Dealing with Idiots
I’ve lately come to remember why I don’t read or respond to mtraven, owner of the Omniorthogonal blog. In short: he’s a fool.
The essential difference between mathematics and the natural sciences is that theorems of mathematics can be proved, whereas theories of natural science can only be disproved. You would not say that mathematics was empirical if you understood the nature of proof.
Both statements are wrong. Disproof is equivalent to proof of its negation; if it were not possible to prove statements about natural science, disproof would be equally impossible. If mathematical statements could not be disproven, they couldn’t be proven either.
‘Proof’ as it is meant in mathematics means that a stated derivation of an assertion has been generated through application of logical operation from more rudimentary operations, and this derivation has been evaluated as valid by analysis. It is fundamentally empirical.
As for ‘social construction’, see the Stanford Encyclopedia of Philosophy on the concept. mtraven is utterly and completely wrong about what it means to say that a thing is socially constructed. The Wikipedia entry on the subject is perfectly acceptable, although mtraven rejects it out of hand.