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Sameness
In philosophy, identity (from , "sameness") is the relation each thing bears only to itself. The notion of identity gives rise to many philosophical problems, including the identity of indiscernibles (if ''x'' and ''y'' share all their properties, are they one and the same thing?), and questions about change and personal identity over time (what has to be the case for a person ''x'' at one time and a person ''y'' at a later time to be one and the same person?). It is important to distinguish between ''qualitative identity'' and ''numerical identity''. For example, consider two children with identical bicycles engaged in a race while their mother is watching. The two children have the ''same'' bicycle in one sense (''qualitative identity'') and the ''same'' mother in another sense (''numerical identity''). This article is mainly concerned with ''numerical identity'', which is the stricter notion. The philosophical concept of identity is distinct from the better-known notion of id ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity (social Science)
Identity is the qualities, beliefs, personality traits, appearance, and/or expressions that characterize a person or group.Compare ''Collins Dictionary of Sociology'', quoted in In sociology, emphasis is placed on collective identity, in which an individual's identity is strongly associated with role-behavior or the collection of group memberships that define them. According to Peter Burke, "Identities tell us who we are and they announce to others who we are." Identities subsequently guide behavior, leading "fathers" to behave like "fathers" and "nurses" to act like "nurses." In psychology, the term "identity" is most commonly used to describe personal identity, or the distinctive qualities or traits that make an individual unique. Identities are strongly associated with self-concept, self-image (one's mental model of oneself), self-esteem, and individuality. Individuals' identities are situated, but also contextual, situationally adaptive and changing. Despite their flu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Of Indiscernibles
The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities ''x'' and ''y'' are identical if every predicate possessed by ''x'' is also possessed by ''y'' and vice versa. It states that no two distinct things (such as snowflakes) can be exactly alike, but this is intended as a metaphysical principle rather than one of natural science. A related principle is the indiscernibility of identicals, discussed below. A form of the principle is attributed to the German philosopher Gottfried Wilhelm Leibniz. While some think that Leibniz's version of the principle is meant to be only the indiscernibility of identicals, others have interpreted it as the conjunction of the identity of indiscernibles and the indiscernibility of identicals (the converse principle). Because of its association with Leibniz, the indiscernibility of identicals is sometimes known as Leibniz's l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Personal Identity
Personal identity is the unique numerical identity of a person over time. Discussions regarding personal identity typically aim to determine the necessary and sufficient conditions under which a person at one time and a person at another time can be said to be the person, persisting through time. In philosophy, the problem of personal identity is concerned with how one is able to identify a single person over a time interval, dealing with such questions as, "What makes it true that a person at one time is the same thing as a person at another time?" or "What kinds of things are we persons?" In contemporary metaphysics, the matter of personal identity is referred to as the ''diachronic problem'' of personal identity. The '' synchronic problem'' concerns the question of what features and traits characterize a person at a given time. Analytic philosophy and continental philosophy both inquire about the nature of identity. Continental philosophy deals with conceptually maintaini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ship Of Theseus
The Ship of Theseus is a thought experiment about whether an object that has had all of its original components replaced remains the same object. According to legend, Theseus, the mythical Greek founder-king of Athens, had rescued the children of Athens from King Minos after slaying the minotaur and then escaped on a ship to Delos. Every year, the Athenians commemorated this legend by taking the ship on a pilgrimage to Delos to honor Apollo. The question was raised by ancient philosophers: After several centuries of maintenance, if every part of the Ship of Theseus had been replaced, one at a time, was it still the same ship? In contemporary philosophy, this thought experiment has applications to the philosophical study of identity over time, and has inspired a variety of proposed solutions in contemporary philosophy of mind concerned with the persistence of personal identity. History In its original formulation, the "Ship of Theseus" paradox concerns a debate over whether ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate (logic)
In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P(a), the symbol P is a predicate which applies to the individual constant a. Similarly, in the formula R(a,b), R is a predicate which applies to the individual constants a and b. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R(a,b) would be true on an interpretation if the entities denoted by a and b stand in the relation denoted by R. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation used to interpret them. While first-order logic only includes predicates which apply to individual constants, other logics may allow predicates which apply to other predicates. Predicates in different systems * In propositional logic, atomic formulas are sometimes regarded as zero-place predicates In a sense, these are nul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. History The origin of mathematics is subject to arguments and disagreements. Whether the birth of mathematics was a random happening or induced by necessity during the development of other subjects, like physics, is still a matter of prolific debates. Many thinkers have contributed their ideas concerning the nature of mathematics. Today, some philosophers of mathematics aim to give accounts of this form of inquiry and its products as they stand, while others emphasize a role for themselves th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate Calculus
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Predicate or predication may refer to: * Predicate (grammar), in linguistics * Predication (philosophy) * several closely related uses in mathematics and formal logic: ** Predicate (mathematical logic) ** Propositional function ** Finitary relation, or n-ary predicate ** Boolean-valued function ** Syntactic predicate, in formal grammars and parsers **Functional predicate *Predication (computer architecture) *in United States law, the basis or foundation of something ** Predicate crime **Predicate rules, in the U.S. Title 21 CFR Part 11 * Predicate, a term used in some European context for either nobles' honorifics or for nobiliary particles See also * Predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quanti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between and is written , and pronounced equals . The symbol "" is called an "equals sign". Two objects that are not equal are said to be distinct. For example: * x=y means that and denote the same object. * The identity (x+1)^2=x^2+2x+1 means that if is any number, then the two expressions have the same value. This may also be interpreted as saying that the two sides of the equals sign represent the same function. * \ = \ if and only if P(x) \Leftrightarrow Q(x). This assertion, which uses set-builder notation, means that if the elements satisfying the property P(x) are the same as the elements satisfying Q(x), then the two uses of the set-builder notation define the same set. This property is often expressed as "two sets that have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Antiquity
Classical antiquity (also the classical era, classical period or classical age) is the period of cultural history between the 8th century BC and the 5th century AD centred on the Mediterranean Sea, comprising the interlocking civilizations of ancient Greece and ancient Rome known as the Greco-Roman world. It is the period in which both Greek and Roman societies flourished and wielded huge influence throughout much of Europe, North Africa, and Western Asia. Conventionally, it is taken to begin with the earliest-recorded Epic Greek poetry of Homer (8th–7th-century BC), and continues through the emergence of Christianity (1st century AD) and the fall of the Western Roman Empire (5th-century AD). It ends with the decline of classical culture during late antiquity (250–750), a period overlapping with the Early Middle Ages (600–1000). Such a wide span of history and territory covers many disparate cultures and periods. ''Classical antiquity'' may also refer to an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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