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*To*: jboske@yahoogroups.com*Subject*: Re: OT: Quine; Cantor (was Re: [jboske] Aristotelian vs. modern logic)*From*: Jordan DeLong <fracture@allusion.net>*Date*: Tue, 14 Jan 2003 19:11:55 -0600*In-reply-to*: <200301141744.MAA04395@mail2.reutershealth.com>*References*: <20030114010827.GC45648@allusion.net> <200301141744.MAA04395@mail2.reutershealth.com>*User-agent*: Mutt/1.5.1i

On Tue, Jan 14, 2003 at 12:33:07PM -0500, John Cowan wrote: > Jordan DeLong scripsit: > > > That's Cantor's paradox: the set of all sets must contain its power set > > > as a member, which is impossible. The whole point of Quine abstraction > > > is that it's eliminable *without* reifying over sets. > > > > I dunno what 'eliminable' means. > > You can rewrite all talk of Quine abstraction in terms of pure quantified > logic without introducing any sets that are the values of variables. > So the pseudo-set x^ = {x | x is even} is just Ax: x is even. Well, it's a little more complicated than that. Rewriting to "All x such that x is even" has problems with russell sets, etc. Ok so now I know what you meant by eliminable (apparently this is from 'eliminate', but it's not in my dictionary). However, sets *are* possible values of variables in Quine[1]... So I still don't know what you mean. [1] Wee, something I can actually proove (using '<' as containment again): |- (x)(x = x) (theorem 182) |- V < V (theorem 210) |- V = x^(x = x) (definition of V) |- V < x^(x = x) (subst of equivalents) |- Ey(V < y . (x)(x < y -> x = x)) (def of abstraction) |- Ex(x = V) (theorem numbers from 'mathematical logic'). I hope I didn't skip a step.... Those "natural deduction" styles of doing proofs are a lot easier to avoid skipping things in... -- Jordan DeLong - fracture@allusion.net lu zo'o loi censa bakni cu terzba le zaltapla poi xagrai li'u sei la mark. tuen. cusku

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**Follow-Ups**:**Re: OT: Quine; Cantor (was Re: [jboske] Aristotelian vs. modern logic)***From:*Jordan DeLong <fracture@allusion.net>

**Re: OT: Quine; Cantor (was Re: [jboske] Aristotelian vs. modern logic)***From:*John Cowan <cowan@ccil.org>

**References**:**OT: Quine; Cantor (was Re: [jboske] Aristotelian vs. modern logic)***From:*Jordan DeLong <fracture@allusion.net>

**Re: OT: Quine; Cantor (was Re: [jboske] Aristotelian vs. modern logic)***From:*John Cowan <cowan@ccil.org>

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