Property (philosophy)
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In modern philosophy, mathematics, and logic, a property is an attribute of an object; 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. If, however, for every predicate there is a corresponding property, then properties are subject to 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 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.
In mathematical terminology, a property p defined for all elements of a set X is usually defined as a function p: X → {true, false}, that is true whenever the property holds; or equivalently, as the subset of X for which p holds; i.e. the set {x| p(x) = true}; p is its indicator function. It may be objected (see above) that this defines merely the extension of a property, and says nothing about what causes the property to hold for exactly those values.
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