property roughly, an attribute, characteristic, feature, trait, or aspect.
Intensionality. There are two salient ways of talking about properties. First, as predicables or instantiables. For example, the property red is predicable of red objects; they are instances of it. Properties are said to be intensional entities in the sense that distinct properties can be truly predicated of (i.e., have as instances) exactly the same things: the property of being a creature with a kidney & the property of being a creature with a heart, though these two sets have the same members. Properties thus differ from sets (collections, classes); for the latter satisfy a principle of extensionality: they are identical if they have the same elements. The second salient way of talking about properties is by means of property abstracts such as ‘the property of being F’. Such linguistic expressions are said to be intensional in the following semantical (vs. ontological) sense: ‘the property of being F’ and ‘the property of being G’ can denote different properties even though the predicates ‘F’ and ‘G’ are true of exactly the same things. The standard explanation (Frege, Russell, Carnap, et al.) is that ‘the property of being F’ denotes the property that the predicate ‘F’ expresses. Since predicates ‘F’ and ‘G’ can be true of the same things without being synonyms, the property abstracts ‘being F’ and ‘being G’ can denote different properties. Identity criteria. Some philosophers believe that properties are identical if they necessarily have the same instances. Other philosophers hold that this criterion of identity holds only for a special subclass of properties – those that are purely qualitative – and that the properties for which this criterion does not hold are all ‘complex’ (e.g., relational, disjunctive, conditional, or negative properties). On this theory, complex properties are identical if they have the same form and their purely qualitative constituents are identical.
Ontological status. Because properties are a kind of universal, each of the standard views on the ontological status of universals has been applied to properties as a special case. Nominalism: only particulars (and perhaps collections of particulars) exist; therefore, either properties do not exist or they are reducible (following Carnap et al.) to collections of particulars (including perhaps particulars that are not actual but only possible). Conceptualism: properties exist but are dependent on the mind. Realism: properties exist independently of the mind. Realism has two main versions. In rebus realism: a property exists only if it has instances. Ante rem realism: a property can exist even if it has no instances. For example, the property of being a man weighing over ton has no instances; however, it is plausible to hold that this property does exist. After all, this property seems to be what is expressed by the predicate ‘is a man weighing over a ton’. Essence and accident. The properties that a given entity has divide into two disjoint classes: those that are essential to the entity and those that are accidental to it. A property is essential to an entity if, necessarily, the entity cannot exist without being an instance of the property. A property is accidental to an individual if it is possible for the individual to exist without being an instance of the property. Being a number is an essential property of nine; being the number of the planets is an accidental property of nine. Some philosophers believe that all properties are either essential by nature or accidental by nature. A property is essential by nature if it can be an essential property of some entity and, necessarily, it is an essential property of each entity that is an instance of it. The property of being self-identical is thus essential by nature. However, it is controversial whether every property that is essential to something must be essential by nature. The following is a candidate counterexample. If this automobile backfires loudly on a given occasion, loudness would seem to be an essential property of the associated bang. That particular bang could not exist without being loud. If the automobile had backfired softly, that particular bang would not have existed; an altogether distinct bang – a soft bang – would have existed. By contrast, if a man is loud, loudness is only an accidental property of him; he could exist without being loud. Loudness thus appears to be a counterexample: although it is an essential property of certain particulars, it is not essential by nature. It might be replied (echoing Aristotle) that a loud bang and a loud man instantiate loudness in different ways and, more generally, that properties can be predicated (instantiated) in different ways. If so, then one should be specific about which kind of predication (instantiation) is intended in the definition of ‘essential by nature’ and ‘accidental by nature’. When this is done, the counterexamples might well disappear. If there are indeed different ways of being predicated (instantiated), most of the foregoing remarks about intensionality, identity criteria, and the ontological status of properties should be refined accordingly. See also ESSENTIALISM , INTENSIONALITY , RELATIO. G.B.