Do Mathematics "exist" in some sort of "Reality" that is different from our Physical Reality

Question

I will explain why I am asking this question. Let's say, there are mathematical truths and truths about our physical reality. But, there is no way we can establish the truth of any statement about our Physical Reality.

Consider a mathematical statement "There are infinitely many primes", I can give a formal proof to establish the truth of this statement.

Consider a statement about our Physical Reality "Sun Exists", I can give many Physical evidences that correspond to the Existence of sun, but still, there is no way I can establish the truth of the statement, like the Mathematical statement.

So, what is this distinction that sets apart Mathematical Truths from Physical truths? Or Is there anything such as Physical truths? Even if so, Mathematical Truths are "kind of" different from truths about the Physical Reality.

Answer 1

The reason for this difference is due to relativity. By relativity I mean "the state of being judged in comparison with other things and not by itself."

Physical reality is based on physical world and we know that it is ever changing. Therefore we cannot establish physical truths. Unfortunately we are not even aware that if there is another, that reality is based on this Physical reality. You would realize its seriousness if you could think about the 'reality of "one"'--the first natural number or 'the element of mathematics'. That means, Mathematics doesn't verify even the reality of one. Mathematics, since it is a subject, it doesn't need to verify the truth about a statement beyond its limits. If it did so, the subject would change and would merge in Physical reality and would grope for another reality.

As I said earlier, because of relativity 'Mathematical reality' seems 'rigid and Mathematical Truths have its own entity'. But the first one itself is baseless as for now. So Mathematics doesn't/can't “exist” in any sort of “Reality” that is different from our Physical Reality.

Answer 2

Mathematics largely deals with formal systems. For example, much of modern mathematics can be constructed in terms of set theory. Once the formal system is established, mathematical "truths" are derived based on the formal rules of the system. If we consider chess as another example of a formal system, then a true statement is loosely equivalent to a sequence of valid moves. Similarly, a true mathematical statement is equivalent to "valid moves" in set theory or another formal system.

On the other hand there is no formal system for physical reality. So we can not establish "truth" through applying formal rules. Instead we generally use observations from physical reality in the form of experiments, etc. to obtain empirical, rather than formal, "truth". This is a crucial distinction in epistemology.

Answer 3

The proof of physical truth is your own consciousness. Your direct awareness of some phenomena cannot be proved by any external or material means. In this sense, your direct conscious experience of Sun in undemonstrable (and all people know this). At the same time you have no doubt that you are experiencing the Sun. And you don't need any proof because you know it - your consciousness is good for it self; it is complete and it doesn't needs any backup proof from outside. Consciousness is self-referential.

Answer 4

Math is based on logic and logic is based on physical experience. Therefore there is no difference between physical and mathematical "truths" other than the level of abstraction.

You could of course make up alternative logics that are not based on experience, but these wouldnt lead to any useable "truth". If mathematically I define bananas to be the same as apples, then say "bananas equal apples", I would have reached a mathematical "truth", but no one would care.

The question of why physics and math are so consistent often pops up and I would answer that : 1)logic is based on experience (A=A because that's what we usually observe)

2)math is based on logic

3)physics is based on math, logic and experience

4) it all works out because nature is consistent with itself

Answer 5

What you call "physical reality" was called by Kant noumenon or thing-in-itself. We can't know it, we don't know it, we have no access to it. Its counterpart is phenomenon, what we can perceive and cognize, which is subjective for every individual. Reality is just a structure of ideas, based on perception, that exists in each individual mind.

Therefore, a “Reality” that is different from our Physical Reality is not possible. The only possible reality is not unique, it is subjective, and is an attempt to model the noumenon.

Mathematics just express facts about such subjective reality. Therefore, it exists on the same realm as objects (objects being a subjective model of part of such reality).