>>11269167>Mathematical structures are equivalent to the functional state of a mind envisioning said structurethey are not equivalent, structures are imminently perceived as objects of thought. If this was not the case, we could not imagine mathematical proofs. A vast number of mathematical proofs are self referential operations, ie objects put through some other function. and so an object of thought cannot be equivalent to the functional state of a mind, because that object also exists as a structure within a function, and a structure with in a function in a function, and so on. Simply put, structure can be thought of as subsets of a state of mind, only defined and conceived of insofar as it has observable relations to the other objects of thought in the mind.
>people posess differing minds, the structure is unique to each mind. Ergo relative.You are right, people don't share minds and so alot of the time, someones concept of something is different then another, even if only slightly.
Its entirely possible,however, that two people posses the exact same concept of "set", for example. That is to say, every potentially conceivable thought they have about "set" is isomorphic in every meaningful sense. In this case, they are, by definition,perceiving the same mathematical object.
Under this realization, we can observe that even though the concept "set" may be different for two people, they are both still ascertaining mathematical objects insofar as they are consistent and non contradictory. All of this is to say that both of those objects are in fact different mathematical object, only unified under a semantic notion of "set". Not a conceptual one. This revelation immediately exposes the sheer magnitude of the universe of mathematical objects.
