ninskigirl ([info]ninskigirl) wrote in [info]aynrandforum,
@ 2007-12-25 12:22:00
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Current mood: awake

A is A.
I have been looking through Aristotle's work (Metaphysics) but i have not seen where he mentioned the LAW OF IDENTITY.

Does anybody know where he discussed the Law of Identity?


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[info]diego001
2007-12-25 04:35 am UTC (link)
Wiki returns this: http://en.wikipedia.org/wiki/Law_of_Identity

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[info]john_j_enright
2007-12-25 04:44 am UTC (link)
It does not appear in this form in Aristotle. It begins to appear in the medieval period, in arguments about whether the law of identity is more fundamental than the law of non-contradiction (A is not non-A). Leibniz seems to be the first to champion the law of identity as the ground for all logic, and to really make a big deal of the "A is A" formula.

Here is a link to what I could find out, including a discussion of who Leonard Peikoff credited with the formula:

http://www.objectivistliving.com/forums/lofiversion/index.php/t2252.html

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[info]felephant
2007-12-25 10:55 pm UTC (link)
The law of contradiction isn't 'A is not non-A.' That's different (and, indeed, is the principle of differentiation or something, but I don't know the name for it offhand). It is epistemically prior if you're a Thomian. The law of non-contradiction is 'something cannot both be and not be in the same way and at the same time.'

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[info]john_j_enright
2007-12-25 11:36 pm UTC (link)
Your version is the correct Aristotelian version.

If you look at the Wikipedia article on this law, you'll see they also show it symbolically in propositional logic form as:

not (P and not-P).

Which drops out Aristotle's careful qualification about the same time and same respect.

http://en.wikipedia.org/wiki/Law_of_noncontradiction

The Boolean version is what I quoted:

"The Greek philosopher Aristotle founded a system of logic based on only two types of propositions: true and false. His bivalent (two-mode) definition of truth led to the four foundational laws of logic: the Law of Identity (A is A); the Law of Non-contradiction (A is not non-A); the Law of the Excluded Middle (either A or non-A); and the Law of Rational Inference."

http://www.allaboutcircuits.com/vol_4/chpt_7/1.html

Sorry if my version was confusing!

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[info]john_j_enright
2007-12-25 11:46 pm UTC (link)
Excuse me, but my brain slipped on my last reply. What I was quoting was the version of the law that Leibniz used. I happened to be quoting it from an article about Boole's logic.

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[info]primary_sources
2007-12-25 06:09 am UTC (link)
The law of identity is actually derived from the law of excluded middle. I learned that in my Aristotle course, and would be able to answer your question if I were not on holiday, but alas, I didn't bring my essential Aristotle text with me ;)

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[info]ninskigirl
2007-12-25 08:05 am UTC (link)
Thank you for the links.

I was really having a hard time looking through Aristotle's Metaphysics.

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