From @YaleVM.YCC.YALE.EDU:LOJBAN@CUVMB.BITNET Tue Dec 7 10:23:00 1993 Received: from ELI.CS.YALE.EDU by NEBULA.SYSTEMSZ.CS.YALE.EDU via SMTP; Tue, 7 Dec 1993 15:34:26 -0500 Received: from YALEVM.YCC.YALE.EDU by eli.CS.YALE.EDU via SMTP; Tue, 7 Dec 1993 15:09:30 -0500 Message-Id: <199312072009.AA04460@eli.CS.YALE.EDU> Received: from CUVMB.CC.COLUMBIA.EDU by YaleVM.YCC.Yale.Edu (IBM VM SMTP V2R2) with BSMTP id 3478; Tue, 07 Dec 93 15:32:39 EST Received: from CUVMB.COLUMBIA.EDU by CUVMB.CC.COLUMBIA.EDU (Mailer R2.07) with BSMTP id 6226; Tue, 07 Dec 93 15:32:30 EDT Date: Tue, 7 Dec 1993 15:23:00 EST Reply-To: protin@USL.COM Sender: Lojban list From: Art Protin Subject: Re: If I were King... (fwd) To: lojban@cuvmb.cc.columbia.edu Status: RO X-Status: Folks, Iain Alexander seems to have said it better than I did: > I'm not convinced there's a genuine problem here. > >> There is a problem with that. The simple logic of 'kanoi' is too >> powerful. Any statement of the form "If then > statement>." is true. >> If I were King, then pigs would fly. >> is true because I'm not King. Swinish aviation is irrelevant. > > This is only half the story. The speaker is not king at the present > time, in the real ({ca'a}) world, but in the hypothetical world which > we want to talk about, he is, and the truth of the statement once more > relies on swinish aviation as you would expect. > > Straightforward predicate calculus and propositional calculus concerns > itself with a simple world (model) where statements are either true or > false. It doesn't deal with complications like tense or hypothetical > worlds, which are a vital part of language. The truth of propositions > varies with time, and we consider alternative realities with very little > ceremony. (I believe there are extensions to predicate calculus which > (attempt to) deal with these issues, although I'm not familiar with them.) I did have the please to be in the audience at an annual conference of the American Association for Artificial Intellegence when one of the great masters, I think it might have Gerald Sussman, did a presentation on the applicability of a whole class of extensions to formal logic and predicate calculus to real world problems. The extensions had to do with including time into the equations and trying to reasoning about sequences of events. The conclusion that was presented rather pointedly was that there could not be any simple mechanism that would do the job in general. Any attempt to use equations of logic requires volumes of equations that embody common sense rules about assumptions to make. The assumptions are required to deal with the abstraction of the real world into formula and what looks like a simple solution breaks down because "equality commutes" but time does not. A conclusion that I drew from that talk was that the logic needed by humans in order to function in the real world is probably noticibly different from the mathematical logic built (if I remember correctly) by, among others, Leibniz, Boole, & Church. The dream of Leibniz is probably unachievable. thank you all, Arthur Protin Arthur Protin STANDARD DISCLAIMER: The views expressed are strictly those of the author and are in no way indictative of his employer, customers, or this installation.