'When Are Relations Neither True Nor False?
in [Math]
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From: Marshall on 15 Apr 2010 22:55 On Apr 14, 9:34 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Did you, as I mentioned > before, define all the n-ary relations (sets) required by model- > definition? Listing out all the tuples is only part of the buffoon-theoretic version of the definition of model. So really that requirement is only binding on you. Marshall
From: Nam Nguyen on 15 Apr 2010 23:14 Marshall wrote: > On Apr 14, 9:34 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Did you, as I mentioned >> before, define all the n-ary relations (sets) required by model- >> definition? > > Listing out all the tuples is only part of the buffoon-theoretic > version of the definition of model. So really that requirement > is only binding on you. Ah! So you'd ignore technical definition! No wonder why your arguments are cohesiveness and incorrect! In the theory T = {Ax[x=a]} I know we could have a model because we could establish the 2-ary relation = which is the set {(a0,a0)} where a0 = {} by definition. So, T has a model, _by definition of model_ . That's how proofs, reasoning, and arguments are done, Marshall. By technical definitions, not by idiotic rambling and attacks! Naturally.
From: Nam Nguyen on 15 Apr 2010 23:15 Nam Nguyen wrote: > Marshall wrote: >> On Apr 14, 9:34 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>> Did you, as I mentioned >>> before, define all the n-ary relations (sets) required by model- >>> definition? >> >> Listing out all the tuples is only part of the buffoon-theoretic >> version of the definition of model. So really that requirement >> is only binding on you. > > Ah! So you'd ignore technical definition! No wonder why your arguments > are cohesiveness and incorrect! "...are not cohesive and incorrect" I meant. > > In the theory T = {Ax[x=a]} I know we could have a model because > we could establish the 2-ary relation = which is the set {(a0,a0)} > where a0 = {} by definition. So, T has a model, _by definition of model_ . > > That's how proofs, reasoning, and arguments are done, Marshall. > By technical definitions, not by idiotic rambling and attacks! > > Naturally.
From: Newberry on 16 Apr 2010 01:36 On Apr 11, 8:18 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Newberry <newberr...(a)gmail.com> writes: > > Such a proof in ZF that PA is consistent is obviously wothless. > > Why? Are all proofs in ZF worthless? Proofs of consistency in ZFC certainly are worthless. > > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Newberry on 16 Apr 2010 01:44
On Apr 11, 8:18 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Newberry <newberr...(a)gmail.com> writes: > > If it absolutely certain that PA is consistent why don't we formalize > > the reasoning? > > Absolute certainty is irrelevant. Why is it irrelevant? > Consistency proofs are every bit as > formalizable as other proofs. We can formalize the trivial consistency > proof for PA in the subtheory ACA of second-order arithmetic, in formal > set theory, in Per-Martin L f's constructive type theory (by a detour > through a double-negation interpretation), and so on. Are these theories consistent? > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, dar ber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |