The End of an Era - That of The Natural Numbers
in [Math]
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From: Alan Smaill on 7 May 2010 06:00 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > 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"). where can I see the proof? -- Alan Smaill
From: Aatu Koskensilta on 7 May 2010 07:35 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > 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"). No there isn't. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Daryl McCullough on 7 May 2010 08:10 Nam Nguyen says... >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"). It's hard to take your thoughts about mathematics seriously when you say things like that. You've got the implication completely backwards. It's not 1. "If GC is true, then it is undecidable in PA" it's 2. "If GC is undecidable in PA, then it is true" -- Daryl McCullough Ithaca, NY
From: William Hughes on 7 May 2010 11:24 On May 7, 12:18 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > This marks the second time that I've seen a poster who criticized a > standard theory (last time it was ZFC, this time it's PA) and then was > asked to define "is." No one asked anyone for a definition of "is", What are you talking about? - William Hughes
From: James Burns on 7 May 2010 13:04
Transfer Principle wrote: > It doesn't matter whether I give the groups labels or not. Well, on this point, we agree. Halleluia! If you will recall, I pointed to your concerns about labels as a /symptom/ of your tendency to throw individuals into the same imagined group, whether they belong together or not. Then you treat anything written by one member of the "group" as though it were written by everyone in this "group". I suppose it it very convenient for you, rhetorically, but, when you do that, you leave reality behind and enter some world of your imagination. > At least I've never asked anyone to define "is." If other > posters really wanted to convince me not to divide them into > two groups, they can give those with whom they disagree the > benefit of the doubt once in a while. If they want me to stop > worrying about five-letter words, then they should stop > worrying about two-letter words, for one thing. Am I in this group of posters who want to convince you not to divide them into two groups? Are you saying that I do not give those with whom I disagree the benefit of the doubt once in a while? Are you saying I worry about two-letter words? If so, what do you base these judgments on? Do you really have any reason to generalize this discussion between two posters to this larger group of posters? /This/ is my criticism of you, /not/ the labels, which you have not used in this post, the labels which, as you point out, do not matter. Jim Burns |