'When Are Relations Neither True Nor False?
in [Math]
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From: Daryl McCullough on 3 Mar 2010 08:18 In article <87sk8hpplv.fsf(a)dialatheia.truth.invalid>, Aatu Koskensilta says... > >Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: > >> I like boiled broccoli. Therefore, as it says in Melvyn Pike's _Titus >> Groans_, Clarice came up to her sister's side and they both looked at >> him. It follows, by Shelah's possible cofinality theory and the book of >> Job, that sometimes snails try to eat people (with very little >> success). From this it is immediate that for no set A is there a set of >> everything not contained in A. > >The relevant reference is of course _Titus Groan_ and not _Titus Groans_ >as I erroneously wrote above. It's too late for a correction. You've lost all credibility on this topic. -- Daryl McCullough Ithaca, NY
From: Frederick Williams on 3 Mar 2010 09:20 Daryl McCullough wrote: > > In article <87sk8hpplv.fsf(a)dialatheia.truth.invalid>, Aatu Koskensilta says... > > > >Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: > > > >> I like boiled broccoli. Therefore, as it says in Melvyn Pike's _Titus > >> Groans_, Clarice came up to her sister's side and they both looked at > >> him. It follows, by Shelah's possible cofinality theory and the book of > >> Job, that sometimes snails try to eat people (with very little > >> success). From this it is immediate that for no set A is there a set of > >> everything not contained in A. > > > >The relevant reference is of course _Titus Groan_ and not _Titus Groans_ > >as I erroneously wrote above. > > It's too late for a correction. You've lost all credibility on this topic. One expect too much from a man who boils his broccoli instead of steaming it.
From: Aatu Koskensilta on 3 Mar 2010 09:36 Frederick Williams <frederick.williams2(a)tesco.net> writes: > One expect too much from a man who boils his broccoli instead of > steaming it. Ah, you fail to take into account that I was lying through my teeth. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Marshall on 3 Mar 2010 10:03 On Mar 3, 6:36 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Frederick Williams <frederick.willia...(a)tesco.net> writes: > > One expect too much from a man who boils his broccoli instead of > > steaming it. > > Ah, you fail to take into account that I was lying through my teeth. We all knew that. Since we are all professional logicians here, it was immediately obvious to us that anyone who likes boiled broccoli is a liar. Marshall
From: MoeBlee on 3 Mar 2010 11:52
On Mar 2, 10:43 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Aatu Koskensilta wrote: > > Gödel's > > proof is not a formal proof, as is apparent on even a brief glance at > > the paper, > > First of all, FOL formal proof is a technical concept and whether or not > Godel's proof is a formal one should be judged on technical evidences, > *not* on a *vague and subjective* opinions such as "as is apparent on > even a brief glance at the paper". Oh come on! The proof is given in German with mathematical notation! The actual writeup of the proof is not a pure "finite sequence of finite srings of characters that are formulas of a formula language and such that each entry is an axiom or is in the relation of modus ponens from previous entries" (or whatever suitable definition of 'formal proof' we have in mind). Sheesh, do you argue against just plain ordinary in-front-of-your-nose facts for the mere sake of arguing? > Secondly, the translated version I > have is 26 page-long and 24 of them are full of FOL proofs and formulas > that one could easily mistake the paper for a prt Shoenfield's modern > textbook on FOL formal systems! And that doesn't at all correlate with > your assessment that his proof isn't a formal proof just because of a > "brief glance" at it. Your translated version is (I guess) in ENGLISH with also mathematical notation. English is not a formal langauge! Damn, WHAT is your problem? > > but we can formalise it to give a formal proof in a suitable > > formal system, such as primitive recursive arithmetic. > > Secondly, if you could formalize what he wrote into a full blown formal > proof then in effect his proof was essentially a formal proof to begin > with! Whatever you mean by "essentially", NO, the proof was given in German and mathematical notation. The actual writeup Godel gave is NOT a formal proof. That we can formalize it doesn't change that it ITSELF is not a formal proof (a sequence of finite ....etc.) > > That the proof doesn't involve > > e.g. any model theoretic considerations we ascertain simply by > > inspecting the proof and the relevant definitions. > > I hate to say it but "simply by inspecting the proof and the relevant > definitions" simply isn't a *technical* explanation of the technical > judgment on whether or not Godel's proof is a FOL formal proof. DAMN! If there's something model theoretic in the proof, then we can find it in the proof! Have you ever been diagnosed? (I'm asking seriously.) MoeBlee |