Law of identity
Encyclopedia
In logic
, the law of identity is the first of the so-called three classic laws of thought. It states that an object is the same as itself: A → A (if you have A, then you have A); While this can also be listed as A ≡ A (A if-and-only-if A,) this is redundant Any reflexive relation
upholds the law of identity. When discussing equality, the fact that "A is A" is a tautology
.
's dialogue Theaetetus
(185a), where Socrates
attempts to establish that what we call "sounds" and "colours" are two different classes of thing.
Parmenides the Eleatic (circa BCE. 490) formulated the principle Being is (eon emmenai) as the foundation of his philosophy.
Aristotle
identifies the law in Book VII of the Metaphysics:
Aristotle highlights "the fact that a thing is itself" because the objective of his inquiry at that point in the Metaphysics concerns "substance
" and to provide answers to the question "what kind of thing substance should be said to be", given that "substance is a principle and a cause" of being. He further argues that while it is true that the question, "why a thing is itself" is meaningless, "the fact that a thing is itself" has meaning because we can then restate the why question to inquire "why something is predictable of something" given that each something is itself unique. For Aristotle, "substance is actuality
" and it is the actual "thing that is itself" something that proceeds another such something in time
.
Aristotle makes the claim that, "the fact that a thing is itself" allows for "a fixed constant nature of sensible things", and thus when confronted with the pronouncement that "this is bread" one can proceed to eat with confidence and not demand that for each and every such pronouncement evidence be provided to demonstrate that "this is not bread". Thus "the fact that a thing is itself" perhaps finds its greatest utility to man by providing "a fixed constant nature of sensible things" in an ever changing universe of being---Metaphysics, Book VII, Part 17
Thus in Aristotle we see the first logical presentation of the law of identity, "the fact that a thing is itself", to help answer the question "what kind of thing should be said to be". However, Aristotle never claimed that [A = A, 1 = 1, or A ≡ A], none of which correspond symbolically to "the fact that a thing is itself," for the simple reason that Aristotle never explicitly made the claim "thing is thing."
Both Thomas Aquinas
(Met. IV., lect. 6) and Duns Scotus
(Quaest. sup. Met. IV., Q. 3) follow Aristotle. 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 Suarez
(Disp. Met. III., § 3) disagreed, also preferring to follow Aristotle.
Leibniz claimed that the law of Identity, which he expresses as 'Everything is what it is,' is the first primitive truth of reason which is affirmative, and the law of noncontradiction
, is the first negative truth (Nouv. Ess. IV., 2, § i), arguing that "the statement that a thing is what it is, is prior to the statement that it is not another thing" (Nouv. Ess. IV.. 7, § 9). Wilhelm Wundt
credits Gottfried Leibniz
with the symbolic formulation, "A is A."
Locke
(Essay Concerning Human Understanding IV. vii. iv. ("Of Maxims") says:
J.S. Mill formulates the law as: "Whatever is true in one form of words, is true in every other form of words, which conveys the same meaning" (Exam. of Hamilton, p. 409). Shakespeare has Juliet Capulet
state the same idea as "A rose by any other name would smell as sweet
", in the 1597 play Romeo and Juliet
.
African Spir
proclaims the law of identity as the fundamental law of knowledge, which is opposed to the changing appearance of the empirical reality.
Ayn Rand
used the "A is A" identity as the basis for a objectivist theory of knowledge. She argued it was axiomatic
that "existence exists", and reasoned that existing implies a specific nature and attributes: "A is A"
Exceptions are only permissible where the users are able to readily discern which of the different concepts they are intended to call to mind by the context in which the designator is used. Since our ability to generate valid conclusions from premises is dependent upon our having a clear understanding of the concepts expressed in those premises, it follows that any ambiguity in the symbolic denotation of those concepts will hamper our ability to reason soundly. It is for this reason that the law of identity is considered the self-evident first principle of thought (reason).
held a petition drive to pass "A = A" as statutory law in Berkeley, California
. Specifically, the proposed law stated that, "every entity shall be identical to itself". Any entity caught being unidentical to itself was to be subject to a fine of up to one tenth of a cent. The law did not pass.
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, the law of identity is the first of the so-called three classic laws of thought. It states that an object is the same as itself: A → A (if you have A, then you have A); While this can also be listed as A ≡ A (A if-and-only-if A,) this is redundant Any reflexive relation
Reflexive relation
In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation ~ on S where x~x holds true for every x in S. For example, ~ could be "is equal to".-Related terms:...
upholds the law of identity. When discussing equality, the fact that "A is A" is a tautology
Tautology (logic)
In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...
.
History
The earliest use of the law appears to occur in PlatoPlato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
's dialogue Theaetetus
Theaetetus (dialogue)
The Theaetetus is one of Plato's dialogues concerning the nature of knowledge. The framing of the dialogue begins when Euclides tells his friend Terpsion that he had written a book many years ago based on what Socrates had told him of a conversation he'd had with Theaetetus when Theaetetus was...
(185a), where Socrates
Socrates
Socrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...
attempts to establish that what we call "sounds" and "colours" are two different classes of thing.
Parmenides the Eleatic (circa BCE. 490) formulated the principle Being is (eon emmenai) as the foundation of his philosophy.
Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
identifies the law in Book VII of the Metaphysics:
Aristotle highlights "the fact that a thing is itself" because the objective of his inquiry at that point in the Metaphysics concerns "substance
Substance
Substance may refer to:*Chemical substance, a material with a definite chemical composition*Drug substance*Matter, the substance of which all physical objects are made*Substance theory, theory positing that a substance is distinct from its properties....
" and to provide answers to the question "what kind of thing substance should be said to be", given that "substance is a principle and a cause" of being. He further argues that while it is true that the question, "why a thing is itself" is meaningless, "the fact that a thing is itself" has meaning because we can then restate the why question to inquire "why something is predictable of something" given that each something is itself unique. For Aristotle, "substance is actuality
Actuality
Actuality may refer to:* Potentiality and actuality * Actuality film...
" and it is the actual "thing that is itself" something that proceeds another such something in time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
.
Aristotle makes the claim that, "the fact that a thing is itself" allows for "a fixed constant nature of sensible things", and thus when confronted with the pronouncement that "this is bread" one can proceed to eat with confidence and not demand that for each and every such pronouncement evidence be provided to demonstrate that "this is not bread". Thus "the fact that a thing is itself" perhaps finds its greatest utility to man by providing "a fixed constant nature of sensible things" in an ever changing universe of being---Metaphysics, Book VII, Part 17
Thus in Aristotle we see the first logical presentation of the law of identity, "the fact that a thing is itself", to help answer the question "what kind of thing should be said to be". However, Aristotle never claimed that [A = A, 1 = 1, or A ≡ A], none of which correspond symbolically to "the fact that a thing is itself," for the simple reason that Aristotle never explicitly made the claim "thing is thing."
Both Thomas Aquinas
Thomas Aquinas
Thomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...
(Met. IV., lect. 6) and Duns Scotus
Duns Scotus
Blessed John Duns Scotus, O.F.M. was one of the more important theologians and philosophers of the High Middle Ages. He was nicknamed Doctor Subtilis for his penetrating and subtle manner of thought....
(Quaest. sup. Met. IV., Q. 3) follow Aristotle. Antonius Andreas
Antonius Andreas
Antonius Andreas was a Spanish Franciscan theologian, a pupil of Duns Scotus.He was teaching at the University of Lleida in 1315...
, 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 Suarez
Francisco Suárez
Francisco Suárez was a Spanish Jesuit priest, philosopher and theologian, one of the leading figures of the School of Salamanca movement, and generally regarded among the greatest scholastics after Thomas Aquinas....
(Disp. Met. III., § 3) disagreed, also preferring to follow Aristotle.
Leibniz claimed that the law of Identity, which he expresses as 'Everything is what it is,' is the first primitive truth of reason which is affirmative, and the law of noncontradiction
Law of noncontradiction
In classical logic, the law of non-contradiction is the second of the so-called three classic laws of thought. It states that contradictory statements cannot both at the same time be true, e.g...
, is the first negative truth (Nouv. Ess. IV., 2, § i), arguing that "the statement that a thing is what it is, is prior to the statement that it is not another thing" (Nouv. Ess. IV.. 7, § 9). Wilhelm Wundt
Wilhelm Wundt
Wilhelm Maximilian Wundt was a German physician, psychologist, physiologist, philosopher, and professor, known today as one of the founding figures of modern psychology. He is widely regarded as the "father of experimental psychology"...
credits Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
with the symbolic formulation, "A is A."
Locke
John Locke
John Locke FRS , widely known as the Father of Liberalism, was an English philosopher and physician regarded as one of the most influential of Enlightenment thinkers. Considered one of the first of the British empiricists, following the tradition of Francis Bacon, he is equally important to social...
(Essay Concerning Human Understanding IV. vii. iv. ("Of Maxims") says:
J.S. Mill formulates the law as: "Whatever is true in one form of words, is true in every other form of words, which conveys the same meaning" (Exam. of Hamilton, p. 409). Shakespeare has Juliet Capulet
Juliet Capulet
Juliet is one of the title characters in William Shakespeare's tragedy Romeo and Juliet, the other being Romeo. She is the daughter of old Capulet, head of the house of Capulet. The story has a long history that precedes Shakespeare himself....
state the same idea as "A rose by any other name would smell as sweet
A rose by any other name would smell as sweet
"A rose by any other name would smell as sweet" is a quotation from William Shakespeare's play Romeo and Juliet, meant to say that the names of things do not matter, only what things are....
", in the 1597 play Romeo and Juliet
Romeo and Juliet
Romeo and Juliet is a tragedy written early in the career of playwright William Shakespeare about two young star-crossed lovers whose deaths ultimately unite their feuding families. It was among Shakespeare's most popular archetypal stories of young, teenage lovers.Romeo and Juliet belongs to a...
.
African Spir
African Spir
Afrikan Aleksandrovich Špir was a Russian Neo-Kantian philosopher of German descent who wrote primarily in German...
proclaims the law of identity as the fundamental law of knowledge, which is opposed to the changing appearance of the empirical reality.
Ayn Rand
Ayn Rand
Ayn Rand was a Russian-American novelist, philosopher, playwright, and screenwriter. She is known for her two best-selling novels The Fountainhead and Atlas Shrugged and for developing a philosophical system she called Objectivism....
used the "A is A" identity as the basis for a objectivist theory of knowledge. She argued it was axiomatic
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
that "existence exists", and reasoned that existing implies a specific nature and attributes: "A is A"
Language
That everything is necessarily "the same with itself and different from another" is the self-evident first principle of language, for it governs the designation or "identification" of individual concepts within any symbolic language, so as to avoid any ambiguity in the communicating of concepts between the users of that language. Such a principle is necessary because a "symbolic designator" (name, word, sign, etc.) has no inherent meaning of its own, but derives its meaning from the language user who correlates the given designator with a conventionally prescribed concept that has been previously learned. To put it another way, the principle (law) states that although it is permissible to call the same concept by many different names, words, signs, etc., a fact that makes it possible for there to be different languages, it is not permissible, within any single linguistic group, to call different concepts by the same designator, else the users of the language will not know which of the possible concepts they are intended to call to mind when they encounter that designator.Exceptions are only permissible where the users are able to readily discern which of the different concepts they are intended to call to mind by the context in which the designator is used. Since our ability to generate valid conclusions from premises is dependent upon our having a clear understanding of the concepts expressed in those premises, it follows that any ambiguity in the symbolic denotation of those concepts will hamper our ability to reason soundly. It is for this reason that the law of identity is considered the self-evident first principle of thought (reason).
Trivia
In 2002 Jonathon KeatsJonathon Keats
Jonathon Keats is an American conceptual artist and experimental philosopher known for creating large-scale thought experiments. Keats was born in New York City and studied philosophy at Amherst College...
held a petition drive to pass "A = A" as statutory law in Berkeley, California
Berkeley, California
Berkeley is a city on the east shore of the San Francisco Bay in Northern California, United States. Its neighbors to the south are the cities of Oakland and Emeryville. To the north is the city of Albany and the unincorporated community of Kensington...
. Specifically, the proposed law stated that, "every entity shall be identical to itself". Any entity caught being unidentical to itself was to be subject to a fine of up to one tenth of a cent. The law did not pass.
See also
- AristotleAristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
's OrganonOrganonThe Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics... - Laws of thought
- Equality (mathematics)
- DialetheismDialetheismDialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is the belief that there can be a true statement whose negation is also true...
- Gilles DeleuzeGilles DeleuzeGilles Deleuze , was a French philosopher who, from the early 1960s until his death, wrote influentially on philosophy, literature, film, and fine art. His most popular works were the two volumes of Capitalism and Schizophrenia: Anti-Oedipus and A Thousand Plateaus , both co-written with Félix...
Allusions
- Rose is a rose is a rose is a roseRose is a rose is a rose is a roseThe sentence "Rose is a rose is a rose is a rose." was written by Gertrude Stein as part of the 1913 poem Sacred Emily, which appeared in the 1922 book Geography and Plays. In that poem, the first "Rose" is the name of a person...
- I Yam What I YamI Yam What I YamI Yam What I Yam is a Popeye theatrical cartoon short, starring William "Billy" Costello as Popeye, Bonnie Poe as Olive Oyl and Charles Lawrence as Wimpy...
- I Am that I AmI Am that I AmI Am that I Am is a common English translation of the response God used in the Hebrew Bible when Moses asked for His name . It is one of the most famous verses in the Torah...
People
- Keith DonnellanKeith DonnellanKeith Donnellan is a contemporary philosopher and Professor Emeritus of the UCLA department of Philosophy. He has made important contributions to the philosophy of language, most notably to the analysis of proper names and definite descriptions...
- David KaplanDavid Kaplan (philosopher)David Benjamin Kaplan is an American philosopher and logician teaching at UCLA. His philosophical work focuses on logic, philosophical logic, modality, philosophy of language, metaphysics, and epistemology. He is best known for his work on demonstratives, on propositions, and on reference in...
- Saul KripkeSaul KripkeSaul Aaron Kripke is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center...
- Hilary PutnamHilary PutnamHilary Whitehall Putnam is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science...
- Ayn RandAyn RandAyn Rand was a Russian-American novelist, philosopher, playwright, and screenwriter. She is known for her two best-selling novels The Fountainhead and Atlas Shrugged and for developing a philosophical system she called Objectivism....
and ObjectivismObjectivism (Ayn Rand)Objectivism is a philosophy created by the Russian-American philosopher and novelist Ayn Rand . Objectivism holds that reality exists independent of consciousness, that human beings have direct contact with reality through sense perception, that one can attain objective knowledge from perception... - W.V. Quine
- John SearleJohn SearleJohn Rogers Searle is an American philosopher and currently the Slusser Professor of Philosophy at the University of California, Berkeley.-Biography:...
- African SpirAfrican SpirAfrikan Aleksandrovich Špir was a Russian Neo-Kantian philosopher of German descent who wrote primarily in German...