Pure math and correspondence to reality

I’ve never been able to get interested in pure math because it fundamentally fails the test of adaequatio rei et intellectus. You expect me to buy that you can rearrange 1 sphere to make 2 or that 0.999… == 1? It’s bad enough that these abstractions obviously can’t be realized in the physical world, but what’s worse is that they’re provably correct statements within the context of the relevant mathematical systems. What that shows is nothing more or less than that those logical systems don’t correspond to reality, which to me is the fundamental drive for all philosophy in the extended sense: theorizing and speculating for the sake of it, pondering about the mysteries of the universe until they are mysteries no longer.

Just to be clear, I am not claiming that 0.999… =/= 1 within the standard formulation of the real number system. What I am claiming is that I have zero interest in working with abstractions according to which 0.999… == 1, as that requires a completed infinity and a physical infinity can never be completed.

I’m also well aware that pure mathematics does sometimes give rise to practical applications, sometimes ones that couldn’t have been foreseen when the underlying concept was originally formulated. But what I’m talking about here is pure math for the sake of pure math. Maybe some people enjoy that. That’s fine.


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