Günther Greindl wrote: >> Math (which is more than formal systems) can handle loopy inference >> quite well. But the modeling vernacular can NOT handle it so well. And > > which mathematics is not a formal system? If it's not formal it's not > math I would say.
Math is the linguistic construct with which one describes a formal system. You can see this clearly if you consider that a formal system can be completely defined in logic, as well. A formal system is just one particular construct. Math is much larger just as logic is much larger. For a concrete example, just consider Russell's and Whitehead's attempt to reduce all math to a formal system and note their failure. Or you can consider Tarski's (and Goedel's) demonstration that any formal system must be at least partly grounded in a larger formal system. "Math" includes all the particular formal systems. Further, one can use math to show how a small formal system is grounded in a larger one (and that larger one is grounded in yet another larger one, etc). So math is not only the formal systems, but also the language in which we describe relations between formal systems. -- 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
