Thus spake [email protected] circa 10-03-22 03:28 PM: > 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.
Excellent! Thanks for knocking that chip off my shoulder. [grin] I'll toss out a defense of my assertion after I specifically address your comments. > 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. You're making these assertions as if there is a _very_ clear separation of syntax, semantics, and pragmatics in natural languages. Now, I'm no linguist; but my guess is that such distinctions are not as clear as you're implying. More importantly, I think it's fairly clear that math is NOT merely syntax. It may be true that pure deduction (or derivation) is pure syntax. But math, "real" math, whatever that may be, isn't wholly deductive. If math were purely syntactic, then Hilbert's programme would not have failed. > 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. Mathematical models are statements in the language of math. So, I definitely did NOT intend to say that a mathematical model is a language for disambiguation. Even in the case where one might call a particular formal system a "mathematical model" (which is not the normal usage of "mathematical model"), I would agree that they're languages; but I would not assert that their purpose or best use is disambiguation. Formal systems, in my ignorant opinion, are for discovering the deductive consequences of the axioms of that language... "playing it out" if you will, what some of us call "simulation" or "numerical analysis". (Sorry for all the quotes... ;-) No, I'm talking about math as a whole. Math is basically a toolkit of (sometimes incommensurate) methods for separating out and talking about various different things and patterns. Granted, math does focus quite a bit more on syntax because its users tend to value quantity (metrics) and clear distinction. Natural language users tend to equally value both metrics and smudging together disparate concepts (as in poetry). Math is almost exclusively used to state things clearly and unambiguously. The best math is that which is used to bring clarity and distinction to concepts that are otherwise conflated in natural languages. Now, if you want to descend into a semantic argument about what constitutes a "language" and what is merely a toolkit of methods, then I'm willing to go that route; but there's really no need. If you'd like, I can change my words as follows: Math is a meta-language, a language of languages, most used for disambiguation. But a language of languages is still a language. p.s. I am NOT a mathematician. So, my ability to "appeal to authority" is lacking. Caveat emptor. ;-) -- glen e. p. ropella, 971-222-9095, http://agent-based-modeling.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
