The End of an Era - That of The Natural Numbers
in [Math]
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From: Aatu Koskensilta on 21 May 2010 02:27 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Where did I say any formula is true in a false model? You wrote earlier, about false models: There's a model in which the universe and all n-ary relations are empty, and this is the model for all inconsistent formal systems. Some formulas are true in such a model, e.g. (x)(x =/= x), and some false, e.g. (Ex)(x = x). This makes nonsense of the idea that they model inconsistent theories. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: William Hughes on 21 May 2010 02:44 Do you claim both an inconsistent system T does not have a model an inconsistent system T does have a model Please answer yes or no.
From: Nam Nguyen on 21 May 2010 03:19 Aatu Koskensilta wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Where did I say any formula is true in a false model? > > You wrote earlier, about false models: > > There's a model in which the universe and all n-ary relations > are empty, and this is the model for all inconsistent formal > systems. > > Some formulas are true in such a model, e.g. (x)(x =/= x), and some > false, e.g. (Ex)(x = x). This makes nonsense of the idea that they model > inconsistent theories. > I'm sure you've heard of "equivalent formulas" in a theory.
From: Aatu Koskensilta on 21 May 2010 03:24 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > I'm sure you've heard of "equivalent formulas" in a theory. What of them? -- 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 03:43
William Hughes wrote: > Do you claim both > > an inconsistent system T does not have a model > an inconsistent system T does have a model > > Please answer yes or no. Is the formula Exy[~(x=y)] provable? That's a yes or no question, in your style of questioning, right? So answer Any rate, I already answered that question in one form or another in my recent responses. As long as you don't offer any analysis about the false models and the related, there's no point for me to repeat or clarify further my answers. |