In a Consistent System, Can a True Sentence Imply a False One?
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From: Marshall on 30 Jul 2010 13:05 On Jul 30, 9:56 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > On Jul 30, 8:00 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > >> If whatever you said below makes sense then the audience wouldn't > >> be Nam > > > Oh please! Don't make it THAT easy. It should be a *little* challenge. > > Like whatever you've said here really has any technical merits. As usual. But lack of technical merit is one of the few things you and I have in common! Don't push me away bro. Marshall
From: Nam Nguyen on 30 Jul 2010 13:18 Marshall wrote: > On Jul 30, 9:56 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Marshall wrote: >>> On Jul 30, 8:00 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>>> If whatever you said below makes sense then the audience wouldn't >>>> be Nam >>> Oh please! Don't make it THAT easy. It should be a *little* challenge. >> Like whatever you've said here really has any technical merits. As usual. > > But lack of technical merit is one of the few things you and I have > in common! Don't push me away bro. You are wrong. I pointed out with _technical details_ why CM's referencing, and AS' defining, the word "disprovable" wouldn't make technical sense in the context of an inconsistent theory. What technical illustrations in what post so far did you have sto illustrate the technical meaning and usage of the word? In fact, it seems you don't even know on whose side of this technical debate you've been (or should be)! So, you're in no way my "bro". And I don't have a feeling the other side would consider you as a "bro" either! To be a clown in this context is to be alone, it'd be my guess. -- ----------------------------------------------------------- Normally, we do not so much look at things as overlook them. Zen Quotes by Alan Watt -----------------------------------------------------------
From: Daryl McCullough on 30 Jul 2010 13:36 Nam Nguyen says... > >Alan Smaill wrote: >> The term "unprovable" already exists; > >Right. To be more precise, "unprovable" in technical definition is >negating "provable". > >> "disprovable" is normally used as above -- >> it does not mean the same thing as "unprovable". > >It actually is, in the context where it's supposed to be used: the >context of a consistent theory. In such case, the set of disprovable >formulas and the set of unprovable ones are _identical_ which is >disjoint from the set of provable formulas. No, Godel's theorem shows that the set of disprovable sentences is *NOT* the same as the set of unprovable sentences. The Godel sentence G for a consistent theory is unprovable, but it is not disprovable. What you mean is for a *COMPLETE* consistent theory, unprovable and disprovable are the same. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 30 Jul 2010 13:39 Nam Nguyen says... > >Marshall wrote: >> On Jul 29, 7:19 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >>> ... AS' answer wouldn't make much sense in this context of an inconsistent >>> formal system: all formulas would be _both_ provable and disprovable! >> >> Both provable and disprovable! Why, that's hard to imagine. > >Don't tell me but tell Alan that: because that's what his definition >would render in the case of an inconsistent theory! I think Marshall is being sarcastic when he says "that's hard to imagine". It is *OBVIOUSLY* the case that for an inconsistent theory, a sentence can be both provable and disprovable. (But it can't be both provable and unprovable). As a matter of fact, we can use the word "inconsistent" to describe a theory such that some formula is both provable and disprovable in that theory. -- Daryl McCullough Ithaca, NY
From: MoeBlee on 30 Jul 2010 16:23
On Jul 30, 12:18 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > To be > a clown in this context is to be alone So does your big red nose honk when you squeeze it? MoeBlee |