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Concept
Law of identity
Summary
In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are built on just these laws.
The earliest recorded use of the law appears to occur in Plato's dialogue Theaetetus (185a), wherein Socrates attempts to establish that what we call "sounds" and "colours" are two different classes of thing:
Socrates: With regard to sound and colour, in the first place, do you think this about both: that they both are? Theaetetus: Yes.Socrates: Then do you think that each differs to the other, and the same as itself?Theaetetus: Certainly.Socrates: And that both are two and each of them one?Theaetetus: Yes, that too.
It is used explicitly only once in Aristotle, in a proof in the Prior Analytics:
When A belongs to the whole of B and to C and is affirmed of nothing else, and B also belongs to all C, it is necessary that A and B should be convertible: for since A is said of B and C only, and B is affirmed both of itself and of C, it is clear that B will be said of everything of which A is said, except A itself.
Aristotle believed the law of non-contradiction to be the most fundamental law. Both Thomas Aquinas (Met. IV, lect. 6) and Duns Scotus (Quaest. sup. Met. IV, Q. 3) follow Aristotle in this respect. Antonius Andreas, the Spanish disciple of Scotus (d. 1320), argues that the first place should belong to the law "Every Being is a Being" (Omne Ens est Ens, Qq. in Met. IV, Q. 4), but the late scholastic writer Francisco Suárez (Disp. Met. III, § 3) disagreed, also preferring to follow Aristotle.
Another possible allusion to the same principle may be found in the writings of Nicholas of Cusa (1431–1464) where he says: ... there cannot be several things exactly the same, for in that case there would not be several things, but the same thing itself. Therefore all things both agree with and differ from one another.
Official source
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