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From: mangoe@umcp-cs.UUCP (Charley Wingate)
Newsgroups: net.philosophy
Subject: Yet Another Spurious Proof
Message-ID: <2004@umcp-cs.UUCP>
Date: Mon, 28-Oct-85 00:14:13 EST
Article-I.D.: umcp-cs.2004
Posted: Mon Oct 28 00:14:13 1985
Date-Received: Thu, 31-Oct-85 22:04:03 EST
References: <1790@watdcsu.UUCP>
Organization: U of Maryland, Computer Science Dept., College Park, MD
Lines: 64

In article <1790@watdcsu.UUCP> dmcanzi@watdcsu.UUCP (David Canzi) writes:

>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.

I've removed the argument to the end, and heavily edited it to shorten it.
The gist of it is that one sets up a statement about whether a function of
that statement can be recognized as true by a person X.  The statement is
constructed so that supposedly the person can erroneously recognize it as
true, or if it is true, he can recognize it as true (since to do so would
contradict the statement.  David Canzi then makes the following claim:

>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.

Unfortunately, this argument is totally bogus when applied to God, possibly
for multiple reasons.  Let us postulate that God has some sort of facility
which erroneously recognizes false statements as true (a function which has
some obvious utility).  We therefore have God's mind recognizing the
statement as true.  Another part, presumably dealing only with true
statements, realizes that the statement is in fact false (since He is
recognizing it somewhere else).  So there is no paradox, and God is still
omnicient (and without resort to semantics!).

What's the hole?  There's an implicit assumption that minds are like formal
systems, and can't maintain contradictions in any useful way.  I think this
assumption is unwarranted; it's not even clear that it's true for humans,
much less gods.

So I don't believe this argument at all.

Charley Wingate  umcp-cs!mangoe
-------------------------------------------------------------
The original argument:

>> 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 "'".

>> Let SQ(T), or T *self*quoted, mean: Q(T) followed by T.

>> 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.