One could simply say, as Werner Heisenberg argued in his book Physics and Philosophy, that there is a need to restore the Aristotelian duality between the potential principle in a thing and the actual principle, where the wave basically expresses the particle in potential, but is not itself a particle until collapse occurs, at which point the particle passes from potentiality to actuality. Physicists sometimes like to offer paradoxical images, and that leads to the mistaken thought as if one can think against the laws of logic with regard to quantum theory—which is complete nonsense.

I’m attaching here a video I uploaded earlier, up to the cosmological proof that I happened to present here in the not-too-distant past, so that Gil may perhaps manage to get around the Rimon block.

I didn’t understand Heisenberg’s claim. But as I understand it, in reality itself (at least in the standard interpretation), the wave and the particle are both only certain manifestations of a wave function. What really exists is an entity that is neither of them. So there is no logical problem here at all, and no need to get tangled up on the logical plane. Physics is complicated enough even without people confusing us on the logical plane.

In my opinion the video is excellent, and therefore I uploaded it to the site in a separate thread. See there a few comments of mine, and maybe it’s worth improving it.
https://mikyab.net/%D7%A9%D7%95%D7%AA/%D7%94%D7%A8%D7%90%D7%99%D7%94-%D7%94%D7%98%D7%95%D7%91%D7%94-%D7%91%D7%99%D7%95%D7%AA%D7%A8-%D7%9C%D7%A7%D7%99%D7%95%D7%9E%D7%95-%D7%A9%D7%9C-%D7%90%D7%9C%D7%95%D7%A7%D7%99%D7%9D-2/

Aristotle’s laws of logic (the classical ones) do not represent the quantum world. Quantum logic gives a structure equivalent to the mathematical structure of quantum mechanics and demonstrates how the “strangeness” of quantum mechanics derives from its mathematics. Your claim that one cannot infer logic from empirical observations is wrong; it is contrary to experience.
Quantum reality is a paradox, and that is why that term is used. For example, the superposition of particles is an intuitive paradox, but it has a physical explanation.

Declarations are nice, but I can’t do anything with declarations.
I explained briefly here why this cannot be. Quantum reality is not a paradox in any sense. If it were a paradox, then nothing could be derived from it (that is, it would have no predictions and therefore no scientific value). Superposition is not a paradox, as I briefly explained here.

You make arbitrary assertions without explanation.
Quantum reality is full of paradoxes, and despite that it is true, and despite that predictions can be derived from it. That is the beauty of quantum theory and the tremendous achievement of its developers. In short: it seems illogical, it gives precise predictions with tremendous accuracy, and we don’t really “understand” it (except through deep mathematical formulation).
Examples of paradoxes: particles can be in several places at once, effects can occur between distant objects without local mediation, and the act of measurement itself changes what is being measured.
But all these are philosophical paradoxes only, arising from a clear mismatch between our intuition and a different physical reality to which we have no experiential access. These paradoxes have a precise explanation in the appropriate language—mathematics (quantum logic is not a layer of quantum mechanics; it is only an auxiliary tool).

You didn’t mention superposition at all. Wave-particle duality is not superposition, if that’s what you meant.

Well, it is clear that despite the great enthusiasm, you don’t know what you are talking about. So I’ll respond briefly and leave it at that.
Let me preface this by saying that I don’t remember what I wrote here. For some reason I thought you were commenting on column 703, which was posted recently and dealt briefly with these topics. So apologies if things I mentioned in my reply to you were not explained here but rather there and elsewhere.

1. Any scientific theory or other theory that contains a paradox within it allows you to derive any prediction you want from it. That is a theorem in logic. If that were the case in quantum theory, it would have no predictions at all. A mismatch with intuition is not a paradox. That is probably the root of your confusion.
2. A particle cannot be in several places. Its wave function can assign a probability to being measured in several locations. That is really not the same statement. There is no particle at all until you measure. There is a wave function. As for that, the fact that there is no location is not a paradox, just as a light wave has no location. See on this briefly in column 703 and elsewhere.
3. Effects between distant objects are a matter for interpretations (EPR): whether one gives up locality or some other property. Be that as it may, action at a distance is not a paradox (at most it is something that has to be reconciled with relativity).
4. The fact that measurement changes something is not a paradox but only something that is hard to understand. See the end of section 1.
5. A wave state is nothing but a superposition among position states, and vice versa.
That’s it.

I appreciate that you answered and understand that you got tired of me…
I’ll respond only to the first two claims; if you want, answer. I find it interesting.

1
“Any scientific theory or other theory that contains a paradox within it allows you to derive any prediction you want from it. That is a theorem in logic.”

That’s not entirely precise. If you are talking about a theory with internal logical contradictions, that is of course correct.
But that does not apply to the case of quantum theory, because here the paradoxes are intuitive, not logical. Therefore, you can derive only predictions that follow from its mathematics, not any prediction you want.

2
“A particle cannot be in several places.”

As long as you haven’t measured, that’s true. Of course. But logically, the statement is correct. And after all, you are dealing here with logic.

That’s it.

Just a note regarding 2.
Even if the particle could be in two places simultaneously, that still would not be a logical contradiction at all. It would only refute our experience. If from the day you were born that had been the reality you were present in, you would not feel any logical problem in it.
A scientific theory that is not subject to logic is contentless for us, because if it does not obey logic, its reports do not even exclude their opposites.

P.S., one more thing,
an “intuitive paradox” is probably not a paradox at all, but simply a mistake in your worldview.
It’s like if I wake up from an afternoon nap and my “intuition” is that it’s now toward evening, but I glance out the window and see that it’s night. Is that a paradox?

I have reservations about the ability of logic (Aristotle’s logic) to help us understand physical reality. It is true that the tools we have developed—the models, the analyses, and the controls on their validity—sit deeply within a logical framework. But the laws of physics themselves are not based on logic (as distinct from the formulation and internal consistency of the laws). As you say (?), God does not obey human logic; I would add that the universe does not either (I distinguish between them). Logic is an essential tool, and at the same time a barrier or intellectual minefield to true and complete understanding. We impose our reason on the universe (along with something else important that we won’t agree on). That in itself is a paradox. Almost funny, you might say.

1. “Intuitive paradoxes” is an empty concept. There is no point in using the term “paradox” here. It is simply something not understood or not fitting our existing understanding. So what? Is an LLM also an intuitive paradox? When I speak about paradoxes, I mean logical contradictions.
2. I hope you understood what you wrote here. It looks like nonsense to me.

As for your last message,
A. The laws of physics certainly are not derived from logic; otherwise we would not need observations.
B. There is no logic other than Aristotle’s. All the rest are logic-like structures that mathematicians call different “logics.” None of them departs from the law of excluded middle, the law of non-contradiction, or the law of identity.
God definitely does “obey” the laws of logic. I have explained in the past that there is not really any “obedience” here, because departing from the laws of logic is a meaningless expression.
C. If logic is a minefield to rational and complete understanding, I wish you good luck.

What you call nonsense may tomorrow be scientific fact, and vice versa. There are many examples of this.

Nonsense:
– Two bodies exert a gravitational force on each other in zero time. One of Newton’s laws, which stood for centuries until Einstein came and explained otherwise. An excellent approximation, but nonsense.
– God. We’ve been waiting for proof for 10,000 years. We’ve seen attempts at proof based on logic from Augustine and Aquinas to the present day. Has anyone succeeded? They found a perfect solution: God does not obey human logic. Of course not, otherwise there would be no need for Him.
– ‘God.’ The quotation marks don’t really help.
– Relativity. At first it was received as complete nonsense.
– The universe is expanding. It seemed absurd. Even Einstein’s imagination tripped him up.

Nonsense?
– Imagination is more important than knowledge (Einstein).
“God does not play dice.” Who is Einstein’s God? Spinoza’s God, a cosmic order. Not the God of Israel. By the way, what did Bohr answer him? “Stop telling God what to do.” Even in physics, you can’t do without humor.

Anyone who calls something ‘nonsense’ needs to possess absolute knowledge. Otherwise it is better to be more careful. Do you possess absolute knowledge? Do you doubt your own knowledge, or for example the existence of God?

*The full quote:
“Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and stimulates progress, giving birth to evolution and discovery.”

This whole message is one big piece of nonsense. I’m done here.

Nonsense. Really?

I would be very careful with assertions like that.

You present a pure rationalist position that places logic before and above the experience of reality.
That is a weighty claim, and one cannot present it as a fact without arguing for it. If you claim that logic is completely a priori and cannot be updated under any empirical circumstances, you need to explain why—otherwise it is not a scientific claim and not a well-founded philosophical claim, but simply a dogmatic position, as I argue it is.

Quantum logic indeed does not satisfy the laws of classical logic in their ordinary sense—for example, the distributive law—but it still gives an excellent and precise description of quantum reality. That is not debatable. It is a fact.

In order to claim that quantum logic is “incorrect” or “just a reformulation,” you need to prove:
– either that it is completely equivalent to classical logic—which is obviously not true.
– or that it fails empirically—which is also not true.

You assume the superiority of logic in advance instead of examining it.
The argument states that logic precedes every observation, but perhaps the laws of logic themselves are also based on a kind of ongoing intuition that is reinforced by the world—that is, perhaps the laws of logic are not completely absolute?

You rule out the possibility of a deep conceptual shift בעקבות science.
For example, quantum theory really does pose challenges to classical logic—concepts such as superposition, collapse, and intermediate states go beyond binary categories. Perhaps there is room to rethink the law of non-contradiction, or at least its scope.

You identify logic with only one formal language.
There are other well-developed logics, such as many-valued logic, intuitionistic logic, and more—one cannot dismiss them as merely a “form of expression” if they offer other interpretations of physical situations.

You ignore the evolutionary aspect of logical thinking.
Perhaps logical thinking itself developed out of adaptation to a certain physical world, and is not “given in advance” but rather the result of biological-cultural development? Hume argued that there is no scientific truth. Without that dramatic statement, Einstein would likely never have dared challenge Newton’s laws.

Thanks for the correction regarding superposition. I didn’t notice it. A beginner’s mistake by someone who doesn’t swim through the concepts from every angle…

You would have been careful, if not for what? 🙂
You are mixing up concepts here. True, people use the term “logic” also to describe mathematical structures used in certain fields. But that is just a borrowed expression. There is no and cannot be any departure from logic anywhere. The discussions of those logical systems themselves are conducted using the tools of ordinary logic.
You are confusing logic with science. Logic is not measured in a laboratory. There is no such thing as facts that contradict logic. Facts can contradict a scientific theory but not logic. The contradiction spoken of here is itself part of logic. So there is no point talking here about evolution and all the rest. Outside logic, no speech has any meaning; therefore it really does not matter whether it is the result of evolutionary constraint or not (though of course it is not).
You can look here on the site for explanations of the difference between the laws of logic and scientific or legal laws. These are not “laws” in the same sense.
There is no way to test logic in a laboratory, even if you wanted to. So of course quantum theory does not challenge anything in existing logic either. The talk about “quantum logic” is in a borrowed sense, as I explained above. I explained all this in previous messages.
I do not rule out conceptual change following scientific findings. Where did you get that idea? I rule out logical change following scientific findings.
None of this has anything to do with rationalism. A complete empiricist must also agree to all this. And if he does not agree—then he is simply confused.

You say:
“ There is no such thing as facts that contradict logic. Facts can contradict a scientific theory but not logic. The contradiction spoken of here is itself part of logic.”

You are absolutely right as long as you are referring to a certain logic from within that same logic.
Your argument assumes in advance that logic is an entity separate from the world, one that cannot be affected by facts and therefore also cannot change because of them. But that is exactly the question—does our logic derive from the structure of the world, or is it a priori? The argument simply assumes the answer, and therefore it is a circular argument. Your basic assumption has not been proven.

Why are you so sure there are no other logics? Why do you think human reason or rationality, coming from our limited brains, is “fit” (I couldn’t find a more suitable term) to determine such a universal truth? To me that is not logical. A person knows and perceives the world through the limitations of the human brain. Logic too is a product of our brain; it is not written on the trees. What part of the universe do we see and grasp, how much of the true picture is missing for us, and whether what we see we even understand “correctly.” Einstein already showed us that we were living in a movie for hundreds, really thousands, of years. Are you completely sure that tomorrow we won’t get hit over the head like that again?

And here is a hard problem for you. If it is impossible to imagine facts that contradict logic, how would you know to recognize such a fact if you encountered one? For example, if you saw a system in which A and NOT A hold simultaneously, would you ignore that fact, or reexamine the law of non-contradiction? That very possibility teaches that logic, even if it is very stable, is not beyond criticism, and like any formal system, it is valid under certain conditions.

Good night and happy holiday (not all that happy).

I referred you to the distinction between the laws of logic and other laws. See for example the article on belief in contradictions.
I’m done.

You can also see here:

על תורת הקוונטים וטענות/אמונות סתירתיות

You don’t really think that logic and mathematics are a branch of the natural sciences?! Actually not even a branch—on your approach they are literally part of physics.

I’m done with this.

I think the truths I know are temporary. I know only one thing for certain—that I do not know.

Case My Rest

…A paradox is true to its name! Therefore a paradox cannot be found in logic!!! Just as the doctrine of contraction is found in the abstract and simple infinite, so too logic can be and be found in the abstract and simple paradox!!!

Ofer, if you know with certainty that you do not know, then you agree to the certainty of logic.
Maybe there is an alternative logic in which your not-knowing is the knowledge that you do not know? Maybe your certainty actually means that you have no certainty?
The moment you raise alternative logic as an option, everything that comes out of your mouth turns into nonsense, including the statement that maybe there exists an alternative logic, because if it indeed exists then by the same token it also does not exist (the law of non-contradiction). You cannot raise as an option that truth is falsehood and also not falsehood, and then evade the consequences.

David,
The logic that both of us know and live by is completely coherent.
That does not rule out the existence of other logics. And there are such.
Aristotelian logic is not valid in the quantum world. At least not directly.
Why? Because it was shaped by the human intellect of 2,400 years ago, a time from which the quantum world is outside. It is not available to our senses, and it is foreign even to the intellect of the ordinary person of the 21st century. Quantum logic could not have been invented in Aristotle’s day, just as one could not then have invented a computer operating system or even a strap for a wristwatch.
The quantum world is not available to our senses, nor to the mind of someone who is not an expert in it.
But the intellect and systematic thought did not rest for a moment among certain people and in certain cultures, and it turns out that it knows how to explain the world contrary to the senses and contrary to common sense.
The intellect invented, or found in the universe (whichever suits you better), a new logic, quantum logic, and it fits quantum theory wonderfully.
No mental-logical pilpul can negate that fact (until it is undermined by experiments or by another accepted method). You should not mix non-scientific claims into the world of science. It is not the same language, and they have no validity there.

I fully understand that there are things that sound like nonsense. But to whose ears? When Einstein published special relativity in 1905, the almost sweeping reaction of the scientific world was: “nonsense.”