Unsolvability of the Entscheidungsproblem as a Corollary of Gödel’s 2nd Theorem
in [Math]
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From: Charlie-Boo on 4 Jun 2010 00:08 On Jun 1, 3:18 pm, George Greene <gree...(a)email.unc.edu> wrote: > On May 31, 12:27 pm, Charlie-Boo <shymath...(a)gmail.com> wrote: > > > Alonzo Church, A note on the Entscheidungsproblem, Journal of > > Symbolic Logic, 1 (1936), pp 4041 > > > Alan Turing, On computable numbers, with an application to the > > Entscheidungsproblem, Proceedings of the London Mathematical Society, > > Series 2, 42 (1937), pp 230265 > > > However, if the Entscheidungsproblem were solvable, then we could > > determine (and thus prove) whether the system is consistent by asking > > whether the sentence 0=1 is provable, as provability is expressible. > > > So dont we have a proof that is (1) way simpler, and (2) way earlier, > > than Church and Turing? > > Why do you say "So" ?? It's way simpler because it's 1% as long. Godel's 2nd Incompleteness Theorem was proven in 1931. C-B > "So" implies that something is following from some prior result. > Where is your prior result? Who simply showed that the Eproblem > was unsovlable PRIOR to this??
From: Charlie-Boo on 4 Jun 2010 00:10 On Jun 1, 3:19 pm, George Greene <gree...(a)email.unc.edu> wrote: > On May 31, 6:35 pm, Rupert <rupertmccal...(a)yahoo.com> wrote: > > > If the Entschiedungsproblem were solvable then you could determine > > whether PA is consistent. But it doesn't necessarily follow that you > > would be able to prove that PA is consistent in PA. Solving the > > Entscheidungsproblem just means you have an algorithm for answering > > the question, it doesn't say anything about supplying a proof in some > > theory T of the answer. > > The question said, "since provability is expressible". > Is provability in PA "expressible" in PA ?? What is the premise for Godel's 1st Incompleteness Theorem? (No, not the hokey ill-defined (vague and informal) "a sufficient amount of arithmetic can be formalized" silliness.) C-B
From: Charlie-Boo on 4 Jun 2010 00:13
On Jun 1, 4:07 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > So dont we have a proof that is (1) way simpler, and (2) way earlier, > > than Church and Turing? > > No. What proof are you thinking of? > > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus What do you call someone who asks questions for which they know the response? Something like "fuckwit", I believe. C-B Posting limit reached. :( |