|
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
|
|
On Mar 14, 1:07 pm, Charlie-Boo <shymath...@gmail.com> wrote: > On Mar 13, 11:36 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > > > > > On Mar 14, 8:25 am, Jan Burse <janbu...@fastmail.fm> wrote: > > > > 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) > > 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
> > > > > > > ------------ > > > 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
|
|