Godels theorem ends in paradox-simply proof
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From: Aatu Koskensilta on 8 Jun 2010 21:25 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Iirc, somewhere in the forum, AK said something to the effect that > the naturals collectively isn't a model (something like the truths > about the naturals aren't model theoretically truths). What on Earth are you on about? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 8 Jun 2010 21:28 stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > I'm not sure what he meant by that. I don't recall saying anything like "truths about the naturals aren't model theoretically truths" whatever it's supposed to mean. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 8 Jun 2010 21:47 "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: > But it ends in meaninglessness, right? As "Australias leading erotic poet" once put it: G�del is a complete failure as he ends in utter meaninglessness. -- 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 8 Jun 2010 21:49 Aatu Koskensilta wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Iirc, somewhere in the forum, AK said something to the effect that >> the naturals collectively isn't a model (something like the truths >> about the naturals aren't model theoretically truths). > > What on Earth are you on about? > That's why I didn't make anassertion. I have to do some searching to cite where I think you said something to the effect. Meantime, are you then saying the naturals is collectively a model of PA? If so how would you prove PA is _syntactically_ consistent to begin with?
From: Aatu Koskensilta on 8 Jun 2010 21:49
Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Aren't these a bit circular: you're explaining the naturals using the > naturals? Why do you think Daryl's definition of a model was an explanation of anything? > But no one has asked for the the truth of every formula. I just > requested for only _1_ formula: (1)! Why should Daryl know whether the formula you described is true or false? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |