I think there's an important distinction between symbols and meaning. The famous Symbol Grounding Problem<http://ai.stanford.edu/%7Enilsson/OnlinePubs-Nils/PublishedPapers/pssh.pdf>asks how (or whether) a symbol manipulating device can ever associate a semantics with the symbols it manipulates. The consensus<http://philsci-archive.pitt.edu/archive/00002542/01/sgpcrfyr.pdf>is that it's not possible, which has resulted in research in situated and embedded systems as an alternative.
We have concepts in our heads; computers manipulate symbols. Of course the only reason we program computers to manipulate symbols the way we have them do it is because of the concepts in our heads. But that doesn't mean that the symbols themselves embody the concepts or that a device capable of manipulating those symbols (no matter how successfully) necessarily understands the concepts. No doubt both are important. The symbols (and formalisms) keep us honest. The concepts, though, are what the symbols are about. By themselves they are not about anything. -- Russ On Mon, Jan 12, 2009 at 3:41 PM, glen e. p. ropella < [email protected]> wrote: > Thus spake Russ Abbott circa 11/01/09 11:21 PM: > > I think you're agreeing with me. It's the concepts that are important, > not > > the equations. To the extent that you can read the equations as > statements > > about concepts the equations talk to you. But a computer can read and > > calculate with those same equations without the concepts. The concepts > are > > in the mind of the person reading the equations, not in the equations > > themselves. > > The truth is that _both_ the formalisms and the concepts are integral to > math. Equations without concepts is not math and concepts without > automatically transformable sentences (e.g. equations) is not math. The > same is true with any language, including English. > > The point is that math (like science) consists largely of an effort to > formalize things so that we can think (as well as delegate, teach, and > repeat) clearly about those things. I don't know what the percentage of > artists is who feel themselves in the business of formalizing the > creation of artifacts; but an artist who understands how important > formalization is to large-scale cooperation will have no trouble > understanding the relationship between equations (or, more generally, > automated deduction) and mathematical concepts. > > My guess about art is that most people who self identify as artists are > against relying on consensus methods, i.e. art is a very personal thing > both for the artist and the audience. (Note that I used "personal" > rather than "subjective".) To rigorize (rigorify?, rigorate?) art is to > remove the art. But I also guess that each artist (or art lineage) has > a set of, fairly rigorous, methods associated with her (it). The rigor > may be contained in the fingers instead of in symbols on paper, but the > rigor would be there somewhere for any artist capable of repeating their > work. (Unless one believes in luck and a "good artist" is just a lucky > person.) > > This tacit vs. explicit methodological dichotomy may be the major cause > for incommensurance between any of the more intuitive human activities > (like entrepreneurship, art, scientific speculation) vs. the more > inferential/reasoned activities (like accounting, manufacturing, > falsification), and those people proficient in one but not the other. > > -- > 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 >
============================================================ 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
