The End of an Era - That of The Natural Numbers
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From: Nam Nguyen on 21 May 2010 01:41 William Hughes wrote: > On May 21, 1:49 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> William Hughes wrote: >>> On May 21, 12:33 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> So yes, an inconsistent formal system written in an L has the _false_ >>>> model per that L. >>> Oh I see, an inconsistent system T does not have a model but it >>> does have a false model. >> Right. > > So can you answer yes or no: Does an inconsistent system > have a model? Yes it does: a false model.
From: William Hughes on 21 May 2010 01:53 On May 21, 2:41 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > William Hughes wrote: > > On May 21, 1:49 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> William Hughes wrote: > >>> ... an inconsistent system T does not have a model ... > >> Right. > > > So can you answer yes or no: Does an inconsistent system > > have a model? > > Yes it does You are being inconsistent about inconsistent systems. -William Hughes
From: Aatu Koskensilta on 21 May 2010 01:57 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Why don't you make some reflections of your own and tell us if F > is true or false in the naturals, The universal closure of (x = 0 \/ 0 < x) is certainly true in the naturals. What does this have to do with anything? > since you seem to believe the knowledge of the naturals is not of > intuitive nature. On your peculiar definition of "intuitive" our knowledge of pretty much anything is indeed intuitive. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Nam Nguyen on 21 May 2010 02:01 William Hughes wrote: > On May 21, 2:41 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> William Hughes wrote: >>> On May 21, 1:49 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> William Hughes wrote: > >>>>> ... an inconsistent system T does not have a model ... >>>> Right. >>> So can you answer yes or no: Does an inconsistent system >>> have a model? >> Yes it does > > You are being inconsistent about inconsistent systems. If you keep chopping away my (technical) explanations, then sure you could say anything you're pleased. Why should that be of any interest in technical/logical arguments?
From: Aatu Koskensilta on 21 May 2010 02:01
Nam Nguyen <namducnguyen(a)shaw.ca> writes: > William Hughes wrote: > >> Does an inconsistent system have a model? > > Yes it does: a false model. Nonsense. An inconsistent theory proves everything, including the sentence (Ex)(x=x), which is not true in a model with an empty universe. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |