Q&A: Questions on "The Science of Freedom"
Questions on "The Science of Freedom"
Question
Hello Rabbi Michael,
In your book "The Science of Freedom," you presented Newcomb's paradox as a proof against determinism.
In my opinion, that proof is not precise. I agree that it proves that such a prophecy cannot exist (not even from God Himself), but the possibility that this information exists in principle still remains.
As I understand it, the root of the paradox is different, and is not connected at all to human free choice. Even if all the participants in the story were computers (a "prophet" computer and a computer that chooses between the boxes), the paradox would still remain, even though the operation of computers is deterministic and nobody imagines that they have free choice.
The root of the paradox lies in the infinite recursion required by a prophecy that influences its own fulfillment. I will try to clarify what I mean with the help of an example I read in Yuval Noah Harari (also about a broken clock, etc.).
Suppose the State of Israel succeeds in developing a computer that weighs all the data in the present and, based on it, predicts the future. Now that computer predicts an Iranian invasion of Israel that will cause many casualties. The State of Israel concentrates forces at the expected point of invasion and succeeds in preventing it. The computer was wrong.
But if so, that means the algorithm did not really compute all the data in the present and all their implications to the end, because the very existence of that computer itself, and the fact that it is going to provide a forecast that will motivate Israel to act, are also part of the data that the algorithm must take into account. If so, the computer should have provided a forecast according to which the invasion would not succeed. But if that had been the forecast, Israel would not have prepared properly, and the invasion would indeed have taken place.
In other words, the computer has to calculate data such that the result of the calculation itself is part of that data. Because the result of the calculation is a relevant datum that affects the result of the calculation. That of course creates infinite recursion, and therefore such a calculation would never finish. Therefore I accept your conclusion that God cannot deliver prophecies about the future when the very existence of the prophecy may prevent it from being fulfilled.
But all this is true only if the existence of the prophecy has an effect on its own fulfillment.
It is still possible that the world is deterministic, and that God knows the entire future. But He will never convey this knowledge to us, and therefore the very fact that He has a forecast ready with Him will not affect what actually happens (it is not relevant data that God's 'computer algorithm' needs to take into account).
B. Another argument you raised there is the vicious circle of determinism. I do not agree with that one either. I will try to explain my criticism of it by comparing it to a parallel argument you raised elsewhere: the vicious circle of evolutionary materialism.
- We arrived at the conclusion that evolutionary materialism is true by means of our brain.
- If evolutionary materialism is true, there is no reason to assume that our brain leads us to correct conclusions (the chance of that is negligible).
- There is no reason to assume that evolutionary materialism is true.
If you add divine design to the picture, the problem is solved:
God designed our brain so that it would lead us to correct conclusions. Therefore it is reasonable to trust the brain's conclusions. The brain led us to the conclusion that God designed our brain. That argument I understand.
Now I will present in the same format the vicious circle of determinism:
- We arrived at the conclusion that determinism is true by means of our brain and the data it absorbed from the world, both operating deterministically.
- If determinism is true, there is no reason to assume that our brain, which operates deterministically, leads us to correct conclusions.
- There is no reason to assume that determinism is true.
I do not understand the justification for step 2. Assuming there is a fit between our brain and the world (intelligent design or any other reason), what difference does it make if our brain is deterministic? Why does that detract from its reliability?
Would a libertarian worldview change the situation? If a deterministic brain (which has only one possible output) is not reliable, why would a libertarian brain, which has a somewhat wider range of possible outputs but still a negligible one compared to the entire vast space of possibilities, be more reliable? I understand why adding an all-knowing God to the picture guarantees reliability. But why is adding human free choice an indication of reliability?
More than that: if I understood correctly, you are assuming here that a person has free choice regarding which intellectual conclusion to reach. That has far-reaching implications. For example, can an unbeliever choose to become a believer, and vice versa? I saw that in this context you used the term "judgment." I did not fully understand what you mean. Is this really free choice, or something 'softer'? I would be glad if you could explain.
These thoughts came to me בעקבות reading "The Science of Freedom." I was reminded of them now while reading "No Man Rules Over the Spirit" (both wonderful books, thank you), and I decided to try to formulate them in writing. I hope I managed to make my intention clear and that I was not too long-winded. I preferred to risk excessive length rather than wording that would be obscure and hard to understand.
In the end, you did convince me that there is free choice (mainly because of the intuition of choice and the intuition of moral judgment), and consequently also that God cannot foresee what we will choose. But I did not understand these two arguments. Please explain to me where my mistake is.
Best regards,
Ariel Winograd
Answer
I do not agree with your circular description. I once saw an article by Ariel Rubinstein in which he argued that a complete economic theory cannot exist, because taking itself into account would change the economic results (the economic situation). But he is mistaken, because there is a function that can also take itself into account. The economic situation would be a fixed point of that function. The same applies in your case. All this is true for deterministic factors. Only if a factor with free choice is involved do you run into a problem, and that is exactly what I said.
Assuming there is a fit, then there is a fit. The question is where that very assumption comes from. I did not understand why the range of possibilities changes anything in the discussion. That is a quantitative matter.
As for judgment, I discussed that in column 35 and 175.
Discussion on Answer
I once wrote about this but did not publish it (it is an article in mathematical economics, not my field). He assumes that there is no function that can take itself into account and give a correct result. But there are such functions. Think of a function G that takes into account all the relevant economic variables and outputs the economic situation. One of the variables is the economic situation itself and our knowledge about it. Therefore G itself will also appear in the argument of the function, just like in Gödel's theorem. That is what is called a "fixed point." Maybe there is no such function, but the very circularity does not force that conclusion.
It is very important that this is not deterministic. If it is deterministic, then the conclusion that God did this and ensured the fit is itself not reliable.
1. That is a different question. I did not explain where we know it from. What I argued is that if we do not assume it, it is impossible to believe our judgment. My answer to the "where from" question is: because I see it (with the eyes of the intellect). Like my answer to the question of how I know that the wall I see in front of me really exists there.
2. Obviously. Because if the system is deterministic, there is a positive reason not to believe it. That is not like skeptical doubts (which is what exists if it is not deterministic). I explained this at length in the book.
3. Non-determinism is not a guarantee of reliability. It only makes it possible. Without that, reliability cannot be assumed.
Thank you for your answer.
I did not understand your explanation of why Ariel Rubinstein is mistaken. I would be glad if you could elaborate more or refer me to an article that does so.
I accept the argument of the vicious circle of evolutionary materialism, and therefore reach the conclusion that there is an intelligent designer who created a fit between my brain and the world. From now on I can trust my brain. What difference does it make if it is deterministic and the conclusions are forced upon me? They are forced upon me, but God made sure they would be correct.
Regarding judgment, from reading column 175 I understood that you define it approximately as "a control system that observes the systems of observation themselves."
1. Why is it not deterministic? It seems to me that in theory one could program a robot that would learn from experience to distinguish between a mirage and a real sight (assuming computers also see mirages; I have no idea).
2. This only shifts the problem one step, but does not solve it. How do I know that that control system is reliable? Is the intuition that tells me my judgment is reliable essentially different from the intuition that tells me my brain and senses are reliable?
3. Even if judgment is not deterministic, why is that fact an indication of reliability? If I *choose* between several closed boxes and have no way of knowing their contents, that is not essentially different from flipping a coin. The fact that I could have chosen other options says nothing about the correctness of my choice. This is what I meant earlier in the paragraph about the range of possibilities.