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Re: I Bet $25 to your $1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent
Posted:
Mar 14, 2013 1:22 PM
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On Mar 14, 1:07 pm, Charlie-Boo <shymath...@gmail.com> wrote:
> On Mar 13, 11:36 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
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> > On Mar 14, 8:25 am, Jan Burse <janbu...@fastmail.fm> wrote:
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> > > Graham Cooper schrieb:
>
> > > > On Mar 13, 4:09 am, Charlie-Boo<shymath...@gmail.com> wrote:
>
> > > >> >1. Tarski: Truth is not expressible.
>
> > > Actually the above is true I guess. It is the
> > > content of Tarski's undefinability theorem:http://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem
>
> > > I think the usual meaning of "truth" is
> > > to be true in some intended model. So
> > > you have some model M, and some sentence
> > > A, and you want to know whether M[A]=1.
>
> > > Truth is not expressible means there are
> > > some intended models, where M[A]=1 is not
> > > formalizable as far as M[A]=1 could be a
> > > derivation from axioms and inference rules.
>
> > > Right?
>
> > > This doesn't mean that you Graham Cooper,
> > > with your Prolog, cannot derive some
> > > truths. But you will not be able to derive
> > > all truths.
>
> > > Right?
>
> > > Bye
>
> > You can't agree with this sentence right?
>
> > That sentence is true right?
>
> > So your chimpanzee is smarter than you right?
>
> > If TRUE(x) doesn't work, what is NOT(NOT(x)) ??
>
> > ------------------------------
>
> > TRUTH TABLE
> > and(X,Y) :- tru(X),tru(Y).
> > and(X,not(Y)) :- tru(X),not(Y).
> > and(not(X),Y) :- not(X),tru(Y).
> > and(not(X),not(Y)) :- not(X),not(Y).
>
> > INFERENCE RULE
> > not(and( even(X) , not(even(s(s(X)))) )).
>
> > MODUS PONENS
> > tru(R) :- not(and(L,not(R))) , tru(L).
>
> > ---------------------------------
>
> > this will actually work out that s(s(s(s(0)))) e EVENS
>
> > not(....) will match inference rules
>
> > tru(....) will match proof methods
>
> > ----------------------------------
>
> > In a formal system
> > THERE IS NO DIFFERENCE BETWEEN
>
> > theorem(X)
> > true(X)
> > proof(X)
>
> > they are just RULES OF DERIVATION
>
> > GODELSTATEMENT <-> NOT(PROOF(GODELSTATEMENT))
>
> Yo.
>
> > GODELSTATEMENT <-> NOT(GODELSTATEMENT)
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> iX-nay. LIARSTATEMENT <-> NOT(LIARSTATEMENT)
>
> C-B
>
You can think of it as:
Liar: "This is not true." has no truth value. (It's only value is as
a conversational piece.)
Gödel: "This is not provable." is TRUE!
:: (Therefore) truth and provability are not the same thing!
C-B
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>
>
> > ------------
>
> > PROOF(X) <-> NOT(NOT(X))
>
> > TRUE(X) <-> NOT(NOT(X))
>
> > THEOREM(X) <-> NOT(NOT(X))
>
> > T-WFF(X) <-> NOT(NOT(X))
>
> > Herc
>
> > --www.BLoCKPROLOG.com
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