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In modern philosophy
Philosophy

Philosophy is the study of general problems concerning matters such as existence, knowledge, truth, beauty, justice, validity, mind, and language....
, mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, and logic
Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
, a property is an attribute
Attribute

The word "attribute" can refer to:* In philosophy, property , an abstraction of a characteristic of an entity or substance* In art, an object that identifies a figure, most commonly referring to objects held by saints - see emblem...
 of an object
Object (philosophy)

In philosophy, an object is a thing, an entity, or a being. This may be taken in several senses.In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all....
; thus 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. Properties are therefore subject to the Russell's paradox
Russell's paradox

Part of fundamental mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory of Gottlob Frege leads to a contradiction....
/Grelling-Nelson paradox
Grelling-Nelson paradox

The Grelling?Nelson paradox is a semantic self-referential paradox formulated in 1908 by Kurt Grelling and Leonard Nelson and sometimes mistakenly attributed to the German philosopher and mathematician Hermann Weyl....
. It differs from the logical concept of class
Class (set theory)

In set theory and its applications throughout mathematics, a class is a collection of Set which can be unambiguously defined by a property that all its members share....
 by not having any concept of extensionality
Extensionality

In logic, extensionality refers to principles that judge objects to be equal if they have the same external properties. It is the opposite concept of intensionality, which is concerned with whether two descriptions are intended to be the same or not....
, and from the philosophical concept of class
Class (philosophy)

Philosophers sometimes distinguish classes from type and natural kind. We can talk about the class of human beings, just as we can talk about the type , human being, or humanity....
 in that a property is considered to be distinct from the objects which possess it.

In classical Aristotelian
Aristotelian

Aristotelian matters may refer to:* Aristotle * List of teachings attributed to Aristotle* Aristotelianism, the philosophical tradition begun by Aristotle...
 terminology, a property (proprium) is one of the Predicables
Predicables

Predicables is, in term logic, a term applied to a Categorization of the possible relations in which a Predicate may stand to its Subject . The list given by the schoolmen and generally adopted by modern logicians is based on the original fivefold classification given by Aristotle : definition , genus , differentia , property , accident...
.






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In modern philosophy
Philosophy

Philosophy is the study of general problems concerning matters such as existence, knowledge, truth, beauty, justice, validity, mind, and language....
, mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, and logic
Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
, a property is an attribute
Attribute

The word "attribute" can refer to:* In philosophy, property , an abstraction of a characteristic of an entity or substance* In art, an object that identifies a figure, most commonly referring to objects held by saints - see emblem...
 of an object
Object (philosophy)

In philosophy, an object is a thing, an entity, or a being. This may be taken in several senses.In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all....
; thus 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. Properties are therefore subject to the Russell's paradox
Russell's paradox

Part of fundamental mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory of Gottlob Frege leads to a contradiction....
/Grelling-Nelson paradox
Grelling-Nelson paradox

The Grelling?Nelson paradox is a semantic self-referential paradox formulated in 1908 by Kurt Grelling and Leonard Nelson and sometimes mistakenly attributed to the German philosopher and mathematician Hermann Weyl....
. It differs from the logical concept of class
Class (set theory)

In set theory and its applications throughout mathematics, a class is a collection of Set which can be unambiguously defined by a property that all its members share....
 by not having any concept of extensionality
Extensionality

In logic, extensionality refers to principles that judge objects to be equal if they have the same external properties. It is the opposite concept of intensionality, which is concerned with whether two descriptions are intended to be the same or not....
, and from the philosophical concept of class
Class (philosophy)

Philosophers sometimes distinguish classes from type and natural kind. We can talk about the class of human beings, just as we can talk about the type , human being, or humanity....
 in that a property is considered to be distinct from the objects which possess it.

In classical Aristotelian
Aristotelian

Aristotelian matters may refer to:* Aristotle * List of teachings attributed to Aristotle* Aristotelianism, the philosophical tradition begun by Aristotle...
 terminology, a property (proprium) is one of the Predicables
Predicables

Predicables is, in term logic, a term applied to a Categorization of the possible relations in which a Predicate may stand to its Subject . The list given by the schoolmen and generally adopted by modern logicians is based on the original fivefold classification given by Aristotle : definition , genus , differentia , property , accident...
. It is a non-essential
Essence

In philosophy, essence is the attribute or set of attributes that make an object or substance theory what it fundamentally is, and which it has by metaphysical necessity, and without which it loses its identity....
 quality of a species (like an accident
Accident (philosophy)

Accident, sumbebekos as used in philosophy, is an attribute which may or may not belong to a subject, without affecting its essence. The use of accident has been employed throughout the history of philosophy with several distinct meanings....
), but a quality which is nevertheless characteristically present in members of that species (and in no others). For example, "ability to laugh" may be considered a special characteristic of human beings. However, "laughter" is not an essential quality of the species human, whose Aristotelian definition of "rational animal" does not require laughter. Thus, in the classical framework, properties are characteristic, but non-essential, qualities.

A property may be classified as either determinate or determinable. A determinable property is one that can get more specific. For example, color is a determinable property because it can be restricted to redness, blueness, etc. A determinate property is one that cannot become more specific. This distinction may be useful in dealing with issues of identity
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....
.

In mathematical terminology
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, a property p defined for all elements of a set X is usually defined as a function p: X → , that is true whenever the property holds; or equivalently, as the subset of X for which p holds; i.e. the set ; p is its indicator function
Indicator function

In mathematics, an indicator function or a characteristic function is a Function defined on a Set that indicates membership of an element in a subset of ....
. It may be objected (see above) that this defines merely the extension
Extension (semantics)

In any of several studies that treat the use of sign s, for example in linguistics, logic, mathematics, semantics, and semiotics, the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs...
 of a property, and says nothing about what causes the property to hold for exactly those values.

See also

  • Abstraction
    Abstraction

    Abstraction is the process or result of generalization by reducing the information content of a concept or an observable phenomenon, typically in order to retain only information which is relevant for a particular purpose....
  • Unary relation


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