Q&A: Empirical Refutation of A Priori Logical Arguments
Empirical Refutation of A Priori Logical Arguments
Question
Hello Rabbi.
I seem to remember reading several times in philosophy (and maybe from you as well) that there are kinds of propositions/assumptions which, by their very nature, cannot be refuted by an empirical finding.
1) I don’t quite remember which propositions fall into that category besides logical propositions. Probabilistic propositions too? (As follows.)
2) For example, it is clear to all of us that the simple does not turn into the complex randomly; after all, this involves probabilistic considerations that are mathematical (something like logical).
Now the neo-Darwinians come and claim that evolution refutes that assumption.
Assuming that I agreed a priori that the simple does not turn into the complex randomly, based on a priori probabilistic considerations, is it correct to say that even before I go into the field and check what happens in the evolutionary process, I should be completely confident that evolution, by virtue of being empirical, cannot refute the claim that the simple does not turn into the complex? Is it correct that it should be clear to me that apparently one of the data points in evolution simply does not fit the proposition (and therefore in any case does not contradict it)? That is: a) Either at the beginning of evolution the situation was not simple (relative to the end). b) Or at its end the situation was not complex (relative to the beginning; really the same thing). c) Or the process was not random (or not entirely random)?
3) Can the Rabbi explain why it is true that empirical refutation is impossible for such propositions?
4) What is the significance of the fact that they are not subject to empirical refutation? Does that strengthen them, or weaken them? (Like a theory that cannot be empirically refuted, and is therefore unscientific).
Best regards, Joseph.
Answer
4. First of all, you yourself mentioned mathematical propositions. From that you can understand that the fact that they cannot be empirically refuted is not due to weakness but, on the contrary, due to their strength. By contrast, claims that have no basis and cannot be refuted are weak (like the celestial teapot).
3. I’m not entirely sure that the claim that the simple does not become complex cannot be empirically refuted. I can imagine a world in which the simple does in fact become complex. In general, when a claim deals with the world and not with ideas alone, it seems to me that it can be empirically refuted. Beyond that, the claim that the simple does not become complex is true without laws governing the process, but with laws it can indeed happen.
According to Kant, there are propositions that are conditions for our cognition and therefore cannot be empirically refuted. I’m not sure there is anything like that beyond logic (for example, he thought this about the fixity of time, and Einstein showed that this is not so).
Discussion on Answer
3. The difference between simple and complex is probabilistic, not physical, and that is certainly true.
1. But the claim that there is no transition from a simple state to a complex one is a claim in physics, not in mathematics (the claim that you don’t just happen to arrive at a state with low probability).
2. Without there being laws of nature at all, apparently you are right, but it seems to me that without laws the question is not even defined. If you are talking about a random lottery, that too is some kind of law of nature. There the chance of such a transition is indeed small. You have to provide a mechanism of transition between states in order to be able to ask the question about the chances of transition. That mechanism is physics.
And indeed, that is my proof.
3. Can one not conceive of a world in which the number of states equivalent to an ordered state equals the number of states equivalent to a disordered state? For example, an imaginary world in which almost any wiring of an electrical circuit would produce something special and functioning? Is there any logical contradiction here? Could even God not overcome that? (Just to sharpen the point.)
4. So I’ll phrase it differently: even before I examined evolution, could I know with certainty that if there is a process in which the simple becomes complex with enormous probability, then it is clear that the laws and conditions operating in it are very rare (= the overwhelming majority of systems of laws would not yield that)?
Here, seemingly, my claim ought to be correct, because I am appealing to the distribution of systems of laws, and according to the Rabbi this is a probabilistic and not a physical argument to say: “The overwhelming majority of systems of laws would not create something as complex as a human being.” Correct?
Joseph, you can see by me here the strong objection that the rabbi ignores:
https://mikyab.net/%D7%A9%D7%95%D7%AA/%d7%90%d7%a0%d7%98%d7%a8%d7%95%d7%a4%d7%99%d7%94-%d7%94%d7%90%d7%9D-%d7%94%d7%90%d7%91%d7%95%d7%9C%d7%95%d7%A6%d7%99%D7%94-%d7%9B%D7%94-%D7%9E%D7%99%D7%95%D7%97%D7%93%D7%AA/
Because the definition of entropy in the notebook is uniqueness.
So a gravitational singular point has the lowest entropy (assuming there is space around it, and not that space itself is the size of the point… like the beginning of the Big Bang). Up to this point, the Rabbi also agrees in the notebook in several places, where he takes care to point out that the point at the beginning of the Big Bang had no space and therefore it was simple…..
This point will occur for any value of a gravitational constant greater than 0 (it just depends how long it takes, somewhere between milliseconds and Graham’s number years), but in the end it will happen.
And therefore, דווקא the probability that the simple will remain simple is only when the gravitational constant is 0. Which means 1/infinity….
So if the purpose of the fine-tuning argument is to present the chances that a human being would emerge, then fine… the atheists need not get excited. But if its purpose is to present the chances that something complex would emerge, then it is making a grave mistake, because the probability of that is actually (for a gravitational singular point) infinity minus 1 = infinity.
Maybe with you he’ll respond as usual. And this time to my question too. Have a peaceful Sabbath.
Hello Rabbi, I’d be glad for answers to my two questions in the last message. I saw that there is another Joseph who asked a question about God; that wasn’t me.
Kobi, what you asked is indeed an interesting question.
I said that I’m taking a break from these topics until further notice.
I think the Rabbi got confused.
My question doesn’t deal with God at all, and you already answered most of it here. Just two last questions!
3. Can one not conceive of a world in which the number of states equivalent to an ordered state equals the number of states equivalent to a disordered state? For example, an imaginary world in which almost any wiring of an electrical circuit would produce something special and functioning? Is there any logical contradiction here? Could even God not overcome that? (Just to sharpen the point).
4. So I’ll phrase it differently: even before I examined evolution, could I know with certainty that if there is a process in which the simple becomes complex with enormous probability, then it is clear that the laws and conditions operating in it are very rare (= the overwhelming majority of systems of laws would not yield that)?
Here, seemingly, my claim ought to be correct, because I am appealing to the distribution of systems of laws, and according to the Rabbi this is a probabilistic and not a physical argument to say: “The overwhelming majority of systems of laws would not create something as complex as a human being.” Correct?
3. I didn’t get confused. I’m taking a time-out from the topics of proofs for the existence of God and entropy and the rest of those nuisances, precisely because they never end (I answered briefly because I thought that would finish it). I’ll answer only this time, and that’s it. One can conceive of such a world, except that in it there would be laws of nature even more special than ours. Even I could create such a world; you don’t need to be God. Just make a short circuit that neutralizes all the circuits.
4. Yes. See the previous section.
That’s all for now.
1) But the Rabbi mentioned several times that the claim that the simple does not become complex randomly is based on probability (the states equivalent to an ordered state are negligible compared to all the other states), and probability is part of mathematics, which is like logic, so by definition it should not be subject to empirical refutation, no?
You mentioned laws, but once there are laws then we are no longer dealing with a random process; that itself is your proof that evolution is irrelevant to faith. If there is a process that turns the simple into the complex (maybe even with 100% certainty), then by definition it is clear that the laws governing it are rare and special = the process is not random. An assembly line also produces complexity “by itself,” but obviously its structure is special (= even though there are no hands operating in it, it is the result of intelligent design).
In your words: “Doesn’t that mean that there is some factor that impaired the randomness a bit?”
I’m not talking about non-randomness in the sense that someone arranges the simple into the complex with his hands, but rather the claim that this proves the laws are rare.
2) “I can imagine a world in which the simple does in fact become complex.” Why imagine? That is exactly our world, and we agreed that the very fact that the simple became complex proves that the laws are special (= the randomness is not complete, like Gould’s drunkard), meaning we assume absolutely that the simple does not become complex randomly, and if we find that it does, that means it is not entirely random (there are mutations and genetics and natural selection).
3) The more correct question to ask is: Is a world possible in which states of order have as many equivalent states as states of disorder?