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

From: Josh Purinton (usenet-noreply.a.jp_at_xoxy.net)
Date: 11/16/04 

Date: Tue, 16 Nov 2004 02:30:57 GMT

In article <3df1e59f.0411151640.5873cb47@posting.google.com>,
Charlie-Boo <chvol@aol.com> wrote:
> Smullyan: "We define the system whose provable formulas are all true."
> [Ullrich]: "when you define provability to be truth you exhibit amazing
> ignorance"
>
> What's the difference?

Smullyan is defining a formal system he calls System N, and then noting
that truth and provability coincide in that system. You, on the other
hand, are claiming that truth and provability coincide for a
pre-existing system - English. This is another kettle of fish entirely.

>> In particular he does not define provability as truth or vice versa,
>
> Then what does he define provability to be?

As I pointed out to you before, on page 1 Smullyan states that the book
is intended for readers who already understand the (separate)
definitions of truth and provability. 

-- 
Josh Purinton

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