In logic, the law of identity states that A = A. Any reflexive relation upholds the law of identity; when discussing equality, the fact that "A is A" is a tautology. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... In set theory, a binary relation can have, among other properties, reflexivity or irreflexivity. ... Tautology refers to a use of redundant language in speech or writing, or, put simply, saying the same thing twice. Within the study of logic, a tautology is a statement that is true by its own definition. ...

The law is often attributed to Aristotle, but no reference to it exists until after St. Thomas Aquinas in the 13th century. By the 17th century, reference to the law was common amongst philosophers, and it is probable that it was posited from Aristotle's teachings sometime between 13th and 17th centuries, leading to the attribution. Aristotle (Ancient Greek: Aristotelēs 384 BC – March 7, 322 BC) was an ancient Greek philosopher, who studied with Plato and taught Alexander the Great. ... Saint Thomas Aquinas (1225 - March 7, 1274) was a Catholic philosopher and theologian in the scholastic tradition, who gave birth to the Thomistic school of philosophy, which was long the primary philosophical approach of the Roman Catholic Church. ... (12th century - 13th century - 14th century - other centuries) As a means of recording the passage of time, the 13th century was that century which lasted from 1201 to 1300. ... (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ...

The phrase "A is A" is a favorite of Ayn Rand, and the idea frequently appears in her Objectivist philosophy. Comic book creator Steve Ditko, himself an exponent of Objectivism, consequently named one of his superheroes "Mr. A". Ayn Rand (IPA: , February 2 [O.S. January 20] 1905 – March 6, 1982), born Alissa Zinovievna Rosenbaum, was best known for developing the philosophy of Objectivism and for writing the novels We the Living, Anthem, The Fountainhead, and Atlas Shrugged. ... Objectivism is the philosophical system developed by Russian-American philosopher and writer Ayn Rand. ... A comic book is a magazine or book containing the art form of comics. ... The Amazing Spider-Man Annual #1 (1964): Cover art by Ditko. ... Superman and Batman, two of the most recognizable and iconic superheroes. ... Mr. ...

Hegel, however, in his philosophy in general, and most especially in the Science of Logic submitted the law of identity to a radical critique. The crux of his point is that there is a passage from the first A to the second in the proposition "A = A". Identity is not self-evident, but asserted. The second A stands outside of the first. Identity contains within itself difference.

See also

• Equality (mathematics)