New essay on Goedel's Incompleteness Theorem
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From: Nam Nguyen on 4 Oct 2009 11:36 Marshall wrote: > On Oct 4, 1:16 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> I don't think you have a proof that I didn't, one way or another, respond to >> your key points in your refute. > > The public record is proof. A dishonest poster could say that much.
From: Marshall on 4 Oct 2009 12:50 On Oct 4, 8:36 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Marshall wrote: > > On Oct 4, 1:16 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > >> I don't think you have a proof that I didn't, one way or another, respond to > >> your key points in your refute. > > > The public record is proof. > > A dishonest poster could say that much. A litterbug could say "a dishonest poster could say that much." So what. Big deal. Rather than dig up the distant past, I refer instead to our interaction in this very thread, on or about Sep. 26-27. You stated that Godel's incompleteness theorem "assumes" the consistency of a theory of arithmetic, requires prime numbers to do encoding, and that certain sets of primes depend in some unspecified way on the Goldbach Conjecture. You also indicated you have doubts about arithmetic on the naturals. I pointed out that other encodings besides those using primes are possible, and that sets of primes don't depend on GC; you didn't respond. I also asserted that we can do arithmetic without knowing anything about GC; you then admitted we could, apparently implicitly abandoning the claim about doubts about arithmetic on the naturals. You parted by trying to put words into my mouth to the effect that since I deny any doubts about arithmetic on the naturals, I probably didn't think Euler and Goldbach were doing serious math. Marshall
From: Aatu Koskensilta on 6 Oct 2009 05:55 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Oh, I don't know Aatu. It's just one's personal note to another > person. No one is obliged to take it but it's free to take. Some > people though do find consolation in contemplation. People can find consolation in anything. > Is it too much to ask you to cut out this kind of "crabby" way of > conversation? It's unrealistic to expect earnest admonitions like this to have any effect. > In the first place, I don't ever recall I ever said anything about the > name "Brouwer": I don't even know what he did or wrote in what field > that made him well known (though apparently he must have). Yes, I owe you an apology -- I had you confused with R. Srinivasan. > You seem fond to make technical conversations sour? This isn't a technical discussion. We are discussing, rather, ways of viewing the world, attitudes, the consoling power of various abstract ideas, etc. > To some of those people, I suspect, it only takes _one_ case. Are you > so sure historically there isn't "anything of the sort" at all? Not > even one case? One case of a lone wolf battling stagnant orthodoxy, their revolutionary ideas understood and appreciated only by later generations etc? I can't really think of any historical figure that would meet this romantic ideal. If we examine the historical facts known about the usual suspects, Roger Bacon or Galois, say, we find very little in the way of the sort of romantic fluff people find comfort in. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon mann nicht sprechen kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 6 Oct 2009 08:27 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Did I say you _literally_ say that? Who knows? Well, perhaps those do who wade through earlier messages. It seems you regard the question whether the language of a theory is determined by its axioms a question of fact. This is a peculiar notion. Whether the language of a theory is determined by its axioms is decided by stipulation, answered by looking up the relevant definitions. There simply is nothing whatever here to argue over. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon mann nicht sprechen kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: David C. Ullrich on 6 Oct 2009 08:36
On Tue, 06 Oct 2009 15:27:44 +0300, Aatu Koskensilta <aatu.koskensilta(a)uta.fi> wrote: >[...] There simply is nothing whatever here to argue over. Heh-heh. You must be new here... David C. Ullrich "Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to." (John Jones, "My talk about Godel to the post-grads." in sci.logic.) |