I posted this comment on Facebook after I found at least two groups on Quine, and another on analytic philosophy. A paradigm shift is waiting around the corner and would be well underway already, were it not for the fact that most professional mathematicians today are uninterested in philosophy.
The comment:
Pragmatical justification of logical or mathematical truth is a misunderstanding that comes from the outdated formalist identification of these truths with truth values of propositions in formal systems. Euclid's mathematics was and is true for two thousand years, even though its various axiomatizations may vary in terms of correctness, completeness, consistency, etc.
Formal systems are not natural, they are artificial languages constructed in order to model the natural process of mathematical discovery. In contrast, many of the results in mathematics are very natural because thousands of years of empirical evidence has not falsified them.
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