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In modern philosophy, mathematics, and logic, a property is an attribute of an object; 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/Grelling-Nelson paradox. It differs from the logical concept of class by not having any concept of extensionality, and from the philosophical concept of class in that a property is considered to be distinct from the objects which possess it.

In classical Aristotelian terminology, a property (proprium) is one of the Predicables. It is a non-essential quality of a species (like an accident), 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 also described as determinate or determinable. A determinable is a property in a larger group of properties - for example, redness is a determinable property in the property of color. A determinate property is a property from which determinable (or more specific properties) are derived.

In mathematical terminology, given any element of a set X, a certain property p is either true or false. Formally, a property p: X → {true, false}. Any property gives rise in a natural way to the set {x: x has the property p} and the corresponding indicator function.

• Abstraction
• Unary relation

• Stanford Encyclopedia of Philosophy entry

This article incorporates material from property on PlanetMath, which is licensed under the GFDL.

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