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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. These five broad types of question are called analytical or logical, epistemological, ethical, metaphysical, and aesthetic respectively. ...
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. 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 arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
In mathematics, the concept of binary relation, sometimes called dyadic relation, is exemplified by such ideas as is greater than and is equal to in arithmetic, or is congruent to in geometry, or is an element of or is a subset of in set theory. ...
In mathematics, a predicate is a relation. ...
When someone sincerely agrees with an assertion, they might claim that it is the truth. ...
↔ ⇔ ≡ For other possible meanings of iff, see IFF. In mathematics, philosophy, logic and technical fields that depend on them, iff is used as an abbreviation for if and only if. Common alternative phrases to iff or if and only if include Q is necessary and sufficient for P and P...
Identity is transitive, symmetric, and reflexive. 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. ...
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 logic and mathematics, a binary relation R over a set X is reflexive if for all a in X, a is related to itself. ...
It is an axiom of most normal modal logics that for all x, if x = x then necessarily x = x. In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. ...
A modal logic, or (less commonly) intensional logic, is a logic that deals with sentences that are qualified by modalities such as can, could, might, may, must, possibly, necessarily, eventually, etc. ...
(These definitions are of course inapplicable in some area 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. The Ship of Theseus is a replacement paradox also known as Theseuss paradox. ...
Gottfried Wilhelm von Leibniz (also Leibnitz) (July 1 (June 21 Old Style) 1646, Leipzig – November 14, 1716, Hanover) was a German polymath, deemed a genius in his lifetime and since. ...
In mathematics, a predicate is a relation. ...
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. Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: why is mathematics useful in describing nature?, in which sense(s), if any, do mathematical entities such as numbers exist? and why and how are mathematical statements true?. Various approaches to answering these questions will...
First-order predicate calculus or first-order logic (FOL) permits the formulation of quantified statements such as there exists an x such that. ...
The identity of indiscernibles, also known as Leibnizs Law, is an ontological principle first forumlated by German philosopher Göttfried Wilhelm Leibniz. ...
In mathematics, two mathematical objects are considered equal if they are precisely the same in every way. ...
Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has media related to: Mathematics Interactive Mathematics Miscellany and Puzzles — A collection of articles on various math topics, with interactive Java...
In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. ...
In computer science and mathematics, a variable is a symbol denoting a quantity or symbolic representation. ...
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.
Qualitative vs. 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). so. ...
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 This article may be confusing for some readers, and should be edited to enhance clarity. ...
Digital Identity is the digital representation of a set of claims made by one Digital entity about itself or another Digital entity. ...
Identity theft (or identity fraud) is the deliberate assumption of another persons identity, usually to gain access to their finances or frame them for a crime. ...
A persons online identity is the facts that are known of a person through means of the internet. ...
In philosophy, the issue of personal identity concerns the conditions under which a person at one time is the same person at another time. ...
In cryptography, pseudonymity is the ability to prove a consistent identity without revealing oneself, instead using a pseudonym. ...
Recognition of acquaintances From nearby, a human individual is mainly recognized by his or her face. ...
Look up reputation in Wiktionary, the free dictionary. ...
Social identity is a theory formed by Henri Tajfel and John Turner to understand the psychological basis of intergroup discrimination. ...
External links - Stanford Encyclopedia of Philosophy:
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