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Must all physical theories conform to the laws of logic, such as being self-consistent? I am asking this because I once had an argument with a friend regarding the physics of time travel. I argued that any physical theory that allows time travel must have a consistent history. That is, no person or thing can go back in time to change what was the case, as that would mean that at some point in spacetime, both X and not-X happened. He argued that physics does not need to conform to logic or even be self-consistent. But what is the truth of the matter? I know that quantum physics has its own kind of logic called quantum logic, which differs from classical logic in some respects, but even there, I think physical theories should be at minimum self-consistent, and obey some basic logical principles.

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  • It is not the laws themselves that conform to logic but their expression in physical theories. And yes, theories, physical or any other, must conform to laws of some logic to be intelligible. There is a theoretical possibility of using a logic that allows some contradictions, paraconsistent logic, but so far physicists did not warm up to such an idea.
    – Conifold
    Oct 31, 2023 at 20:14
  • Why not post this on the physics stack exchange? Nov 1, 2023 at 1:45
  • A self contradictory theory of physics wouldn't be very useful anyway, if it can't be used to make accurate predictions.
    – armand
    Nov 1, 2023 at 3:58
  • Logic and the conditional is an aspect of language and thought, and so if you concede that physical theories are linguistic and intellectual representations, then it is important to note that logical truths should cohere. en.wikipedia.org/wiki/Coherence_theory_of_truth That being said, physics is tolerant to some contradictions with the understanding that future physicists will dissolve contradictions one way or another. en.wikipedia.org/wiki/Confirmation_holism
    – J D
    Nov 1, 2023 at 13:46
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    How would we ever know if a logic contradicted physics? Logic is an abstraction, and we can only ever apply an interpretation to logic, not asses the logic directly. Unless you've found Plato's world of forms, care to share the location? For example, lets say we found an object in the real world which is not equal to itself- it apparently contradicts the identity axiom , but how do we know the real world notion of equality is actually the same as the logical notion of equality? - i.e. how do we know it actually breaks the axiom? Nov 1, 2023 at 23:14

4 Answers 4

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As you note, coherence is a highly thought of screen to sort out bad theories, and few science theories are considered plausible if they do not satisfy it.

And yes, there are multiple logics, and satisfying classical logic is not the only possible one that a science theory could hold by. A science theory can instead satisfy an alternate logic from the basically infinite set of possible logics.

However, physics is a science, not a theory. It is just a field of study, and is filled with a collection of bottom-up theories developed to characterize specific phenomena. Physics itself is not coherent today. Its two most dominant theories, quantum mechanics and general relativity, are not coherent with the other. One of these theories is deterministic, the other is probabilistic. AND -- there are a variety of other local theories in physics that are not coherent with either of these major ones, primarily in the areas of solid state physics, and also in the field of emergent phenomena.

The non-coherence of science becomes even more apparent when one considers the other sciences. Evolutionary biology, for instance, does not reduce to cellular biology, and the concepts of ecosystem, ecological niche, breeding population, phenotype drift, etc., are meaningless at the cellular level, chemistry level, or physics level. Science as a whole is radically not coherent, and the SEP article on scientific reductionism in section 5 suggests it never will be.

This is discussed in a prior answer: Can findings in one science contradict those in another?

However, as you noted, coherence tests of science theories ARE STILL an important filter to toss out poor theories. And finding coherence within a science, and between sciences, remains a desirable goal. But as with all other areas of science, there are no absolutes. We may find that an incoherent model is our best explanation of some part of our world, and that as the SEP article implies, that incoherence in science as a whole and in each field may just be what our world is like.

Regarding logic in particular -- there is a major problem for all of the sciences as most logics require that A=A, the law of identity, hold. But over time, all of the objects, the A's, of science hypotheses, tend to change, such that A=/=A. Many of them change slowly, so that one can approximate A=A over short or medium time frames. But the lack of absolute A=A over time, makes all of science problematic relative to logics, as to apply a logic, all of its assumptions must be true, not just nearly true.

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  • Eg, Ship of Theseus, & Heraclitus' 'You can nevdr step in the same river twice'
    – CriglCragl
    Nov 2, 2023 at 23:40
  • @CriglCragl -- Yes the Ship of Theseus -- is there such a thing? It sure seems so, but then its nature eludes detailed characterization. A is only approximately A.
    – Dcleve
    Nov 3, 2023 at 1:04
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Physical theories are represenations of reality and as such - in order to have a meaning to us - must confront some way or another to the laws of logic, as you say. But physical reality - which is the real thing we are trying to represenat in a theory - does not have to obey logic: indeed, if that was the case, then everything that happens would be logical; but it isn't, or at least we are not always able to identify it as such.

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    ie. The Problem of Induction, & the necessarily tentative nature of scientifuc knowledge
    – CriglCragl
    Nov 2, 2023 at 23:52
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Up to a point, yes, physics needs to be logical. Or to put it another way, a physics theory that was patently illogical would not get much traction in the physics community. However, you have to bear in mind that physics is a patchwork of theories that each tries to model a subset of observable phenomena, and the individual theories are not always mutually consistent. That said, the realty they attempt to model is self-consistent in many important respects, so an individual theory which led to conflicting outcomes would be immediately suspect.

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  • Like wave-particle duality. That's why I reject all physical theory in its entirety.
    – J D
    Nov 1, 2023 at 13:44
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    @JD that's what I like to see- a man who knows his own mind! On a more serious note, my own experience is that to understand a complicated scientific theory properly you need to cogitate and dwell on it for orders of magnitude longer than the attention span of the average person. As a consequence, vloggers, bloggers, teachers, journalists and the like perpetuate misleading simplifications of science ideas which then get a life of their own and we end up with all kinds of nonsense being spouted about them. Nov 1, 2023 at 14:09
  • @MacroOcram I read science until the age of 38, and one day asked myself, what is science, and after writing three pages to gather my thoughts, realized I had no idea. The only people who can claim some measure of competency are those who devote their daily occupations, esp. those who are paid to, to make sense of it all. Every philosophy book I buy and read just makes me dumber.
    – J D
    Nov 1, 2023 at 18:01
  • @JD -- Popper, Popper vs. Kuhn, Quine vs. Popper, and then Lakatos finding a way to integrate the best of each, will not make you dumber.
    – Dcleve
    Nov 1, 2023 at 19:03
  • “No, no, you're not thinking; you're just being logical.” ― Niels Bohr. Quantum ideas were considered a najir challenge to classical logic, with complimentary & delicalisation etc etc. Non-Euclidean geometry also violated what were considered hallowed logical axioms/dsfinitions, like the Parallel Postulate. Tachyonic Fields, & the Unruh Effect, are modern examples of how confirming to our common sense of what is logical is not required for traction in physics
    – CriglCragl
    Nov 2, 2023 at 23:50
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No, ultimately. Since there is no natural order to the Kosmos, something has to arbitrarily assemble it into the order we take for granted.

Logic, one could say, then, is derived from this need for order.

God exists. Q.E.D.

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    "If god did not exist we would have to invent him"?
    – CriglCragl
    Nov 2, 2023 at 23:53

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