The End of an Era - That of The Natural Numbers
in [Math]
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From: Marshall on 29 May 2010 15:19 On May 29, 10:58 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > On May 29, 10:32 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> Note my "the only way" in the question. If FOL, by the technicalities > >> vested in all of its layers, doesn't insist that that's the only way, > >> then technically other ways are equally possible > > > Yes, but: > > >> and Marshall's counter > >> stipulation that x=x is true in all contexts of FOL is incorrect in one > >> of those possible ways > > > doesn't follow. FOL puts *some* restrictions on what the > > mapping can be. One such restriction is that x=x must > > be true in all contexts. > > And I've refuted this in the same post, via the truth of some > meta statements A and B. No you didn't. Marshall
From: William Hughes on 29 May 2010 15:23 On May 29, 4:03 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > William Hughes wrote: > > On May 29, 2:55 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > >> But when U = {}, there's no flexibility at all > > > So your claim is that > > > There does not exist an x such that blue(x) > > > must be false? You can refer to as many mappings > > and definitions of "truth" as you want. At the end > > of the day if all formula are false in a model with > > empty universe, then > > > There does not exist an x such that blue(x) > > > must be considered false. > > It must have been the case you either didn't read or wasn't > paying attention or wasn't able to understand what I said > about the truth preemptive characteristics of the meta statement > B in the post. > > It doesn't matter what I "want" here: that's Tarski's definition Ok, rephrase. At the end of the day your claim is that, using Tarski's defintion of truth, all formula are false in a model with empty universe Then There does not exist an x such that blue(x) must be considered false. - William Hughes
From: Nam Nguyen on 29 May 2010 16:22 William Hughes wrote: > On May 29, 4:03 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> William Hughes wrote: >>> On May 29, 2:55 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> But when U = {}, there's no flexibility at all >>> So your claim is that >>> There does not exist an x such that blue(x) >>> must be false? You can refer to as many mappings >>> and definitions of "truth" as you want. At the end >>> of the day if all formula are false in a model with >>> empty universe, then >>> There does not exist an x such that blue(x) >>> must be considered false. >> It must have been the case you either didn't read or wasn't >> paying attention or wasn't able to understand what I said >> about the truth preemptive characteristics of the meta statement >> B in the post. >> >> It doesn't matter what I "want" here: that's Tarski's definition > > Ok, rephrase. > > At the end of the day your claim is that, > using Tarski's defintion of truth, > all formula are false in a model with empty universe > > Then > > There does not exist an x such that blue(x) > > must be considered false. Are you saying that "There does not exist an x such that blue(x)" is a FOL formula of L(T4)? (I wouldn't think so).
From: Nam Nguyen on 29 May 2010 16:23 Marshall wrote: > On May 29, 10:58 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Marshall wrote: >>> On May 29, 10:32 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> Note my "the only way" in the question. If FOL, by the technicalities >>>> vested in all of its layers, doesn't insist that that's the only way, >>>> then technically other ways are equally possible >>> Yes, but: >>>> and Marshall's counter >>>> stipulation that x=x is true in all contexts of FOL is incorrect in one >>>> of those possible ways >>> doesn't follow. FOL puts *some* restrictions on what the >>> mapping can be. One such restriction is that x=x must >>> be true in all contexts. >> And I've refuted this in the same post, via the truth of some >> meta statements A and B. > > No you didn't. And your _technical reasons_ for saying that is ...?
From: Marshall on 29 May 2010 17:00
On May 29, 1:23 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > On May 29, 10:58 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> Marshall wrote: > >>> On May 29, 10:32 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >>>> Note my "the only way" in the question. If FOL, by the technicalities > >>>> vested in all of its layers, doesn't insist that that's the only way, > >>>> then technically other ways are equally possible > >>> Yes, but: > >>>> and Marshall's counter > >>>> stipulation that x=x is true in all contexts of FOL is incorrect in one > >>>> of those possible ways > >>> doesn't follow. FOL puts *some* restrictions on what the > >>> mapping can be. One such restriction is that x=x must > >>> be true in all contexts. > >> And I've refuted this in the same post, via the truth of some > >> meta statements A and B. > > > No you didn't. > > And your _technical reasons_ for saying that is ...? My technical reason for saying that you didn't refute that x=x is true in all FOL contexts is that you didn't. Have you figured out yet that you are wrong about vacuous truth yet? You dropped the ball on that subthread. Marshall |