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 ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
