property (philosophy)
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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. 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.
(1) A determinate property is one that cannot become more specific. This distinction may be useful in dealing with issues of
identity.
(2)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.
See also
References
-
[JOURNAL,weblink Divine hiddenness and the nature of belief, Ted Poston and Trent Dougherty, Religious Studies, Cambridge University Press, 2007-06-01, 2008-02-02]
