Information about Identity (philosophy)

In philosophy, identity is whatever makes an entity definable and recognizable, in terms of possessing a set of qualities or characteristics that distinguish it from entities of a different type. Or, in layman's terms, identity is whatever makes something the or .

Logic of identity

In logic, the identity relation is normally defined as the relation 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 iff x is the same thing as y. Identity is transitive, symmetric, and reflexive. It is an axiom of most normal modal logics that for all x, if x = x then necessarily x = x. (These definitions are of course inapplicable in some areas of quantified logic, such as fuzzy logic and fuzzy set theory, and with respect to vague objects.)

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 changes over time? (Is applet the same as applet+1?)
  • If an object's parts are entirely replaced over time, as in the Ship of Theseus example, in what way is it the same?
A traditional view is that of Gottfried Leibniz, who held that x is the same as y if and only if every predicate true of x is true of y as well.

Leibniz's ideas have taken root in the philosophy of mathematics, 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 may be an equation that holds true for all values of a variable. 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. 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 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 shoulder (perhaps true even for the most strict standard of exact similarity).

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 is numerically identical with Superman 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.

See also

People: Friedrich Wilhelm Joseph Schelling, Baruch Spinoza
General: Being positive philosophy, The Golden Rule, Personal identity, Shunyata, Pseudonymity, ontological difference
Identity:Recognition of human individuals, Cultural identity Digital identity, Ethnic identity, Social identity, absolute identity, Reputation, Online identity, Identity theft, Counterpart theory

External articles and references

Books and publications

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 Mar, 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 Apr, 2002.
  • Erich Fromm Interview Excerpt. youtube.com.
Philosophy is the discipline concerned with questions of how one should live (ethics); what sorts of things exist and what are their essential natures (metaphysics); what counts as genuine knowledge (epistemology); and what are the correct principles of reasoning (logic).
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layman or layperson originated from the use of the term laity, but over the centuries, changed definition to mean a person who is a non-expert in a given field of knowledge.
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Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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In mathematics, a binary relation (or a dyadic or 2-place relation) is an arbitrary association of elements within a set or with elements of another set.

An example is the "divides" relation between the set of prime numbers P and the set of integers
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common. We use the notation P(x) to denote a sentence or statement P concerning the variable object x. The set defined by P(x) written , is just a collection of all the objects for which P is sensible and true.

For instance, is the set .
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True is the adjectival form of truth.

True may also refer to:

In business:
  • True Corporation, a Thai communications group whose subsidiaries include True Internet, True Move and True Visions
In music:

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IFF, Iff or iff can stand for:
  • if and only if, a mathematical and logical connector indicating that either both statements are true or both are false
  • Identification friend or foe, an electronic radio based identification system utilizing transponders

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In mathematics, a binary relation R over a set X is transitive if it holds for all a, b, and c in X, that if a is related to b and b is related to c, then a is related to c.
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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.
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In set theory, a binary relation can have, among other properties, reflexivity or irreflexivity.

At least in this context, (binary) relation (on X) always means a relation on X×X, or in other words from a set X into itself.
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axiom is a sentence or proposition that is not proved or demonstrated and is considered as self-evident or as an initial necessary consensus for a theory building or acceptation.
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In formal logic, a modal logic is any logic for handling modalities: concepts like possibility, existence, and necessity. Logics for handling a number of other ideas, such as eventually, formerly, can, could
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Fuzzy Logic may refer to:
  • Fuzzy Logic (album), the debut album by the Super Furry Animals
  • Fuzzy logic, an application of fuzzy set theory

For the music album, see Fuzzy Logic (album)


Fuzzy logic
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Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets have been introduced by Lotfi A. Zadeh (1965) as an extension of the classical notion of set. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent
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Change denotes the transition that occurs between one state to another.

Physical

Throughout history, change has been defined by varying points of view. In ancient Greek philosophy, while Herachical position may have an influence on the perception of change.
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The Ship of Theseus is a paradox also known as Theseus' paradox. It raises the question of whether an object, which has had all its component parts replaced, remains fundamentally the same.
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Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz
Born July 1 (June 21 Old Style) 1646
Leipzig, Electorate of Saxony
Died November 14 1716
Hannover, Hanover
Nationality German
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common. We use the notation P(x) to denote a sentence or statement P concerning the variable object x. The set defined by P(x) written , is just a collection of all the objects for which P is sensible and true.

For instance, is the set .
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Philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics.

Recurrent themes include:

* What are the sources of mathematical subject matter?

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predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas contain variables which can be quantified.
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The identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical (are one and the same entity), if and only if they have all their properties in common.
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equal if and only if they are precisely the same in every way. The complementary notion is distinctness. This defines a binary relation, equality, denoted by the sign of equality "=" in such a way that the statement "x = y" means that x
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Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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equation is a mathematical statement, in symbols, that two things are the same (or equivalent). Equations are written with an equal sign, as in
.


The equation above is an example of an equality: a proposition which states that two constants are equal.
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variable (IPA pronunciation: [ˈvæɹiəbl]) (sometimes called a pronumeral) is a symbolic representation denoting a quantity or expression.
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Georg Wilhelm Friedrich Hegel (IPA: [ˈgeɔʁk ˈvɪlhɛlm ˈfʁiːdʁɪç ˈheːgəl]
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Georg Wilhelm Friedrich Hegel (IPA: [ˈgeɔʁk ˈvɪlhɛlm ˈfʁiːdʁɪç ˈheːgəl]
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Qualitativ e properties are properties that are observed and can generally not be measured. It should be mentioned that qualitative properties are most of the time at least as important as quanti tative properties.
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