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

From: Charlie-Boo (chvol_at_aol.com)
Date: 01/03/05 

Date: 3 Jan 2005 11:01:14 -0800

Daryl McCullough wrote:
> Charlie-Boo says...
>
> >1. Is provability the same as truth in system N? (Answer: Yes.)
> >
> >2. Who defined System N? (Answer: None other than Raymond Smullyan
> >himself.)
> >
> >Now those are some relevant questions.
>
> No, they aren't relevant. The issue was whether Smullyan *defined*
> provability to be the same as truth. He didn't. That's a
*consequence*
> of his choice of axioms.

That's how axiomatic systems work. You choose the axioms (and rules)
and the theorems are a consequence of that choice. That's how you
define an axiomatic system.

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?
C-B

> --
> Daryl McCullough
> Ithaca, NY

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