[CCd to the mathematical thinking list; followups should be made mindfully.]
Nick, for some reason this one message in the thread has never arrived here, though ones before and after it have. So I'm replying to Russ's reply to you, without actually quoting Russ...well, actually I'm replying to Glen, but I am only doing it because you picked up his phrase which I'm about to tear into. > > Glen, > > > > you wrote > > > > " Math is a language for disambiguation". > > > > Forgive me if I have asked you this before: Have you ever read Byers HOW > > MATHEMATICIANS THINK? One thing I can say is that *this* mathematician thinks that calling mathematics a "language" is neither helpful nor accurate. To put that unnegatively--I welcome explanations as to why it is helpful and accurate to say it. A natural human language (at least) has syntax, semantics, and pragmatics: rules (more or less) determining how to describe sayings in the language, rules (more or less) for *interpreting* sayings in the language as *referring* to Things in The World, and rules (more or less) for *checking* these interpretations against The State of The World (including in The World, of course, the human social world). Of these, mathematics *as such* has--arguably--only syntax. Mathematical models, on the other hand, have all three; and I think it is both accurate and helpful to say "mathematical models are languages". Whether they're (all, or any) "languages for disambiguation", I'm less sure: I'd rather say that, to they extent that they are successful, mathematical models are languages that help us control the amount of ambiguity in ways that are useful for the purposes at hand. ============================================================ 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
