Law of identity

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.

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Related concepts (4)

Logic

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language.

Law of thought

The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. Generally they are taken as laws that guide and underlie everyone's thinking, thoughts, expressions, discussions, etc. However, such classical ideas are often questioned or rejected in more recent developments, such as intuitionistic logic, dialetheism and fuzzy logic.

Law of noncontradiction

In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "p is the case" and "p is not the case" are mutually exclusive. Formally, this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case" holds.