Glenn, I personally agree with your analysis of what mathematics is either in large part or wholly.
But there are others who do not. The field of mathematical philosophy has many branches of opposing belief. None of which has been proven for the most part and the subject has mostly languished for the last 100 years or so. I suppose mainly due to Gödel and our interpretation and use of his work. One of the more opposite views, however, is the Platonist view (I think I have that right) where mathematical concepts are a set of universal truths and we just discover them as opposed to creating them. We touched on this many months (maybe even a year) ago when someone (I think Paul?) suggested, perhaps impishly, that pi was "magic" which of course raised my hackles. But I have to admit it is strange how pi, e and other transcendental numbers pop up in a number of places mathematically. Others pointed that out when I protested, I don't remember their names either - sorry. We have also talked about the lack of rigorous mathematical representation of complexity and that being a barrier to progress in the science. So I think conversations like these are very relevant and necessary. On Jul 11, 2008, at 11:58 AM, glen e. p. ropella wrote: > Nicholas Thompson wrote: >> Somebody called it "neutral", i.e., neither of the mind nor of the >> world by lying between. > > This is a weird discussion. But, it seems like I ought to point out > that math is a language just like any other. Granted, it is less like > English and more like first order logic; but, it's a language none > the less. > > So, the study of mathematics is exactly analogous to linguistics. > It's > not that math isn't _about_ anything, any more than English isn't > about > anything. Languages are methods by which we communicate, describe, > and > represent. So, the study of language is the methodology of > communication, description, and representation. > > Various constructs (stories, arguments, etc.) in the language (e.g. > the > Calculus) do build up over time. But we have to distinguish between a > build up of the language, itself (methods in the toolbox), versus a > build up of any given construct within the language. > > It's been shown (dead horse alert) that mathematics, itself, as the > study of a set of formal languages, is ill-defined in the same sense > (but more precisely) that English is ill-defined. But there are > particular constructs within mathematics that are well-defined. > > Mathematics, as a language, is a toolbox created, evolved, and used by > humans to describe aspects of reality. The constructs in math like > the > Calculus represent some idealization/abstraction/aspect of reality > (e.g. > the apparent smoothness of spatio-temporal extent, velocities, > acceleration, etc.). Other constructs described in math (e.g. graphs) > describe other (again particular) aspects of reality. > > But it is a mistake to confuse the language with the constructs in the > language. That's like confusing a John Grisham novel (a particular > construct) with English (the language in which the construct is > written). > > -- > 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 ============================================================ 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
