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From: dmcanzi@watdcsu.UUCP (David Canzi)
Newsgroups: net.philosophy
Subject: God knows.
Message-ID: <1790@watdcsu.UUCP>
Date: Fri, 25-Oct-85 04:10:56 EST
Article-I.D.: watdcsu.1790
Posted: Fri Oct 25 04:10:56 1985
Date-Received: Thu, 31-Oct-85 05:48:13 EST
Reply-To: dmcanzi@watdcsu.UUCP (David Canzi)
Organization: U of Waterloo, Ontario
Lines: 57

The following constitutes a proof that for some random arbitrary person,
"Tom", there is at least one true statement that Tom doesn't know --
in fact *can't* know.  I've borrowed it from an article posted by
lambert@boring.  (rn exhibited unpleasantly surprising behaviour when
I tried to follow up that article.)  Feel free to skip over it to my
comments at the end, on your first reading.

> Consider texts (some of which represent statements, such as: "Two times two
> equals four" and "`Two times two equals four' is a true statement about
> natural numbers", and some of which do not, like "Who? Me?"  and "Don't
> `Aw, mom' me".).  Some of these texts contain *internal* quoted texts.  If
> T is a text, then let Q(T), or, in words, T *quoted*, stand for another
> text, consisting of T put between the quotes "`" and "'". So if T is
> 
>     "Two times two equals for",
> 
> Q(T) is
> 
>     "`Two times two equals for'".
> 
> Let SQ(T), or T *self*quoted, mean: Q(T) followed by T.
> 
> So if T is
> 
>     " contains no digits"
> 
> then T, selfquoted, is
> 
>     "` contains no digits' contains no digits"
> 
> (which is a true statement).
> 
> Now consider the text S =
> 
>     "`, selfquoted, is not recognizable as true by the mind of Tom',
>      selfquoted, is not recognizable as true by the mind of Tom".
> 
> S is a statement, and states that some text T, selfquoted, is not
> recognizable as true by the mind of Tom.
> 
> So can Tom (or his mind) recognize SQ(T) as true, and is SQ(T) true in the
> first place?
> 
> If Tom can recognize SQ(T) as true, then S is apparently false.  But note
> that T is the text
> 
>     ", selfquoted, is not recognizable as true by the mind of Tom",
> 
> so SQ(T) = S.  So Tom would have recognized a false statement as true.  If
> we collectively assume that Tom would never do such a thing, then all of us
> non-Toms can now recognize S as true, something Tom can not.

Now, this proof that there is at least one true statement that Tom doesn't
know still works if we substitute the word "God" for "Tom".  So much for
omniscience.
-- 
David Canzi		"Permission is not freedom."