This question is one that has been bothering me for some time now. We have assumed, based on our observations, that the universe is subservient to the principles of classical logic. But is it necessarily so? Could it be that the universe is not logically classical but only behaves in that manner under the limits we can observe?

Additionally, there are known to be several gaps in modern theory. Is it possible that some (though not necessarily all) of them arise out of applying the limits of classical logic on systems that do not adhere to classical logic?

It seems highly unlikely, and the question feels extremely isolated from physical reality, but I cannot convince myself that it is trivial enough to be straightforwardly dismissed. So, to sum up:

Can we be absolutely certain that our universe is a system that adheres to the laws of classical logic?

Edit: Just to be clear, I do not refer to classical physics but to classical logic, the system of logic in which the principle of explosion, the principle of noncontradiction, and the law of excluded middle holds.

  • $\begingroup$ Absolutely... not. Ultimately, everything is determined from the quantum interactions. What we see as classical is the average of those phenomenon, whose error compared to the quantum picture is negligibly small. All phenomenon from the shining of stars to electric flow of current is actually dictated by rules of quantum physics.And I didn't address your question. What exactly are you asking? $\endgroup$ – Kalpak Gupta Jan 9 '17 at 10:55
  • $\begingroup$ @KalpakGupta I do not mean classical physics. I mean classical logic: the system of logic that adheres to the principle of noncontradiction, the principle of explosion, and the law of the excluded middle. $\endgroup$ – user3460322 Jan 9 '17 at 11:15
  • $\begingroup$ Related: physics.stackexchange.com/q/14939/2451 , physics.stackexchange.com/q/94560/2451 , physics.stackexchange.com/q/46015/2451 and links therein. $\endgroup$ – Qmechanic Jan 9 '17 at 11:26

The universe is not a mathematical theory.

Nonetheless, its behavior can be modelled quite effectively with suitable mathematical theories. The ones used successfully insofar are theories of classical logic, within the ZFC set theory.

It is however possible that models of nonstandard logic would model the universe as well, or better, but for the moment there is none that can reproduce the same predictions as the standard theories.

In addition, the difference between standard and nonstandard logic is mostly on the way to prove mathematical results rather than on which results can be obtained. Therefore I strongly doubt that the type of logic chosen would play a major part in defining the correct mathematical setting describing the universe.

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