Identity (philosophy) - AbsoluteAstronomy.com

Philosophy

Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

, identity, from (“sameness”), is the relation each thing bears just to itself. According to Leibniz's law

Identity of indiscernibles

The identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical if they have all their properties in common. That is, entities x and y are identical if any predicate possessed by x is also possessed by y and vice versa...

two things sharing every attribute

Property (philosophy)

In modern philosophy, logic, and mathematics a property is an attribute of an object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property however differs from individual objects in that...

are not only similar

Similarity

-Specific definitions:Different fields provide differing definitions of similarity:-In computer science:* string metric, aka string similarity* semantic similarity in computational linguistics-In other fields:...

, but are the same thing. The concept of sameness has given rise to the general concept of identity

Identity

-Philosophical topics:* Identity , also called sameness, is whatever makes an entity definable and recognizable* Law of identity, principle of logic stating that an object is the same as itself...

, as in personal identity and social identity

Identity (social science)

Identity is a term used to describe a person's conception and expression of their individuality or group affiliations . The term is used more specifically in psychology and sociology, and is given a great deal of attention in social psychology...

.

An entity

Entity

An entity is something that has a distinct, separate existence, although it need not be a material existence. In particular, abstractions and legal fictions are usually regarded as entities. In general, there is also no presumption that an entity is animate.An entity could be viewed as a set...

can only be fully identical with itself. Any difference

Difference (philosophy)

Difference is a key concept of continental philosophy, denoting the process or set of properties by which one entity is distinguished from another within a relational field or a given conceptual system...

gives rise to a separate identity. Thus identity is whatever makes an entity definable and recognizable, in terms of possessing a set of qualities or characteristics that distinguish it from other entities. In layman

Layman

A layperson or layman is a person who is not an expert in a given field of knowledge. The term originally meant a member of the laity, i.e. a non-clergymen, but over the centuries shifted in definition....

's terms, identity is whatever makes something the same or different.

Logic of identity

In logic

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 identity relation (also called "equality") is normally defined as the binary relation

Binary relation

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = . More generally, a binary relation between two sets A and B is a subset of...

that holds only between a thing and itself. That is, identity is the two-place predicate, "=", such that for all x and y, "x = y" is true

True

True may refer to:* Truth, the state of being in accord with fact or reality-Music:* True , 1996* True , 2002* True , 1983** "True"...

If is a conjunction that can introduce a conditional clause.If may also refer to:-Music:* If , a 1951 hit song by Perry Como.* If , 1970s British progressive jazz-rock band* If...

x is the same thing as y. Identity is transitive

Transitive relation

In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c....

, symmetric

Symmetric relation

In mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.In mathematical notation, this is:...

, and reflexive

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:...

. It is an axiom

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...

of most normal modal logic

Modal logic

Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...

s that for all x and y, if x = y then necessarily y = x. That is, identity does not hold contingently, but of necessity.

Put in these terms (above), it can seem rather trivial, but the point, of course, is that the same number, object, or person, can have different "guises", and it is far from trivial if two or more guises refer to the same same number, object, or person. For example, 1+1=2 because '1+1' and '2' are different "guises" for the same number. Similarly, for personal identity over time, "me today" and "me yesterday" are different guises for the same person.

Metaphysics of identity

Metaphysicians, and sometimes philosophers of language and mind, ask other questions:

What does it mean for an object to be the same as itself?
If x and y are identical (are the same thing), must they always be identical? Are they necessarily identical?
What does it mean for an object to be the same, if it change
Identity and change
The relationship between identity and change in the philosophical field of metaphysics seems, at first glance, deceptively simple, and belies the complexity of the issues involved. This article explores "the problem of change and identity".- Change :...

s over time? (Is apple_t the same as apple_t+1?)
If an object's parts are entirely replaced over time, as in the Ship of Theseus
Ship of Theseus
The Ship of Theseus, also known as Theseus' paradox, or various variants, notably grandfather's axe and Trigger's Broom is a paradox that raises the question of whether an object which has had all its component parts replaced remains fundamentally the same object.The paradox is most notably...

example, in what way is it the same?

The Law of identity

Law of identity

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 ; While this can also be listed as A ≡ A this is redundant Any reflexive relation upholds the law of identity...

originates from classical antiquity

Classical antiquity

Classical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, comprising the interlocking civilizations of ancient Greece and ancient Rome, collectively known as the Greco-Roman world...

. The modern formulation of identity is that of Gottfried Leibniz

Gottfried Leibniz

Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

, who held that x is the same as y if and only if

If and only if

In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....

every predicate true of x is true of y as well.

Leibniz's ideas have taken root in the philosophy of mathematics

Philosophy of mathematics

The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...

, where they have influenced the development of the predicate calculus as Leibniz's law. Mathematicians sometimes distinguish identity from equality. More mundanely, an identity in mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

may be an equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...

that holds true for all values of a variable

Variable (mathematics)

In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...

. Hegel argued that things are inherently self-contradictory and that the notion of something being self-identical only made sense if it were not also not-identical or different from itself and did not also imply the latter. In Hegel's words, "Identity is the identity of identity and non-identity." More recent metaphysicians have discussed trans-world identity -- the notion that there can be the same object in different possible worlds. An alternative to trans-world identity is the counterpart relation in Counterpart theory

Counterpart theory

In philosophy, specifically in the area of modal metaphysics, counterpart theory is an alternative to standard possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but differs in certain important respects from the Kripkean view...

. It is a similarity relation that rejects trans-world individuals and instead defends an objects counterpart - the most similar object.

Qualitative versus numerical identity

Arbitrary objects a and b can be said to be qualitatively identical if a and b are duplicates, that is, if a and b are exactly similar in all respects, that is, if a and b have all qualitative properties

Qualitative properties

Qualitative properties are properties that are observed and can generally not be measured with a numerical result. They are contrasted to quantitative properties which have numerical characteristics....

in common. Examples of this might be two wine glasses made in the same wine glass factory on the same production line (at least, for a relaxed standard of exact similarity), or a carbon atom in one's left hand and a carbon atom in one's right hand.

Alternatively, a and b can be said to be numerically identical if a and b are one and the same thing, that is, if a is b, that is, if there is only one thing variously called "a" and "b". For example, Clark Kent

Clark Kent

Clark Kent is a fictional character created by Jerry Siegel and Joe Shuster. Appearing regularly in stories published by DC Comics, he debuted in Action Comics #1 and serves as the civilian and secret identity of the superhero Superman....

is numerically identical with Superman

Superman

Superman is a fictional comic book superhero appearing in publications by DC Comics, widely considered to be an American cultural icon. Created by American writer Jerry Siegel and Canadian-born American artist Joe Shuster in 1932 while both were living in Cleveland, Ohio, and sold to Detective...

in the sense that there is only one person (who happens to wear different clothes at different times). This relationship is expressed in mathematics with the "=" symbol, e.g., a = b, or Clark Kent = Superman.

External references

General Information

Stanford Encyclopedia of Philosophy: Identity, First published Wed Dec 15, 2004; substantive revision Sun Oct 1, 2006.
Stanford Encyclopedia of Philosophy: Identity over time. First published Fri 18 March 2005.
Stanford Encyclopedia of Philosophy: Personal identity. First published Tue Aug 20, 2002; substantive revision Tue Feb 20, 2007.
Stanford Encyclopedia of Philosophy: Relative identity. First published Mon 22 April 2002.
Erich Fromm Interview Excerpt. youtube.com.

Citations

Books and publications

Andrew Bowie, Schelling and modern European philosophy. Routledge. Page 55-90. ISBN 0415103460
James, W., & Perry, R. B. (2006). Essays in radical empiricism. New York: Longmans, Green, and co. Page 134, 197, 202. (lib.uchicago.edu)
MacVannel, J. A. (1967). Hegel's doctrine of the will. New York: AMS Press.
Hegel, G. W. F., & Sterrett, J. M. (1893). The ethics of Hegel; translated selections from his "Rechtsphilosophie,". Boston: Ginn and Co.
Baldwin, J. M. (1913). History of psychology; a sketch and an interpretation. A history of the sciences. New York and London: G.P. Putnam's Sons.
Dessoir, M. (1912). Outlines of the history of psychology. New York: The Macmillan company.
Shaw, C. G. (1908). The precinct of religion in the culture of humanity. London: S. Sonnenschein.
Alexander, A. B. D. (1907). A short history of philosophy. Glasgow: J. Maclehose and Sons.
MacVannel, J. A. (1905). The educational theories of Herbart and Froebel. New York: Teachers college, Columbia University.
Schade, A., & Rocholl, R. (1899). The philosophy of history. Cleveland, O.: A. Schade. Page 140 - 142.
Külpe, O. (1897). Introduction to philosophy: a handbook for students of psychology, logic, ethics, æsthetics and general philosophy. London: S. Sonnenschein.
Courtney, W. L. (1895). Constructive ethics, a review of modern moral philosophy in its three stages of interpretation, criticism, and reconstruction. London: Chapman and Hall.
Manning, Jacob Merrill (1872). Half truths and the truth. Oxford University.
Paksoy, H.B. (2001) IDENTITIES: How Governed, Who Pays? Florence: European University/Carrie.

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Logic of identity

Metaphysics of identity

Qualitative versus numerical identity

See also

External references