Editing Law of identity (section)

===Contemporary philosophy===

====Analytic====
In the ''[[Foundations of Arithmetic]]'', [[Gottlob Frege]] associated the number [[one]] with the property of being self identical. Frege's paper "[[On Sense and Reference]]" begins with a discussion on equality and [[Meaning (philosophy of language)|meaning]]. Frege wondered how a true statement of the form "a = a", a trivial instance of the law of identity, could be different from a true statement of the form "a = b",  a genuine extension of knowledge, if the meaning of a term was its referent.

[[Bertrand Russell]] in "[[On Denoting]]" has this similar puzzle: "If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other without altering the truth or falsehood of that proposition. Now [[George IV]] wished to know whether [[Walter Scott|Scott]] was the author of [[Waverley (novel)|''Waverley'']]; and in fact Scott was the author of ''Waverley''. Hence we may substitute “Scott” for “the author of ''Waverley''” and thereby prove that George IV wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.”

In his "[[Tractatus Logico-Philosophicus]]", [[Ludwig Wittgenstein]] writes that "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."<ref>{{cite book |last1=Desilet |first1=Gregory |title=The Enigma of Meaning: Wittgenstein and Derrida, Language and Life |date=2023 |publisher=McFarland |page=133}}</ref>

In the [[logical form|formal]] logic of analytical philosophy, the law of identity is written "''a'' = ''a''" or "For all ''x'': ''x'' = ''x''", where a or x refer to a [[Singular term|term]] rather than a [[proposition]], and thus the law of identity is not used in [[Propositional calculus|propositional logic]]. It is that which is expressed by the equals sign "=", the notion of [[Identity (philosophy)|identity]] or [[Equality (mathematics)|equality]].

====Continental====

[[Martin Heidegger]] gave a talk in 1957 entitled "Der Satz der Identität" (The Statement of Identity), where he linked the law of identity "A=A" to the [[Parmenides]]' fragment "to gar auto estin noien te kai einai" (for the same thing can be thought and can exist).{{cn|date=October 2023}} Heidegger thus understands identity starting from the relationship of Thinking and Being, and from the belonging-together of Thinking and Being.
 
[[Gilles Deleuze]] wrote that "[[Difference and Repetition]]" is prior to any concept of identity.{{cn|date=October 2023}}