Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site peora.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!drutx!mtuxo!mtunh!mtung!mtunf!ariel!vax135!petsd!peora!jer From: jer@peora.UUCP (J. Eric Roskos) Newsgroups: net.singles,net.math Subject: Re: Logic (for logicians) Message-ID: <1252@peora.UUCP> Date: Tue, 9-Jul-85 14:16:11 EDT Article-I.D.: peora.1252 Posted: Tue Jul 9 14:16:11 1985 Date-Received: Fri, 12-Jul-85 00:41:13 EDT References: <456@ttidcc.UUCP> <457@ttidcc.UUCP> <1586@hao.UUCP> Followup-To: net.math Organization: Perkin-Elmer SDC, Orlando, Fl. Lines: 58 Xref: watmath net.singles:7739 net.math:2132 Gee, I didn't know there were any intuitionists out there. I remember references to intuitionistic logic in Mendelson's text, though they were just cursory. >Yeah, this probably doesn't belong on net.singles; at least, I've never had >any success starting a romantic conversation with "Whose your favorite logi- >cian?" Still, maybe some of you out there.... |-). I have, though! In fact, that is close to how I met my most recent SO; one day I was working on the University computer, and saw this person who had "Logical" in her login name. So I asked her, "What kind of logic does a Logicaluse?" And this was how we met. Now... to get down to what you were talking about here... I have some reservations about claiming that there is any problem with my stating the "classical" notion that A(x)y <=> ~E(x)~y; I mean, you can make complete & consistent logics that contain the above, can't you? It seems to me merely a philosophical question; the fact that the logics exist and are "ok" in this formal sense should be enough as far as mathematics is concerned, I would think. > Mr. Roskos has (un?)knowingly raised a philosophical issue ^^ >The difference? In the above example, the constructive philosophy requires >that we give a procedure for proving y for any x, while the classical frame- >work has no such requirement. In this sense then, constructive logic has an >inherent computational flavor, while constructive logic does not.... I am not much of an expert on this constructive logic, but don't there exist proofs for which no effective procedure exists? Consider any theorem containing an existential quantifier which can only be proved by choosing elements out of the universe at random and trying them to see if they make the quantified predicate "true"; e.g., theorems that say something like "There exists a number with property x," where it is not possible to compute the number given the property effectively. Or does this relate to the question of whether there exist any languages recognizable by a nondeterministic finite-state automaton that aren't recognizable by a deterministic one in polynomial time? I am not sure, though there seem to be vague analogies there, since the epsilon- transitions in an NFA are roughly analogous to "guesses," as are (I think) the non-polynomial equvalent DFAs (which just try all the guesses by enumeration rather than by nondeterministic transitions). But I don't know for sure... it has been several years since I studied that stuff, and now I am left with mostly just the intuitive recollections... If you post a reply to this (which will go to net.math), please mail me a copy too, since I don't read net.math, since I'm not a mathematician really. -- Shyy-Anzr: J. Eric Roskos UUCP: ..!{decvax,ucbvax,ihnp4}!vax135!petsd!peora!jer US Mail: MS 795; Perkin-Elmer SDC; 2486 Sand Lake Road, Orlando, FL 32809-7642 "Gurl zhfg hcjneq fgvyy, naq bajneq, Jub jbhyq xrrc noernfg bs gehgu." -- WEY