Properties

1. The nature of properties

What was said in the opening section serves to introduce the topic of properties. But it does not amount to a theory of properties. Too many important questions remain. For instance, do properties exist outside of space and time? Platonists take properties to be transcendent entities: entities that exist outside of space and time. Aristotelians take properties to be immanent entities: entities that exist in space and time. Again, can a property exist if nothing has that property? Platonists typically say yes, Aristotelians typically say no. A related question is whether properties exist necessarily. For example, even if it is a contingent truth that some red things exist, is it a necessary truth that the property of being red exists?

Here is another issue. Just as you may appear to cite various properties of a tomato, you may also appear to describe your neighbour’s tomatoes as having the same properties - as being the same colour and age as yours. But how can distinct individuals be the same in any respect? Your tomato and your neighbour’s are distinct tomatoes. So how can your tomato and your neighbour’s literally have the same redness, the same size, or the same shape? Platonists and Aristotelians think that they can. In modern terminology, a distinction is drawn between numerical and qualitative identity (see Identity §1). No tomato is numerically identical with any distinct tomato. But distinct tomatoes may be qualitatively identical in many respects. Platonists and Aristotelians take tomatoes to be qualitatively identical in respect of redness if and only if the tomatoes have one and the same (numerically identical) property, namely the property being red. On this view, a property is a repeatable entity which distinct particulars can each have at the same time. Whereas tomatoes are particulars, properties are not; they are universals. (see Particulars; Universals)

Other philosophers disagree. According to them, properties are just as much particulars as tomatoes are. One view along these lines, trope theory (see Particulars §4) says that your tomato has a particular property of redness, and your neighbour’s tomato has another particular property of redness. There is nothing that is literally identical between the two tomatoes. Instead, their particular rednesses – their red tropes - exactly resemble each other. It is only in that sense that the two tomatoes are both red. (For this view, see Campbell (1981)).

Other views that take properties to be particulars are available. Some philosophers take properties to be sets. A non-modal version of this view takes the property of being red to be the set of its instances – the set of all and only red particulars. A modal version of this view takes being red to be the set of its actual and possible instances – the set of all actual and possible red particulars. (For this modal version, see Lewis (1983)). Such views are broadly reductive. They seek to reduce talk of properties to talk of certain sets. An advantage of such views is that the resources of set theory (and, in Lewis’s case, possible worlds semantics) can be put to direct use in studying the nature of properties. (see Possible worlds; Set theory)

What partly guides each of these and other views of properties are thoughts about the explanatory role of properties: what theoretical work properties can undertake (see Swoyer (1999)). Philosophers want properties to perform certain roles in their chosen projects. Since these projects may be diverse ones in metaphysics, semantics, or epistemology, different philosophers may write different ‘job specifications’ for properties. Perhaps no single category of entity can meet every, or even most, of these specifications. As always, philosophers need to take care that they are not talking past each other when they argue about what properties are supposed to be, or argue about whether properties exist.