Newsgroups: alt.philosophy.jarf,alt.philosophy.objectivism,alt.philosophy.zen,comp.ai.philosophy,sci.philosophy.meta,sci.philosophy.tech,talk.philosophy.humanism,talk.philosophy.misc
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!howland.reston.ans.net!gatech!psinntp!psinntp!psinntp!psinntp!scylla!daryl
From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: The Search For Truth
Message-ID: <1995May19.200930.9025@oracorp.com>
Organization: Odyssey Research Associates, Inc.
Date: Fri, 19 May 1995 20:09:30 GMT
Lines: 91
Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:28203 sci.philosophy.meta:18215 sci.philosophy.tech:18099

jalway@icsi.net (John Alway) writes:

>    Let's examing the concept of "true and false"... that appears to
>be the issue here.  If I pointed to a block of wood and asked you is
>it "true or false?"  Does that statement have any meaning?  If I asked
>you "Is that block of wood red?" "True or false?" Then you have
>something to reference.  It seems to me that truth is a correspondence
>between what is said and what one is saying about something.  If that
>condition doesn't exist then you shouldn't use the words "true or
>false".

Okay, let's adopt your convention, that only sentences that are
"about" something can be meaningfully said to be true or false.  So
let me introduce a new term, "truth-bearing" which is a property of
character strings. We will say that a string S is "truth-bearing" if
(1) it expresses a statement (that is, it is "about" something), and
(2) the statement it expresses is true. A meaningless statement like
"This statement is false" would be rejected as not
truth-bearing. (That doesn't make it false, since only meaningful
statements can be false.)

Let's define the "self-application" of a string S to mean the
string formed from S by prepending its own quotation. For example, the
self-application of

     Daryl

is

    "Daryl" Daryl

Let's define a string S to be "self-describing" if the
self-application of S produces a truth-bearing string. For example,

    has three words

is self-describing, because the string

    "has three words" has three words

is truth-bearing (expresses a true statement).

Now, let G be the string

     "is not self-describing" is not self-describing

Is G meaningful, or not? It would seem that there are three
possibilities: (1) G is meaningful, and expresses a true statement,
(2) G is meaningful, and expresses a false statement, or (3) G is
meaningless (is not "about" anything).

By definition of "truth-bearing", we say in case (2) or (3) that
G is not truth-bearing. So let's assume that G is not truth-bearing.

    1. G is not truth-bearing

    Assumption.

    2. G is the self-application of the string "is not self-describing"

    Definition of G.

    3. the self-application of "is not self-describing" is not truth-bearing

    By 1 and 2

    4. "is not self-describing" is not self-describing

    By definition of "self-describing".

Notice, that conclusion 4 is G itself. So under the assumption that
G is meaningless (not about anything), we can prove G.

What I think that this shows is that we cannot consistently reason
about absolute truth (or absolute meaningfulness)---we can only reason
about limited notions of truth or limited notions of
meaningfulness. If we replaced "truth-bearing" above by
"truth-bearing0", where "truth-bearing0" means "expresses a true
statement that does not involve the notion of truth", and we defined a
string to be "self-describing0" if its self-application was
truth-bearing0, then there would be no paradox---the statement

    "is not self-describing0" is not self-describing0

would be true, but it wouldn't be truth-bearing0, since its meaning
involves the notion of truth.

Daryl McCullough
ORA Corp.
Ithaca, NY

