-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Nicholas Thompson on 01/01/2008 10:59 PM: > thus, to be a good formalism, a formalism has to be in > some sense informal, right?
This is a difficult question phrased in a misleadingly simple way. We now know that mathematics is _more_ than formal systems (thanks to Goedel and those that have continued his work). I.e. we cannot completely separate semantics from syntax. The semantic grounding of any given formalism (regardless of how "obvious" the grounding is) provides the hooks to the usage of the formalism. Hence, by the very nature of math, any formalism can be traced back to the intentions for the formalism (though the original intentions may be so densely compressed or that uncompressing them may be hard or impossible). And in that sense, including your statement above, all formalisms will then be good formalisms because they all have a semantic grounding. But just because all formalisms assume a semantic grounding doesn't mean they're "informal". The hallmark of a formalism is that it encompasses all the assumptions in axioms that are well-understood and clearly stated up front. I.e. a good formalism won't let new axioms slip in anytime during inference. So, that's what it now means to be "formal". An informal inferential structure loosens that constraint and will allow one to introduce new semantics as the inference chugs along. - -- glen e. p. ropella, 971-219-3846, http://tempusdictum.com It's too bad that stupidity isn't painful. -- Anton LaVey -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.6 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iD8DBQFHe98oZeB+vOTnLkoRAjKfAJ0fFwhcKlZulDmkoXZaDKb3a/b76QCfXjC5 WZaDT213cIPPOhP1bRH8rQE= =cWA0 -----END PGP SIGNATURE----- ============================================================ 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
