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There's something truly evil about psychologizing math.

If anyone feels compelled by this you should probably start by learning about the many rock-solid antipsychologistic arguments out there that are at least 130 years old:

https://plato.stanford.edu/entries/psychologism/#FreAntArg



Not sure why you are getting downvoted, as I believe there is a kernel of truth to what you are saying. Although I am sympathetic to the idealist position, based on what we know today about computers, I have come to believe that the thing some would call mathematics today is not grounded in reality. Whenever mathematics departs from reality, it leads those who practice it down a path that ends with insanity.

In the same way that psychology can be harmful to the pursuit of truth, there is an evil or deformity in what pure mathematics represents (or became), as Cantor and Gödel both discovered trying to eliminate its paradoxes. Mathematics as practiced by, e.g., Leibniz and Euler, was much more interested in calculation, i.e., mechanization. It is this form of "mathematics", as the thing has come to be called, that should have been developed, instead of trying to axiomatize infinite sets, explain the continuum, or fix impredicativity.

But despite the many paradoxes of mathematics (e.g., AoC, LEM) and machines (i.e., bugs), computer science has happily chugged along and made many practical contributions which explain the universe and shed light into people's minds, fulfilling the role that pure mathematics once served. Today, we are very close to mechanizing both minds and mathematics, and can replicate many aspects of reality (i.e., mathematical or otherwise) inside computers. It is not unimaginable that one day, computer science as it is practiced today will be seen as a kind of telescope for revealing the nature of mathematics and/or reality, which the mind alone cannot fathom.


Intuitionism has nothing to do with psychologizing math. The intuitionist is perfectly fine accepting that "the mind of the mathematician" is merely a metaphor for some system capable of mathematical constructions, and that the "mathematician" in this argument can be replaced by a computer performing the same steps. In fact, a lot of computer science, particularly programming language theory, depends on this very notion.




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