Re: Foundations of Mathematics


Peter_Smith wrote:
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?


Do not take on so, Mr. Smith. It is not my intention to trample
obliviously over those great texts nor to strut boastfully at the head
of hard-earned recognition.

To rightfully place my humble opinions in the proper scheme of things
(for it is tempting to say that even at this juncture that if I should
read Shapiro, I'd rather he should read me), I did view Shapiro askance
via another author. Shapiro is tiresome to read apparently, but does
make some cogent points. His structuralism I feel and its place in
philosophy does not quite get to grips with the genesis of mathematical
forms that, for example, is tackled by Husserl. Indeed, Husserl's "the
concrete life-world ... is the grounding soil of the scientifically
true world" bears similarities to what I have written above.

And do not forget Mr.Smith, that after Nietszche, Wittgenstein, and
perhaps Schopenhauer were installed in academia they were little
concerned with what had gone before, or during, their lives and
ignoring texts rather than trampling on them was the order of the day.

.

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