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Topic: I Bet \$25 to your \$1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent

Replies: 20   Last Post: Mar 19, 2013 1:32 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: I Bet \$25 to your \$1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent

Posted: Mar 13, 2013 11:36 PM

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))

GODELSTATEMENT <-> NOT(GODELSTATEMENT)

------------

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

Date Subject Author
3/13/13 Graham Cooper
3/13/13 Graham Cooper
3/14/13 Charlie-Boo
3/14/13 Charlie-Boo
3/14/13 Graham Cooper
3/14/13 Charlie-Boo
3/14/13 Graham Cooper
3/14/13 Charlie-Boo
3/14/13 Graham Cooper
3/15/13 Charlie-Boo
3/19/13 Graham Cooper
3/19/13 Charlie-Boo
3/19/13 Charlie-Boo
3/15/13 Graham Cooper
3/15/13 Charlie-Boo
3/15/13 Graham Cooper
3/19/13 Charlie-Boo