Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem

From: Daryl McCullough (daryl_at_atc-nycorp.com)
Date: 01/03/05 

Date: 3 Jan 2005 11:28:42 -0800

Charlie-Boo says...

>How else can you arrange for provability to coincide with truth in
>System N, if not by letting the axioms be the true sentences and the
>rules, in effect, be inconsequential?

The rules aren't inconsequential. The rules for Smullyan's system are the usual
rules for first-order logic. 

--
Daryl McCullough
Ithaca, NY

Relevant Pages

  • Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem
    ... Charlie-Boo says... ... if not by letting the axioms be the true sentences and the ...
    (sci.math)
  • Re: need help in understanding Torkels ZFC comment
    ... Charlie-Boo> I beat him by 19,725 steps. ... Ullrich> That's not a formal proof from the axioms of ZFC. ... meaning of a concept. ...
    (sci.math)
  • Re: need help in understanding Torkels ZFC comment
    ... Charlie-Boo> I beat him by 19,725 steps. ... Ullrich> That's not a formal proof from the axioms of ZFC. ... meaning of a concept. ...
    (sci.logic)
  • Re: Help writing a paper on Godels Incompleteness Thorem
    ... One of these is the following: for every arithmetically definable collection R of sentences we can effectively find a sentence G_R, s.t. if R contains only true sentences G_R is not in R. So whatever new axioms or rules you wish to introduce - as long as you wish only true sentences to be provable - they can't be arithmetically definable. ... So e.g. effectively recognizable axioms and effective rules of inference are ruled out since they are all arithmetically definable. ... essentially proves photons cannot exist - a photon is a particle only if it has the properties of a wave and a photon is a wave ...
    (sci.logic)
  • Re: does sqrt(2) exist in CM?
    ... >> In the language of arithmetic, the theory whose axioms are exactly ... >> true sentences. ... I was just testing Torkel's dexterity. ... Yeah, right. ...
    (sci.logic)
Loading