

[Speaker C] And what do you think?

[Rabbi Michael Abraham] What? I doubt whether there really is a basis for seeing Rosh Hashanah as the Day of Judgment. But it is a good occasion for self-examination, to see where you came from and where you are going, so one can make use of the opportunity.

[Speaker B] Exactly.

[Speaker E] But Rabbi, what you’re saying already appears in the Talmud, tractate Rosh Hashanah 16. What? There the dispute is when a person is judged, and Rabbi Natan says a person is judged at every hour. What you probably mean — this is likely what the Sages were aiming at. At every moment a person can repent, for example, and in that he is judged.

[Rabbi Michael Abraham] That is certainly true, certainly true. But there is somehow some kind of special Day of Judgment on Rosh Hashanah, even though a person is judged at every hour. There is some sort of special Day of Judgment on Rosh Hashanah. At least that is the accepted view. I’m not sure where that came from. In the Torah itself I don’t see any hint of it. I also don’t — but even in the Talmud there’s no hint of it. It seems there too they don’t — why?

[Speaker C] There is. No, the Talmud explicitly says that three books are opened and so on, judgment, judge — of course. What, no. In fact the question here is where the Sages got it from. That’s the question. Because in neither the Torah nor the Hebrew Bible is it mentioned at all.

[Rabbi Michael Abraham] Exactly. I just had on the site — I said that I had an article about blowing the shofar on Rosh Hashanah when it falls on the Sabbath. So I asked there: how can it be that the Sages, by rabbinic enactment, cancel the duty to blow the shofar, which is a Torah-level obligation? So someone said to me: what do you mean? But they are uprooting a Torah matter through passive omission — they can uproot a Torah matter through passive omission. I said to him, yes, but in terms of what is written in the Torah, the essence of the day of Rosh Hashanah is shofar-blowing. So to cancel the shofar-blowing is not to cancel some aspect — it is to cancel the day itself. The whole day is a day of teruah, of trumpet-blast. That is what the day itself is. They told me, no, it is a Day of Judgment; that’s accepted among the Sages, and so on. And I don’t know. When I read the Torah in its plain sense, everywhere I understand that this thing is a day of teruah. That’s it — that is the essence of the day. So to cancel it out of concern lest someone carry the shofar four cubits in the public domain, and because of that to change the essence of the day from the root up, seems very strange to me.

[Speaker B] So what does the Rabbi answer?

[Rabbi Michael Abraham] You are getting here to — I answer that it isn’t rabbinic, it’s Torah-level. Like the Jerusalem Talmud says. Rosh Hashanah that falls on the Sabbath — from the outset you don’t have to blow. It’s not a cancellation because of lest he carry it four cubits in the public domain.

[Speaker G] Your question applies to all of “what the religious court declares ownerless is ownerless,” to the power the Sages gave themselves to uproot things. No, no, no — that’s what I’m saying. No.

[Rabbi Michael Abraham] No, because the Sages can uproot a Torah matter through passive omission. From where? What do you mean? The Talmud says so in many places.

[Speaker G] Fine, that is their interpretation, which gives them power to uproot things from the Torah, but it is not from the Torah itself.

[Rabbi Michael Abraham] Fine, true. They are allowed to.

[Speaker G] But that interpretation is their interpretation.

[Rabbi Michael Abraham] My interpretation? The tradition says so. No, not yours.

[Speaker G] No, no, no — not yours.

[Rabbi Michael Abraham] And if you take that, then argue, no problem. I’m working within that framework.

[Speaker G] No, no, no — not your interpretation, but the interpretation of the Sages. The Sages, okay, gave an interpretation that gave them power over what does not appear in the Torah.

[Rabbi Michael Abraham] Correct. So what?

[Speaker G] Okay, so without their interpretation there is no source in the Torah at all for doing such things.

[Rabbi Michael Abraham] I accept the interpretation of the Sages.

[Speaker C] By the way, according to the Book of Jubilees…

[Rabbi Michael Abraham] I have no argument in principle with the interpretations of the Sages. Specifically regarding Rosh Hashanah, I don’t know whether the determination that it is a Day of Judgment is an interpretation of the verses, or whether the determination of it as a Day of Judgment is some later invention. Because I don’t see anywhere that they derived it from a verse, that they determined — I don’t know — I don’t remember at the moment at least — that they interpreted some verse in such a way. Rather, they decided that it is a Day of Judgment, and you know, in that sense this is not a normative question, it is a factual question. The question whether in heaven they sit and really judge us on that day — that is a factual question. The Sages cannot determine that.

[Speaker G] Why does that scare you less? Why does that scare you less than their uprooting, their declaring a person’s property ownerless? You mentioned several times that even according to legal theory and all that, ownership is prior even to the Torah, and yet the Sages declared the…

[Rabbi Michael Abraham] No, they did not uproot the concept of ownership. They uprooted the ownership of a particular person over a particular piece of property in certain circumstances.

[Speaker G] Okay. Okay, fine, so what — so what, that’s more concentrated, but what difference does it make?

[Rabbi Michael Abraham] One person and the whole world. No legal system in the world does not do that. What — is there a legal system that does not levy taxes? What exactly is the problem here? I don’t understand.

[Speaker G] No, because there are laws. We submit to the laws of the legal system.

[Rabbi Michael Abraham] And what are those laws? The laws that take our money from us. That’s one thing. Second, every governmental system has permission to declare property ownerless, when it is done lawfully and proportionately and for worthy purposes. I’m talking like a jurist now, but yes, in Jewish law too it is like that.

[Speaker B] Can you hear, Rabbi Mikey?

[Speaker C] According to the Book of Jubilees, according to the calendar mentioned there, Rosh Hashanah never falls on the Sabbath. Okay. So it may be that there is some justice in what Rachel Elior says about the calendar having been changed. Possible — I’m not an expert, I don’t know.

[Rabbi Michael Abraham] Ah, okay.

[Speaker C] There is such a suspicion.

[Rabbi Michael Abraham] In a moment…

[Speaker D] Is there still time? Because I had a few questions also about… I also skipped over question two, but let’s leave that. Regarding moral facts being part of God’s essence — you propose that as an interpretation… Again? That moral facts are part of God’s essence. That moral facts are essence, aspects of God’s states. That moral facts — this is a quote from… moral facts are part of God’s essence, aspects of His states. And you propose that as a third interpretation of the Euthyphro dilemma, that they are like an integral part of Him, but — and you formulated it there in the article, you bring it as the opinion of… what, in D, B, B, 4, 5, 7? 4, 5, 7, yes. What… you bring it, you say that it’s… I don’t remember this wording. I, yes, quoted it from the article, so I know it’s a quote — but you bring it as an example of a statement, I forgot whose, of… what, that the nature of the beneficent is to do good? You bring it as an example that…

[Rabbi Michael Abraham] The nature of the good is to do good. Okay.

[Speaker D] Yes, you bring it as an example that this is… so I wanted to ask whether such a conception doesn’t contradict divine unity.

[Rabbi Michael Abraham] I don’t know what divine unity means. Those vague concepts mean nothing to me.

[Speaker D] That He is a simple substance.

[Rabbi Michael Abraham] What does simple substance mean? Substance… I also don’t know what it means that He is one, and I don’t know what it means that He is simple. No, I don’t understand those concepts. A simple substance… means nothing to me. In my opinion it means nothing to anyone, but in any case it doesn’t mean anything to me.

[Speaker D] By simple substance they usually mean something that exists by virtue of itself and is the only part of itself — it is not composed of different parts.

[Rabbi Michael Abraham] But there can be… there can be something very complex that is one organism, so is that simple or not simple? It’s an organism.

[Speaker D] An organism is not… simple or not simple? It is not simple. It is composed of parts. One can… it’s like… it reminds me that in logic there are propositions… atomic propositions. There are propositions that can’t be divided any further, yes? I don’t know, x, y is an atomic proposition. But there are more complex propositions that can be divided into atomic propositions. So atomic propositions would be, as it were, an analogy here for a simple substance.

[Rabbi Michael Abraham] The question is what composition means. When I say that… when people speak of a composite substance versus a simple substance, I don’t quite understand that definition. To me, an organic entity is a simple entity, even if it has many, I don’t know, complexities, because it is one entity. In other words, it’s not an assembly of parts. Something composed of parts is always something non-organic. If it is non-organic, then it is composed of parts. But if it is organic, then it is one whole.

[Speaker G] But it… but change applies to it. Change applies to it. Even if it is one organic thing, if it is composed of several parts, then change applies to it — unlike the unity of the Holy One, blessed be He. Yes, change applies, right. So what’s the problem? Then it’s not necessary. It does not apply to the Holy One, blessed…

[Rabbi Michael Abraham] Why is it not necessary?

[Speaker G] If it changes, then it’s not necessary. How can something necessary change?

[Rabbi Michael Abraham] Its form, which has changed, perhaps is not necessary. But it itself, its existence, is necessary. What, no… how? He and His existence are one.

[Speaker D] That is, existence… you understand existence…

[Rabbi Michael Abraham] He doesn’t change in the sense that He disappears. He still exists. What do you mean? He and… he changes in willing. Before He wanted this and now He wants that, or I don’t know, things like that. Before He… well, people philosophized about these things too, that He… after all, “He and His knowledge are one,” that’s what people often say, yes? All kinds of vague statements that don’t say much. But He and His knowledge are one. So when He knows something that happens now in the world, something is renewed in Him that wasn’t there before. So there — a change occurred in Him.

[Speaker D] That’s why He cannot learn things, and that would be the extreme, radical position.

[Rabbi Michael Abraham] So what? So He can’t learn that there are things He didn’t know before they were done, and after they were done He does know them? Fine, so…

[Speaker D] That already gets into a dispute, but it still seems that then He isn’t necessary — let’s focus on necessity.

[Rabbi Michael Abraham] No, I’m telling you: His existence is necessary, not His state. His existence is necessary.

[Speaker D] What is the difference between His existence and His state? I mean…

[Rabbi Michael Abraham] What’s the difference? His existence is the simple fact that He exists, but if He wants x or wants y, it is still He who exists.

[Speaker D] Once He wants x and once He wants y. Existence is some property… how do you understand existence? Do you understand existence as some predicative property that… no, precisely, existence is not a predicate. Okay, if existence is not a property, then what does it mean to say that His existence is necessary?

[Rabbi Michael Abraham] That His existence is necessary means He cannot fail to exist.

[Speaker D] What is the subject of that proposition?

[Rabbi Michael Abraham] There cannot be a state of affairs in which God does not exist.

[Speaker D] But existence is not a property, so what does that proposition even mean?

[Rabbi Michael Abraham] That there cannot be a situation in which there is no God. What’s unclear here? Very simple.

[Speaker D] But you… you are making a predication here about something that, in your opinion, is not a predicate. No, no, I’m not making any predication here.

[Rabbi Michael Abraham] Existence is not a predicate.

[Speaker D] How are you not making a predication? You’re presenting a conditional claim here, no? You just said now… that His existence is necessary; that His existence is a claim…

[Rabbi Michael Abraham] A modal claim. There cannot be a reality in which there is no God.

[Speaker D] Okay, fine. What I don’t understand is how you separate His existence from His state. That seems to me completely absurd. Why? The existence of a thing — because the existence of a thing is in a certain state. When the state changes, its existence becomes the existence of a different thing.

[Rabbi Michael Abraham] I don’t understand. I exist now, and in a moment — in a moment I’ll stop speaking. I’m speaking now. So what — when I stop speaking I won’t exist, or it won’t be me, or what? No. I’m not…

[Speaker D] No, I’ll put it in terms of essential properties and accidental properties. Your accidental properties change. You’re not…

[Rabbi Michael Abraham] Fine, if you say there are essential properties, then the essential properties do not change and the accidental properties do change.

[Speaker D] You mean to say that a necessary being has accidental properties?

[Rabbi Michael Abraham] Of course. Why not? What’s the problem?

[Speaker D] How can that be? If they are accidental properties, then that is something that changes and is also composite.

[Rabbi Michael Abraham] No, it doesn’t change!

[Speaker C] But existence…

[Rabbi Michael Abraham] …is not a property.

[Speaker D] Its properties, its properties. Sorry…

[Speaker C] Existence is not a property. The Rabbi has explained this to you many times.

[Speaker D] No, no, I understood that existence is not a property, that he doesn’t present it as a predicate, that I understood. But what I don’t… I think the distinction between existence and state, and the view that… change — that it has the option of changing and still remaining necessary — seems to me completely absurd.

[Rabbi Michael Abraham] I don’t understand. In another moment, in another moment…

[Speaker D] I’ll stop speaking. Am I the same one? You’re not a necessary being, that’s not…

[Rabbi Michael Abraham] …not necessary. Am I the same one?

[Speaker D] You are the same one. Why? Because I understand your identity as the set of your essential properties. What I perceive are accidental things.

[Rabbi Michael Abraham] No, my identity is not a set of properties. My identity is myself. The properties are my properties; they are not me.

[Speaker B] Who said…

[Rabbi Michael Abraham] He isn’t… who said, who said that the Rabbi is not a necessary being?

[Speaker B] How can you prove that the Rabbi is not a necessary being…?

[Rabbi Michael Abraham] What is relevant about that now?

[Speaker B] No, according to Spinoza I’m not sure I’d agree with you that… I don’t think Spinoza is relevant as a model right now.

[Rabbi Michael Abraham] Spinoza would say…

[Speaker B] …that the Rabbi, on his part, is necessary.

[Rabbi Michael Abraham] I have a proof, Shmuel. Seventy years ago I wasn’t here.

[Speaker C] No, but in principle that’s not… Lior, no. Necessary, but now that there is — a property of something is not a property…

[Speaker B] I didn’t say necessary forever…

[Speaker D] I also understand existence as not a predicate…

[Rabbi Michael Abraham] That means nothing. It’s…

[Speaker D] I too understand existence as not a predicate — that’s not my problem. My problem is the same problem that Maimonides would raise. If we understand, say, let me define it this way, substance — just a definition that occurred to me now, off the top of my head — say that once I can’t divide it and still preserve the content, the meaning, the semantic content, then that is already a simple substance. And say with regard to God’s existence, if I can divide some substance into other substances that exist with or without dependence on each other, then I would say it is composite. So with God, if He changes, and you say that only accidental properties can change, then He is already composite.

[Rabbi Michael Abraham] Properties are not parts of Him.

[Speaker D] How are there no contradictions here?

[Rabbi Michael Abraham] There’s a confusion of concepts here. Properties are not parts of Him; properties are His state. Why are you connecting properties with parts?

[Speaker D] I didn’t say that properties are… so what does that have to do with the question of whether He can be divided or not? Because what? That He has properties? Because if He has accidental properties, that means He can change. No, accidental properties — so what? Because if He has accidental properties He can change, agreed? Right, obviously.

[Rabbi Michael Abraham] If…

[Speaker D] If He can change, then what changes in Him are the parts that are not essential…

[Rabbi Michael Abraham] No, then you are going back again to saying that properties and parts are the same thing, and I’ll go back again to saying they are not.

[Speaker D] What changes in Him?

[Rabbi Michael Abraham] All the parts remain exactly as they are, and yet once He knew something and now He doesn’t know it — or the other way around, yes? Once He didn’t know and now He knows. Once He created a world and before that He did not create a world, so He has a different state. There — now He is creating a world; before that…

[Speaker D] …He didn’t create…

[Rabbi Michael Abraham] …a world.

[Speaker D] To say “once He created a world” is already… well, I’ll move to the next question because there are still two questions. But to say “once He created a world” is a whole can of worms in itself. In this context — okay, a short clarifying question. You said there in the moral context that even if one value is overridden by another value, I should still feel sorrow or dissonance over the fact that I violated the overridden value.

[Rabbi Michael Abraham] Just to be clear, “must feel sorrow” is a metaphorical expression, because there are no obligations on emotion…

[Speaker D] Yes, that’s exactly what I didn’t understand.

[Rabbi Michael Abraham] No, no. There are no obligations on emotion. The point is: you have to understand that there is a price here. That’s…

[Speaker D] So then that seems to me somehow connected to the categorical imperative. Was that your intention with dissonance? That I perceive my action as something non-universal, as it were? Is there some sort of self-contradiction in me?

[Rabbi Michael Abraham] No, no. Why did you jump to the categorical imperative?

[Speaker D] I don’t see why. Because the categorical imperative arises from the need to make morality universal. It arises from the need, as it were… universal entirely — what, I didn’t understand? Well, when I act — no, no, there’s no problem with that, wait, let me finish my question because I think I wasn’t understood properly. The dissonance in connection with the categorical imperative is that the categorical imperative arises from the need to make morality universal, yes? To act in a way that I can will that everyone act, so the moment I act in such a way I am in self-contradiction with my own reason — so that’s what I thought you meant by dissonance. No, what on earth? There is…

[Rabbi Michael Abraham] …a price. The moment I trample one moral value for the sake of another moral value, I need to be aware that there is a price to the step I am taking, even though from the outset one should do it; there is no… and it is universal, everyone should do it. And still, if I hurt a person in order to, I don’t know, heal him, draw his attention to something, I slap him because otherwise something terrible will happen to him — then you should slap him, but still the act of slapping is some kind of moral cost, because you are not supposed to hurt a person.

[Speaker D] Fine, great. Good thing I asked, because there really was something to clarify. And one unrelated question, but still something you return to a lot and that is not clear to me — and it connects to many very central things in your whole approach — when you say there is no certainty about anything. So I wanted to ask about a person’s knowledge of himself, regarding the cogito and your idea about human maturity and the metaphor you always bring with the stages. So I do…

[Rabbi Michael Abraham] I have a column about the cogito, and there I explain that in my opinion the cogito is not an analytic argument and not an ontological argument, but rather an observational argument. Okay.

[Speaker D] It’s not entirely clear to me what that means. Empirical? Is that what you mean by observational? What? What do you mean by observational — empirical? Yes.

[Rabbi Michael Abraham] Okay. Quite right of course, but it is still empirical.

[Speaker D] In your opinion is there certainty here regarding your own existence?

[Rabbi Michael Abraham] What — is there what?

[Speaker D] Certainty. Can you be certain of your own existence? No. Now when you talked about doubt, I remember that when you talk about doubt you mean the very possibility of being wrong. That is, I have doubt in the… not, I mean in the philosophical sense as you call it, not in the practical sense. I have doubt because there is a possibility of error. How can there be error for me with regard to my own existence? Here I see no room for error at all.

[Rabbi Michael Abraham] No, you say how can there be an error, but when you speak about one’s own existence, the alternative is not that I make an error, but that there is an error in the argument. No, after all I don’t exist, so what does it mean to say I make an error? It’s like the problem of wrongful birth. In the problem of wrongful birth, you sue your parents for why they didn’t have an abortion, why they brought you into the world. In most legal systems in the world you can’t file such a claim, and there are places where you can. And there are different explanations why you can’t. One explanation is that you can’t sue because it’s a tort claim. A tort claim is always a comparison between the state in which no harm was done to you and the state in which harm was done to you, and the gap between them is what you sue for. But here, if they had not brought you into the world, it’s not that you would have been in a better state; you simply would not have been. And now that they brought you into the world, you are in a bad state. So there is no way to compare those two states, and therefore you can’t sue.

[Speaker D] Fine, but I don’t really see how that answers the question. So there is a possibility that I do not…

[Rabbi Michael Abraham] I didn’t say that there is a possibility that I am mistaken in thinking that I exist.

[Speaker D] No, not possibility — there is a possibility that there is an error.

[Rabbi Michael Abraham] In what sense?

[Speaker D] That also seems to me to contradict your whole conception of truth and falsehood. After all, you understand truth and falsehood as things that exist in reality, yes? When the person’s mental state corresponds to reality, then the claim is true. And you also clarify — as I think correctly — that facts are not true, they are simply the state of affairs. Right. So the very semantics of your concept of proposition — and define this cognition that asserts however you want to define it, that’s not the relevant issue here. It can be a dream of a king.

[Rabbi Michael Abraham] No, you… the cogito cannot fit into that schema, because in the cogito you are discussing your very existence. Clearly it cannot fit into the schema of whether I am mistaken or right, whether my mental state corresponds to the state of affairs in the world or does not correspond to it, because we are speaking about the very owner of the mental state itself — whether he exists or does not exist. When you talk about error there, you are not talking about error in the sense of my error; you mean an error, I don’t know, of whom.

[Speaker D] No…

[Speaker C] I thought you were saying… okay, fine. Rabbi, for you the cogito is “I think, therefore I am”?

[Rabbi Michael Abraham] Not “for me” — that’s what the cogito is called, yes.

[Speaker C] Ah, of Descartes, right? Yes.

[Rabbi Michael Abraham] Yes.

[Speaker D] Why is it…

[Speaker B] Why is it so important whether I exist or not?

[Rabbi Michael Abraham] All these arguments… no, I also explained there in the column, I don’t think what troubled Descartes was whether he exists or doesn’t exist. Exactly. Descartes tried to save rationalism against empiricism. He tried to show that we can arrive at a factual claim about the world by means that are not observational, by means of a philosophical argument. A conceptual one. And he used his own existence as an example of that. And that is exactly where everyone attacks him, because the question is whether this really is a purely conceptual argument or not.

[Speaker H] It is completely synthetic, supposedly. Yes.

[Rabbi Michael Abraham] Fine, friends. Interesting. Yes. All right? Thanks. Thank you very much.

[Speaker D] Thank you very much.

[Speaker B] Anyway, have a…

[Rabbi Michael Abraham] Happy new year.

[Speaker B] Happy new year, happy new year. Happy new year and may you be sealed for good.

[Rabbi Michael Abraham] Goodbye. Happy new year.