In a Consistent System, Can a True Sentence Imply a False One?
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From: Marshall on 30 Jul 2010 18:51 On Jul 30, 3:43 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > On Jul 30, 5:26 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > > For example, if you merely defined a prime as one having only 1 and > > itself as divisors, then you shouldn't get angry when I or anybody > > confront you with the question like: Does your "prime" definition > > make sense in the case of 1? > > Yes, 'disprovable' makes sense whether the theory is consistent of > inconsistent! > > It makes sense in either case. > > Do I have to write it in ox blood for you? > > It makes sense in either case. > > It makes sense if the theory is consistent, if the theory is > inconsistent, if the theory is from the planet Mars, if the theory is > song by the Mormon Tabernacle Choir, it MAKES SENSE! Moe, He's just not worth it. Seriously. I mean, look at how people like JSH and Archimedes Plutonium persist for years and years in the face of withering contempt; *nothing* will convince Nam that he isn't totally logical, brilliant and right about every important matter. Just picture him in that clown outfit, waving his coffee-stained copy of Schoenfeld, ranting at the undergrads outside the clown college. Marshall
From: MoeBlee on 30 Jul 2010 18:53 On Jul 30, 5:41 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > I'm sorry: I'm not interested in your cooking knowledge. When you have > anything technical to say then get back to the subject. I wrote you a LIST of technical definitions and theorems!!! Technical? I should write it in the primitive language of set theory? For the the excruciatinglyizth time: A formula P is disprovable in a theory T iff ~P is provable in T. PERIOD. Whether T is consistent, or inconsistent, complete, or incomplete, a figment of the brain of Willy Wonka from his Chocolate Factory, or an encoded message from a future civilization of genius cross-dressing caterpillars. Just TRY to say: "Oh, now I see. 'disprovable' just means 'the negation is provable'. It's not complicated at all. And thanks to Daryl for the example I asked for." You don't have to mean it; but just TRY to see if you can say it. MoeBlee
From: Nam Nguyen on 30 Jul 2010 19:06 MoeBlee wrote: > On Jul 30, 5:41 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> I'm sorry: I'm not interested in your cooking knowledge. When you have >> anything technical to say then get back to the subject. > > I wrote you a LIST of technical definitions and theorems!!! Where in that list would it contain your explanation why the given definition of "disprovable" would make sense in the case of an inconsistent theory? -- ----------------------------------------------------------- Normally, we do not so much look at things as overlook them. Zen Quotes by Alan Watt -----------------------------------------------------------
From: Daryl McCullough on 30 Jul 2010 19:06 Nam Nguyen says... >If you clarified so. Now then, as I asked before, if e.g. I tell you I have >a T that has a disprovable formula in it, would you be able to tell if that >T is consistent, or not? No, because *every* theory (inconsistent or not) has disprovable formulas in it. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 30 Jul 2010 19:11
Nam Nguyen says... >You have not yet illuminated why such definition (of "disprovable) would >make any technical sense in the case of an inconsistent theory. What kind of sense do you want it to make? What's wrong with the conclusion that, if T is inconsistent, then every sentence is both provable and disprovable in T? It's a technical claim which follows from the technical definitions of "provable" and "disprovable". What more do you want? -- Daryl McCullough Ithaca, NY |