[ggm]

In other words, we're still taking sides. The existence of asymmetry in the universe, isomers, strongly suggests foundational elements of mathematical logic are inherently part of things, and that we can construct all the usual inductive layers up from and/or/not in some form mechanistically, purely from things as they are, reason absent. Beyond inductive, philosophical questions and completeness and p/np are perhaps innately artefacts of conciousness. Most of the maths of things as they are lies outside these problems. It's a very big universe to argue humans define all states of being... but I grant that the idea of a number which is one more than the value you count to, before entropy prevents all counting is "out there" as a value beyond existence as we understand it, and doubtless countless other numbers and values and expressions. I live in hope some shrimp like thing, or a gas giant conscious cloud is working on that problem.

[syki]

The logic used by most mathematicians is uses exclusive or, law of the excluded middle, and is first order logic. There are some mathematicians that don’t use all of these and there are branches of math that don’t use all of them. So when someone claims math is an intrinsic part of the universe without addressing these nuance it gives the impression of an opinion without a good foundation. Assuming a finite universe (and the observable universe is finite) then math is much bigger. At most, one should say a subset of math is intrinsic to the universe.

[ggm]

Fair. I like Polyani so I shall put a Polyani quote here which I feel goes to your point: Mathematics as a purely formal system of symbols without a human being possessing the know-how for dealing with the symbols is impossible (1969) the wiki page I found it on is the Brouwer-Hilbert controversy (constructivism vs formalism, which seems a reasonable laymans take on a component of your point) and says: Despite the last-half-twentieth century's continued abstraction of mathematics, the issue has not entirely gone away. which is I feel, what I first said. It's a continuing difference, and as a non mathematician I take heart in that. All of these observations stem from looking at the law of the excluded Middle btw. There was a causal chain of weblinks to get there, I didn't just grab at random.