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From: dwyer@vixie.UUCP (Bill Dwyer)
Newsgroups: talk.philosophy.misc
Subject: Dwyer's Response to Wexelblat on the Law of Identity
Message-ID: <157@vixie.UUCP>
Date: Thu, 9-Oct-86 15:21:27 EDT
Article-I.D.: vixie.157
Posted: Thu Oct  9 15:21:27 1986
Date-Received: Thu, 16-Oct-86 05:39:49 EDT
Reply-To: dwyer@vixie.UUCP (Bill Dwyer)
Distribution: world
Organization: Vixie Enterprises, San Mateo, CA
Lines: 150

In article <WEX@MCC.ARPA>,

Alan Wexelblat  comments on my reply to Brad Templeton wherein I state:  

    "If you can have a consistent metaphysical system in which A is not A,
    then what would an INCONSISTENT metaphysical system be?  One in
    which A is A?  What consistency means is a context in which you do not
    have both A and not A (at the same time and in the same respect)".

He says:  

    "I have two problems with this.  First, it doesn't seem (intuitively)
    right.  I don't think I need identity to have a consistent system."

But to say that one needn't have identity to have a consistent system is to
say that one can have a consistent system that is self-contradictory, i.e.,
inconsistent.  Again, "If you can have a consistent metaphysical system in
which A is not A, then what would an INCONSISTENT metaphysical system
be -- and how would one determine it?"  In other words, on what basis
does Wexelblat decide whether a system is consistent or inconsistent if
not on the basis of whether or not it is self-contradictory?   He  continues:

    "The second problem has to do with your assumption that P and not(P)
    are all that can be talked of.  There is something called the law of
    excluded middle which is used in some forms of logic and not used in
    others.

But the law of excluded middle is a corollary of the law of
non-contradiction.  It is because A and non-A cannot exist at the same
time and in the same respect that a thing must either be A or non-A (but
not both) at the same time and in the same respect.  Nowhere do I assume
that the law of non-contradiction is all that can be talked of.  What I argue
is that it is a necessary condition -- not that it is an exhaustive 
statement -- of a consistent metaphysical system.

Wexelblat continues:

    "In logics which use the excluded middle, the formula (P or not(P)) is
    always true.  However, there are other logics in which this is not the
    case.  In these logics, asserting not(not(P)) is not the same as asserting
    P."

    "This sort of thinking is used in "intuitionist" logics . . . .

But all non-Aristotelian (including any so-called "intuitionist") logics
presuppose, and are to be judged by, the Aristotelian laws of identity,
non-contradiction and excluded middle.   I.e., either these non-Aristotelian
logics are valid or they are not -- they cannot both be valid and invalid --
they are what they are -- A is A.   Wexelblat continues:

    "More interestingly,  [this sort of intuitionist thinking] corresponds to
    some situations I encounter in the "real world."  For example, say I edit
    a 300-page book.  I a