From: brian@quake.sylmar.ca.us (Brian K. Yoder)
Newsgroups: alt.individualism
Subject: Re: A = A. Isn't this obvious?
Date: Sun, 27 Sep 1992 10:20:30 GMT
Organization: Quake Public Access

In article <exukjb.231.717344336@exu.ericsson.se> exukjb@exu.ericsson.se (ken bell) writes:
>In article <Bv1sAC.7JE@newcastle.ac.uk> Chris.Holt@newcastle.ac.uk (Chris Holt) writes:
>>From: Chris.Holt@newcastle.ac.uk (Chris Holt)
>>ECL4JN2@MVS.OAC.UCLA.EDU (Jack B. Nimble) writes:

>>>This discussion is bordering on the ridiculous. A = A, or the
>>>idempotence property of identity, is a law of logic and is applicable
>>>to any domain of discourse, not only algebras.

>>You have to guarantee certain properties relating to the mapping
>>between the domain of discourse and the logic you want to use.
>>If you want to look up the algebraic foundations of logic, you
>>might be interested in toposes, in category theory.

You are getting WAY ahead of yourself here.  How can you even talk about
algebra, logic, idempotence, etc. without first accepting that a thing is 
what it is?  A=A is not an algebraic statement, it is a shorthand way of
referring to the fundamental idea that a thing is what it is and not 
something else.  Thus, if you arrive at a contradiction, you can conclude
that a given set of premises or reasoning is wrong.

>>>Expressed in the
>>>vernacular, it simply states that anything whatsoever is identical to
>>>itself. This has nothing to do with religion.

>>It is an assumption about the meta-language you are using that
>>cannot be proven.  When stated with vehemence, it appears to be
>>an article of faith, i.e. a religious belief.

>>>If you believe this is not true, would you be kind enough to supply
>>>us with a counterexample?

>>The morning star is the evening star.  Surely you know the
>>difference between denotations and connotations.

Surely you know that this is not a contradiction.  It amounts to saying
"Venus is Venus".  I don't think you honestly think that such a contrived
example is a violation of the law of identity, do you?

>Frege's distinction between sense and reference is entirely irrelevant to
>an evaluation of the objectivists' idea that A=A. We all know its a formal
>rule of logic and that one ends up assuming it in his denial of it. 
>Aristotle's advice to anyone who encountered a skeptic of such laws as 
>identity and noncontradiction was to hit them over the head with a mallet.

Indeed, and if the skeptic complains, just explain that it was NOT a mallet.
Then see how long the skeptic continues to insist that things are not what 
they are.

This reminds me of one of my favorite bits from Aristotle.  A skeptic
told him that he didn't believe in the law of identity.  Aristotle responded
that he was quite pleased to hear that the skeptic had come over to his
way of thinking on the issue.  The skeptic explained, "No, what I said was
that I DON'T agree with the law of identity." to which Aristotle responded
"It warms my heart to hear that you are such a staunch advocate of the law
of identity.".  A bit annoyed, the skeptic said "Look, I said that I DON'T 
agree with the law of identity!  I DID'NT say that I agree with it.  After 
all, those statements are contradictory and therefore cannot both be true.".
Aristotle replied, "As I said, I am pleased to hear that you have adopted 
the law of identity so completely into your thinking."  (Of course the words
were different, but that was the essence of it.)
 
>There's no question of proving either that A=A or that A!=A, because any
>attempt at proving them will end up using them.

Indeed.  That's why analyzing such a statement via complex mathematics is
nonsensical since all such analysis relies on identity.

>But objectivists have to meet the, to my mind anyway, serious issue of
>cognitive emptiness of mere formal rules, and to indicate just how you
>can get from recognition of this formal rule to saying something substantive
>about the world.  

I think that in the sense you mean it, A=A is not a "formal rule".  When you 
get down to asking things like "Why can't something be both true and false?"
identity steps in and says "That can't be, things are what they are and they 
can't be two different things at the same time an d in the same respect.  IT's
not empty, it's just not something really hard to understand.  I should also
point out that it is not the case that Objectivists merely deduce the rest of
philosophy (or even epistemology) from A=A.  Where you under the impression
that this was the case? 

>And it just is not true, or enlightening, to say that 
>existence is identity.  In general, when I say of x that it "exists"--or 
>more ponderously--that it "has being" or "is real", I am not making any
>judgement directly about identity.

Sure you are.  Her point was that when analyzing something, eventually you
get down to brute facts which are simply true and cannot be further analyzed.
They are just truths and that's it.  

--Brian