Deconstructing Godel
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From: Frederick Williams on 10 Feb 2010 15:22 HawkLogic wrote: > > On Feb 10, 11:20 am, Frederick Williams > <frederick.willia...(a)tesco.net> wrote: > > HawkLogic wrote: > > > 3. There may be false statements in first-order logic which have been > > > proven true. > > > > May there? Do you have an example? > > No, the point being that proof methods may have created one without > warning. Yes, FOL _may_ be unsound but who thinks it in the least likely? -- .... A lamprophyre containing small phenocrysts of olivine and augite, and usually also biotite or an amphibole, in a glassy groundmass containing analcime.
From: Frederick Williams on 10 Feb 2010 15:24 HawkLogic wrote: > > On Feb 10, 8:27 am, Frederick Williams <frederick.willia...(a)tesco.net> > wrote: > > HawkLogic wrote: > > > Use that. > > > > > Set A = > > > { 1. Both statements in this set are false, > > > 2.Godelcreated a mess. } > > > > > If 1 is true then both are false, therefore, 1 is not true. > > > If 1 is false then at least one statement is true, therefore 2 is true. > > > > Once is enough :-) > > > > You (or Smullyan or someone) are assuming that 1. is a statement S > > subject to > > > > if S is not true then S is false > > > > but some (Russell for example) would maintain that 1. is not well-formed > > and has no truth value. > > It is the same self-referencing technique that Godel used to prove > Theorem VI in 1931 (1st Incompleteness > Theorem), where Flg(k) is the set of axioms and proven formulae. Godel's 1931 proof was entirely syntactic, no reference was made to truth or falsity. -- .... A lamprophyre containing small phenocrysts of olivine and augite, and usually also biotite or an amphibole, in a glassy groundmass containing analcime.
From: MoeBlee on 10 Feb 2010 15:38 On Feb 10, 2:22 pm, Frederick Williams <frederick.willia...(a)tesco.net> wrote: > Yes, FOL _may_ be unsound but who thinks it in the least likely? What do you find doubtful in the ordinary proof that first order logic is sound? MoeBlee
From: Frederick Williams on 10 Feb 2010 15:49 MoeBlee wrote: > > On Feb 10, 2:22 pm, Frederick Williams <frederick.willia...(a)tesco.net> > wrote: > > > Yes, FOL _may_ be unsound but who thinks it in the least likely? > > What do you find doubtful in the ordinary proof that first order logic > is sound? Nothing. But I also know that I am fallible. -- .... A lamprophyre containing small phenocrysts of olivine and augite, and usually also biotite or an amphibole, in a glassy groundmass containing analcime.
From: HawkLogic on 10 Feb 2010 16:48
On Feb 10, 2:16 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > On Feb 10, 1:03 pm, HawkLogic <hawklo...(a)gmail.com> wrote: > > > Is there any way to know that accepted methods of logical proof do not > > lead to contradiction. > > Yes.You're not familiar with the soundness theorem for first order > logic? > > MoeBlee Godel seems to have found a way around soundness. |