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From: tmoody@sjuvax.UUCP (T. Moody)
Newsgroups: net.philosophy
Subject: Consistency
Message-ID: <2449@sjuvax.UUCP>
Date: Wed, 23-Oct-85 20:21:11 EST
Article-I.D.: sjuvax.2449
Posted: Wed Oct 23 20:21:11 1985
Date-Received: Thu, 31-Oct-85 01:33:05 EST
Distribution: net
Organization: St. Joseph's University, Phila. PA.
Lines: 48

[]
     Logicians recognize two kinds of consistency, at least: semantic
and syntactic.  Here are some definitions.

--> A set of statements, S, is semantically consistent if and only if
the members of S could all be true in the same possible world.

--> A set of statements, S, is syntactically consistent if and only if
no statement of the form P & ~P is derivable, using formal logical
principles, from S.

     What makes the first kind of consistency semantic is its use of
the concept "truth."  The second definition uses only formal or, if
you prefer, typographical concepts -- as long as you understand
"statement" to refer to a subset of typographical strings.

     I think that semantic consistency is what most of us mean when we
wonder whether the human mind is often, or ever, consistent.  We want
to know whether all of the things we believe could be true in this,
the actual world, or in any possible world.

     I offer the following pair of statements; I think that most of us
would assent to both of them.

     S1.  Take any particular belief of mine that you choose; I hold
that belief to be true, since that's what it means for something to
*be* a belief.

     S2.  I believe that some of my beliefs are false.

     The first statement is a necessary truth.  The second statement
is an inductively grounded conclusion, based on past experiences of
being wrong.  The point is that individually I hold my beliefs to be
true; there is not a belief of mine that I hold to be false.  But one
of my beliefs is the belief that at least one of my beliefs -- I can't
specify which one -- is false.  Call this the Principle of Humility.

     I think that virtually everyone accepts the Principle of
Humility.  But the set { S1, S2 } is obviously inconsistent.  For
those who have been wondering whether the mind is consistent, I think
that this example at least shows that the belief systems of most --
perhaps all -- of us are in fact inconsistent.


Todd Moody                 |  {allegra|astrovax|bpa|burdvax}!sjuvax!tmoody
Philosophy Department      |
St. Joseph's U.            |         "I couldn't fail to
Philadelphia, PA   19131   |          disagree with you less."