I had a seemingly simply question today, that goes as following.
What do we need for a mathematics to exist in a universe, or a system, more broadly speaking?
Is it a matter of having the ability to define axioms, or regularities and certain patterns?
How much does it hinge on us having the cognitive functionality that we currently do?
I am not very familiar with the work of Kurt Gödel, but I suppose it might also have connections to what I am pondering.
Thank you in advance for your consideration of this question.
This seemingly simple question and some variation thereof (‘where does math come from?’ or ‘what is the basis of math?’ or ‘what justifies math?’) is often asked on this site, but (as you probably suspect) it has no simple answer.
Indeed, this question is probably more suited for the Philosophy.SE site, and I would also recommend taking a course or consulting a text in the philosophy of mathematics, where you will learn about a wide variety of views on this.
That said, it seems like you are leaning towards some kind of cognitive basis of math. Now, for that, I would actually recommend staying away from consciousness, since consciousness is such a quagmire by itself. However, I think you may enjoy the book “Where Mathematics comes from” by Lakoff and Nunez, where they try to relate our mathematical abilities to more basic cognitive abilities to perceive and interact with the environment, and how our ‘embodiedness’ and ‘situatedness’ not only effects, but largely creates such concepts as ‘up’ and ‘down’, ‘before’ and ‘after’, etc. which in turn effect how we think of things like numbers, orders, shapes, etc.