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 13:09:02 -0800

Charlie-Boo says...

>Ok, then consider the following two systems:
>
>1. System N as defined by Smullyan.
>
>2. System N' which is System N minus the rules of inference, i.e., it
>simply has no rules of inference.
>
>Now, what is the consequence of having the rules in N vs. no rules in
>N' i.e. what is the difference between N and N'?
>
>Answer: None. They have the same theorems.

Right. That's a consequence of the fact that logical deduction preserves truth.
So if you start with all true sentences, then logical deduction doesn't give you
anything new. 

--
Daryl McCullough
Ithaca, NY