XPost: sci.math

[I'll post here since I cannot post there.]

I think most people believe that mathematical truths are logically necessary.

Most people don't even know what necessary vs contingent means.
(Non-trivial) mathematical truth is (necessarily!) contingent, on
mathematical definitions and rules! (Even those who believe God
gave us the integers, should remember that at least the rest is man
made.) Indeed, logic and mathematics rather are *opposite* poles!

The fact that sqrt(2) is irrational doesn't depend on who proved it,
when they proved it, whether they liked it, or any other contingent historical facts.

In fact, contingent does not reduce to historical, it's not even in
the same category... Truth rather is that almost nobody can even
guess anymore what *logic*, even more so *philosophy*, even is: and
any *value* or *judgment* that is not just by arbitrium and abuse.

-Julio

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