Conceptualism

Brother Danny said:

“To answer your question about numbers:
Do ‘numbers exist other than as a concept? Do concepts exist other than inside minds?”

So Danny resorts to conceptualism. There’s nothing wrong with this in principle. Indeed, I agree with him that numbers are mental entities.

i) The question, though, is the kind of mind in which they inhere.

How can a human mental act—the act of a finite, mutable mind—constitute an actual infinite object like the Mandelbrot set?

To be an actual infinite, it must be a given totality. Unless all it’s members are given, it cannot be a set.

ii) What is more, if numbers inhere in human minds, then there were no numbers before there were human minds.

Hence, there was no third planet from the sun before hominids evolved to the point where they could conceive of the number “3”—assuming evolutionary epistemology, which is a version of naturalized epistemology.

At that point the earth suddenly became the third planet from the sun.

If everyone were comatose, would the earth suddenly cease to be the third planet from the sun?

iii) Furthermore, conceptualism is only as good as your philosophy of mind. If you’re a physicalist, then in what sense is an actual infinite object like the Mandelbrot set exemplified in time and space? Finitely or infinitely?

“Do minds exist which do not supervene on the physical brain?”

Yes. God. Angels. Discarnate souls.

“What is your explanation for numbers? God poofed them, and there they were?”

This is a good example of a man who dismisses Christian theology without ever knowing what he’s even dismissing.

The answer is found in the exemplarist tradition, which goes back to Philonic Platonism, Neoplatonism, and Augustinian Platonism, according to which it is the infinite and timeless mind of God that constitutes abstract universals.

They didn’t come into existence. Rather, they are consubstantial with God, as mental attributes.