On Thu, 15 Jun 1995 [EMAIL PROTECTED] wrote: > One could imagine, then, undertaking an essentially mathematical > argument in which none of the words have been replaced by symbols. > . . . > would become a living nightmare. To put it the other way around, you > could think of mathematical symbols as a certain special type of > words. But this leads to the second comment: mathematical argument > involves a particular, highly restrictive use of concepts, in which > "that which is not allowed is forbidden", to quote again from Spencer- > Brown. That is, none of the ambiguity which makes literary prose > potentially so rich and multilayered (take FINNEGANS WAKE as an > extreme example) is allowed. Why not? This leads to the 2nd point. For a related and complementary point see Calvin Schrag's *Radical Reflection (I forget the subtitle)*. He makes a simple, similar point (in the introduction or first chapter) about the meaning of mathematics but also makes it quite clear that use of mathematics does not privelege argument in any way. I realize Gil would agree but his well written defense left out some caveats. > My favorite analogy here is jazz, since that has clearly been subject > to dialectical change in its history. Once a jazz musician discovers > new ground, s/he and others work to elucidate the content implicit in > it. A striking illustration of this comes from Ornette Coleman, one > of the originators of "Free jazz", a seemingly lawless permutation of > modern jazz: "I knew I was onto something when I found that I could > make mistakes." Alternatively, a jazz musician may, in discovering > the limits of a particular structure, go beyond those limits. > Thus Charlie Parker discovering bebop in that chili house in New > York, by taking the givens of swing and extrapolating beyond them. > The immediate critical reaction? That's not jazz! Subsequently, of > course, bebop gets folded into an enlarged conception of jazz which > establishes new limits....etc. I realize this is comletely off the economic topic and can see the dialectical movement of history in jazz and agree as well that you offer two good examples that elucidate your point about mathematics. However, in light of jazz's recent reactionary history in which bebop/rebop/bop has done far more to constrict the limits of jazz than establish any new limits, I must make a point. The jazz fascists of today thump the virtues of the once shunned bebop and jazz has probably had its most regressive 15 years in all its history (that is, if you allow the word "jazz" to stand in your way). There are innovations along free jazz lines (Charlie Hunter Trio/ T. H. Kirk) but my favorite innovations are in dancefloor jazz, "acid jazz", "trip hop", etc. areas and certainly all get a deafening "That's not Jazz" from the established community. This music is much more true to the original history of jazz (oppressed peoples out to have a wailing good time) than any of the Modern Jazz flavors (which suffers from either too much intellect or too much avant garde). Listen to 9 Lazy 9, United Future Organization, El Malo, Takemura's stuff, Wagon Christ, Snowboy, and on. Unlike other past movement's of the Jazz Dialect this will probably never become "jazz" simply because popular music is no longer "jazz." Let the reactionaries listen to their jazz, the rest of us will have a lot more fun and be able to establish new limits. Peace, Jim Westrich "Twenty years of kindness made her sad -- kindness never gave her enough to live so she sold the very last thing that she had" -- Paul Heaton
