Some of the confusion here may come from different uses of the word argument. From Dic.com
ar·gu·ment (ärgy-mnt) n. 1. a. A discussion in which disagreement is expressed; a debate. b. A quarrel; a dispute. c. Archaic A reason or matter for dispute or contention: "sheath'd their swords for lack of argument" (Shakespeare). 2. a. A course of reasoning aimed at demonstrating truth or falsehood: presented a careful argument for extraterrestrial life. b. A fact or statement put forth as proof or evidence; a reason: The current low mortgage rates are an argument for buying a house now. c. A set of statements in which one follows logically as a conclusion from the others. I hate and deplore arguments in sense 1. I have a lot of reverence for arguments in sense 2a. N Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([email protected]) http://home.earthlink.net/~nickthompson/naturaldesigns/ > [Original Message] > From: Owen Densmore <[email protected]> > To: The Friday Morning Applied Complexity Coffee Group <[email protected]> > Date: 7/13/2009 10:41:50 AM > Subject: Re: [FRIAM] Philosophy, Mathematics, and Science > > Nick and I had an off-list discussion that may speak to some of the > recent posts. > > Begin forwarded message: > > > From: Owen Densmore <[email protected]> > > Date: July 13, 2009 10:38:08 AM MDT > > To: [email protected] > > Cc: John Kennison <[email protected]>, Owen Densmore <[email protected] > > > > > Subject: Re: Cauchy sequence - Wikipedia, the free encyclopedia > > > > On Jul 12, 2009, at 10:30 PM, Nicholas Thompson wrote: > >> http://en.wikipedia.org/wiki/Cauchy_sequence > >> > >> Sorry. I dont know why this came up. I see that it's some nice > >> mathematics,but I dont see its relevance. > > > > The sub-theme was "Bridging the Gap" .. in this case between > > philosophy and mathematics. In the above case, the CS is a > > delightful example of bridging the gap between the CONtinuous and > > disCRETE in Don Knuth's Concrete Mathematics .. a topic we've > > discussed in the past. > > > > Or possibly more formally, applying the epsilon/delta idea to both > > the continuous and discrete as discussed in the book we read last > > summer, Journey Through Genius. > > > >> While I have your attention, is a mathematical proof a kind of > >> algorithm? > > > > Although they share a step-wise approach, I think not. > > > >> Do you agree, that mathematical proofs are very rigorous arguments? > > > > Not arguments as in a way to resolve disagreements. But arguments > > as a line of thought. Certainly rigorous. > > > >> Is a symbolic logical proof an example of mathematics? > > > > I'd say yes, but others might be more comfortable separating math > > and logic. > > > >> Or of Philosophy? > > > > See the word comfortable above. > > > >> Was Bertrand Russel a mathematician or a philosopher? > > > > Both. Wittgenstein studied under him, so the Both applies to him > > too, as it does for Kant and others. > > > >> Since I think of mathematics as a kind of tremendously rigorous > >> extension of the art of argument from philosophy, I would expect > >> that most of these questions are bad questions. > > > > No, but you do feel argument is a sort of sport, not unlike > > wrestling! This is really more key that you might imagine. > > Mathematicians and scientists, even though they do have > > disagreements, generally argue/discuss means to an end (solving a > > problem, creating a proof) rather than argue right and wrong. > > > >> You can take this on the list, if you like. I think your answers > >> would be interesting to list members, but I am leery of being > >> called on the carpet for starting another philosophical discussion. > >> > >> I have cc'ed my mathematician friend John Kennison to see what he > >> might say. > >> > >> Nicholas S. Thompson > >> Emeritus Professor of Psychology and Ethology, > >> Clark University ([email protected]) > >> http://home.earthlink.net/~nickthompson/naturaldesigns/ > > > > > > > ============================================================ > 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
============================================================ 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
