Thus spake John F. Kennison circa 10/07/2008 06:32 PM: > I see your > interpretation of Wittgenstein's statements as his way of saying that > mathematical argument does not do a good or reliable job of > establishing truth. Am I characterizing your position correctly?
Well, I think W. was arguing against Platonism in mathematics. That's subtly different from saying that math argument does not do a good or reliable job of establishing "truth" (i.e. reality)[*]. But, basically, yes. I think if pressed, W. would agree with your statement. He would actually go far far beyond your statement and say that math is a pathological perversion of thought. Indeed, it is a dangerous and misleading perversion (though it may be effective in highly skilled hands). The point W was trying to make was that to fixate on math and elevate it to science is a grave mistake. Doing so will prevent you from learning how the world really works. To be clear, my position is different from W's. I think math is related to reality because we (biological animals) invented math as a way to help us navigate the world. I think there are both evolutionary and psychological justifications for the relationship between reality and math. [*] We have to be careful to distinguish between the validity of a statement and the soundness of a statement. Validity has to do with whether or not a statement is mathematically well-formed. If it is (and if the language is complete), then it is either true or false. But just because a statement is true doesn't mean it's sound ... i.e. backed up by data taken from reality. -- glen e. p. ropella, 971-219-3846, http://tempusdictum.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
