This is a question about a thesis I have encountered regarding the relation of abstract mathematics ( Category Theory in particular ) with reality and the nature of human cognition.

The argument goes a lot like this:

""Category Theory" is more about the human mind rather than the actual world.

Humans are primates that evolved a brain as a response to their environment and the challenges it posed for their survival. The use of abstract notions of "identity" and "composition" which underlie Category Theory are, effectively, the (lower possible) limits of the granularity of the human brain.

Humans can "see" elementary objects that can be composed as a matter of the problem-solving equipment that evolution bestowed upon them.

In that sense, the arsenal of Category Theory (eg the "monad" or any other categorical construct, for that matter) when it is applied to some problem, it doesn't reveal something about the world-despite the coincidence of the structure of the particular problem with the categorical concept or abstraction that is used to study/model/tackle it-but only reflects that part of the world that is knowable in terms the human brain understands."

My question has to do with the kind of the argument presented above. What is it saying exactly? Is it about the world, or is it about the human brain?

Is this thesis a way to separate what "is"-which is probably considered unknowable-from "what is knowable"-namely those features of the world that are consonant with the human cognitive abilities?

To the extent I can understand the argument, I find it somewhat appealing because it seems to provide an argument to circumvent unnecessary complications about the unknowable "nature" of things in the interest of concentrating cognitive efforts to the things that can be actually "understood" given the evolved facilities of human cognition.

But is this the full argument?

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    Why does it have to be either or? Or only apply to the category theory? Any feature of our world picture can be suspected to be grounded in the reality out there or in our own attributes (biology, culture, etc.). The former is called realism and the latter anti-realism about the particular feature in question.
    – Conifold
    Aug 20, 2019 at 20:59
  • @Conifold I mean, it could very well be a matter of conjunction, I don't know; that's the point; also, my understanding is that the thesis is universal in the sense that by accepting it you need to adhere to it for all "attributes of the world picture" to use your phrase, not just for some arbitrary selection; and I don't understand what would guarantee such a rigid disposition; although, like I said, on some level it does make sense Aug 21, 2019 at 17:00
  • No, you can pick and choose. It is common to be a realist about physics, and an anti-realist about ethics and mathematics, for example. But I do not quite understand the question: the argument is for anti-realism about the category theory, is that all you are asking? There is a popular view that all of mathematics is a collection of representational aids, and has more to do with our constitution (biological and cultural, not just the brain) than with "the nature of things".
    – Conifold
    Aug 21, 2019 at 17:47


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