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[[Category:Libertarian Propaganda Terms]]
[[Category:Objectivism]]
[[Category:Fallacies Of Philosophy]]
[[Category:Failures Of Libertarian Philosophy]]
{{DES | des = Also known as the law of identity, is a worthless piece of philosophical drivel that plainly doesn't apply to the real world and seems to be unnecessary in mathematics.  Objectivists use it as a [[shibboleth]]. | show=}}
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Contrast "A is A" with "A is possibly A" or "A might not be A".

"A is A" cannot apply to the real world because the real world has time in it, and A at time 1 is not necessarily the same as A at time 2.  It's never the same water in the river, and even protons can spontaneously decay.  For "A is A" to apply to the real world, it has to be limited to an instant at time T.  However, that makes it inappropriate for real-world issues, since they generally involve time spans.  So at best, for real world issues, "A is A" is an approximation, that may vary wildly in accuracy over time for different subjects.

The modern formulation of identity is that of Gottfried Leibniz, who held that x is the same as y if and only if every predicate true of x is true of y as well.  [Cribbed from wikipedia.]  This makes it pretty obvious that A's at different times are not identical if only because there is a "time at" predicate.

Another major problem is that we never know "A": we only have our own views and concepts of an aspect of A, as in the story of the [[Blind men and an elephant]].  Thus, use of "A is A" would have to be restricted to a precise aspect of A, rather than A itself which is fundamentally unknowable.

Ludwig Wittgenstein writes (Tractatus 5.5301): "That identity is not a relation between objects is obvious." At 5.5303 he elaborates: "Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing." [Cribbed from wikipedia.]

The [http://aynrandlexicon.com/lexicon/identity.html Ayn Rand Lexicon describes identity] with a bunch of hand-waving, pseudophilosophical gobbledegook.
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