Fascinating!
Now, using the definition "Philosophy is what Philosophers do" ..
would a Philosopher agree with you?
-- Owen
On Jul 10, 2009, at 8:41 AM, glen e. p. ropella wrote:
Thus spake Owen Densmore circa 07/09/2009 07:17 PM:
So the question to the philosophic amongst us: what is the answer
to the
above question? Is there a way in which philosophy can build on past
work in the same way mathematics does? Is there an epsilon/delta
breakthrough just waiting to happen in that domain? Will there be a
"Modern Algebra" unification within philosophy, finding the common
ground amongst widely different concepts like symmetry groups,
fields,
rings, Hilbert spaces and the like?
Personally, I believe that philosophy (by which I mostly mean
analytic)
is the larger system in which mathematics is grounded. I tend to view
it as if philosophers are trail-blazing mathematicians. They foray
out
into the wild and whittle away at the fuzzy thoughts out there,
preparing them for the more fastidious, civilized, mathematicians who
follow. (Note that I believe programmers to be a form of
mathematician... less fastidious than their more formal brethren,
applied mathematicians who are still less fastidious than their
brethren, pure mathematicians.)
At each stage, the reliance on the semantic grounding of the
formalisms
is whittled away until you have, at the pure math stage, formalisms
grounded solely in identifiable axioms like zero, reciprocal, axiom of
choice, etc.
So, in my (fantasy) world, philosophy will never be as rigorous as
math
because philosophy _is_ math and math is philosophy... they're just at
different stages in the process. Philosophy is "upstream" and math is
"downstream". This leads to the following direct answers to your
questions:
Why is it that philosophy does not build on prior work
in the same way mathematics does?
Because philosophy is a frontier, wilderness activity, where prior
work
is less important than solving some case specific, imminent, problem.
Is there a way in which philosophy can build on past
work in the same way mathematics does?
No, because the domains in which philosophy are useful are aswim in
meaning and syntactically impoverished. Philosophy is an embedded,
situated, open-ended, activity where everything constantly shifts
around. Foundations are built on sand, not granite.
Is there an epsilon/delta
breakthrough just waiting to happen in that domain? Will there be a
"Modern Algebra" unification within philosophy, finding the common
ground amongst widely different concepts like symmetry groups,
fields,
rings, Hilbert spaces and the like?
Yes! But there is not just ONE breakthrough/unification coming.
There
are many, just like there have been many. And once those
breakthroughs
come, they congeal into a mathematics that is then adopted by an army
consisting of a different, more fastidious, type of philosopher. The
trail blazers move on to the next wild frontier while the "settlers"
move in and bring mind-numbing order to the region surrounding the
breakthrough.
--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com
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