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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.

Mauro ALLEGRANZA
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tadas turonis
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  • if "with the work of Kurt Gödel" you are alluding to GIT, the answer is: not necessarily. – Mauro ALLEGRANZA Mar 01 '24 at 10:37
  • "What do we need for a mathematics to exist in a universe..." But math is a human activity, or a product of it, if we think in terms of theorems written on books. So, the trivial answer is: the presence of some sort of "intelligence" using some sort of language. – Mauro ALLEGRANZA Mar 01 '24 at 10:39
  • Math is a distilled form of pattern identification. Arguably all we need to develop some proto-mathematics is consciousness. – Amitai Mar 01 '24 at 10:41
  • There is only one universe. That's the 'uni' part. – Chad K Mar 01 '24 at 10:49
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    There is no answer to your questions. That mathematics and mathematical objects exists independently of humans is the philosophical position of Mathematical Platonism. – Randy Marsh Mar 01 '24 at 10:51
  • @Amitai Thank you for your comment. Are you familiar with the works of either neuroscientist Giulio Tononi, or biologist Michael Levin? Respectively, they argue for a similar point, which is that consciousness is a continuum. Tononi has coined IIT, and Levin has, similarly, explored the primitives of intelligence using classical sorting algorithms. What do you think about the implications on mathematics, and this kind of thought? – tadas turonis Mar 01 '24 at 11:05
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    This is not a mathematical question that admits a right answer. It is an invitation for loose non-fact-based discussion, and as such is not suitable for this site. – Alex B. Mar 01 '24 at 12:09

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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.

Bram28
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