Re: Foundations of Mathematics

Sigh .... There is a kind of offensiveness about this combination of
sophomoric ignorance and sheer pretension. As if the labours of all
those great mathematicians and philosophers who have struggled with
these matters since Frege's Grundlagen (and before) count for nothing
at all. As if we can talk about "abstract ideas" as if no-one has
thought about the problems surrounding this notion since Locke. As if
what is true of symbols must be true of what they symbolize. As if the
Hilbertian distinction between those areas of 'read' mathematics which
are arguably grounded in quasi-sensory "intuition" and infinitary
'ideal' mathematics had never been made. As if ....

I'd say, for heaven's sake, before sounding off read a decent
discussion of the metaphysics of mathematics, like Shapiro's book
"Philosophy of Mathematics: Structure and Ontology". But then working
through serious philosophical treatments of these issues and actually
discovering something about the options here is really hard work isn't
it?

.

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