The End of an Era - That of The Natural Numbers
in [Math]
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From: William Hughes on 6 May 2010 17:26 On May 6, 3:42 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > On May 6, 1:08 pm, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > > On May 6, 1:02 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > > On May 6, 9:25 am, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > > Of course "define your terms" can be used to block > > > > debate "it all depends on what you mean by 'is'", > > > > (Perhaps you're referring to Clinton? If not, then disregard my > > > remarks here.) Clinton didn't block debate with that comment. > > > Actually, he drew a crucial distinction that needed to be made in the > > > interview. He referred to the fact that use of 'is' is accurate or not > > > depending on what point in the chronology was being referred to. The > > > remark struck people as evasive (which would be his right anyway) and > > > silly. But on appreciation of the actual point in question, the remark > > > was not silly. > > > The statement > > > "It all depends on what you mean by 'is'" > > > is evasive pretty much independent of context. > > Someone who makes such a comment is not trying > > to further a discussion. As such, the use of the > > statement to illustrate the use of a demand for > > definition ofterms to block debate seems > > justified. > > But in the particular case of Clinton, his remark was justified. The > answer to the question put to him really did depend on what "is" meant > (what its temporal sense was). If Clinton had wanted to further the discussion he could have said something like "There is a crucial matter of timing..." The remark he made was clearly not meant to further discussion. The question of whether the remark was correct is entirely irrelevant. > > > The quote is infamous. However, like many attributions > > the attribution to Clinton may be false. > > No, it's real. Which bit of "I neither know nor care" did you fail to understand? The "quote" is a good example whether or not the attribution is correct. > (If I recall, it was something like "it depends on what > the definition of 'is' is".) But it was ridiculed unjustifiably. Out > of context it sounds like he was just playing games with words; but in > the actual context the particular sense of the word 'is' was crucial. > I suppose that if the remark was correct you might have to say he was "playing with words" rather than "*just* playing with words". I fail to see a big difference. The remark does not become a good remark just because it was correct. - William Hughes
From: Nam Nguyen on 7 May 2010 00:13 William Hughes wrote: > On May 5, 2:38 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> what's the difference between >> your "if GC is true we can show that it is true" and >> my "can show GC true if it's true" in my question to you? > > Nothing. However note, I am not claiming that > > A: we can show GC true if it's true > > A is not yet known and may never be known. > I am claiming that A is my *guess*. There's a meta theorem stating that if GC is true then it'd be undecidable in PA (or any system T "as strong as arithmetic"). Would you still make the same "guess" A, in light of this meta theorem? > The question is not whether my guess is right > or wrong, the question is whether my guess > qualifies as an intuition. That's you question and interest, not mine. I'm interest in any guess or intuituion's being correct or not.
From: William Hughes on 7 May 2010 00:36 On May 7, 1:13 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: <snip> > There's a meta theorem stating that if GC is true then it'd be > undecidable in PA (or any system T "as strong as arithmetic"). > > Would you still make the same "guess" A, in light of this meta > theorem? > Since this meta theorem is obviously idiotic I would ignore it completely. - William Hughes >
From: Nam Nguyen on 7 May 2010 00:56 William Hughes wrote: > On May 7, 1:13 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > <snip> > >> There's a meta theorem stating that if GC is true then it'd be >> undecidable in PA (or any system T "as strong as arithmetic"). >> >> Would you still make the same "guess" A, in light of this meta >> theorem? >> > > Since this meta theorem is obviously idiotic > I would ignore it completely. Are you saying that GC is decidable in, say, PA then?
From: William Hughes on 7 May 2010 02:35
On May 7, 1:56 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > William Hughes wrote: > > On May 7, 1:13 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > > <snip> > > >> There's a meta theorem stating that if GC is true then it'd be > >> undecidable in PA (or any system T "as strong as arithmetic"). > > >> Would you still make the same "guess" A, in light of this meta > >> theorem? > > > Since this meta theorem is obviously idiotic > > I would ignore it completely. > > Are you saying that GC is decidable in, say, PA then? No, it is not known if GC is decidable or not. I am saying that it is possible for GC to be true and decidable. [I think you may have your meta theorems mixed up. There is a meta theorem that says that if GC is undecidable it must be true, i.e. it is not possible for GC to be false and undecidable] - William Hughes - William Hughes |