Nominalism

Nominalism is a family of views in philosophy that deny the existence of universals. A variety of different nominalist views exist which attempt to provide an account of the phenomena that a theory of properties needs to explain: general term reference, predicate reference and causal similarity. Nominalism also refers to positions in other areas of philosophy that deny the existence of abstract objects; the term can often be suffixed by what position one is denying - e.g. "nominalism about universals".

Generally, nominalist theories about properties must ground said theories in the instances themselves, although trope theory allows the properties to be separable instances which themselves have some kind of non-universal relations.

Class nominalism
The most primitive nominalist theory is that of class nominalism, which asserts that the meaning of a general term or predicate is simply the class of objects which satisfy this. D. M. Armstrong attributes this view to G. E. Moore.

Class nominalism seems to provide a relatively simple ontology for general terms and one-place predicates like "is red" or "contains nitrogen", and unlike other explanations - realist or nominalist - set theory provides a mature understanding of classes including identity conditions. Relations are slightly more complicated to explain in a class nominalist account, but can be done by constructing a class of relation-classes, where each relation class is a pair.

Thus $$aRb$$ and $$cRd$$ can be reduced to the set $${, }$$, and further reduced (using the Wiener-Kuratowski procedure of converting ordered pairs into unordered classes of classes) to $${{{a}, {a, b}}, {{c}, {c, d}}}$$.

To critics of this position, it seems highly counterintuitive - there must be more to being red than simply being in the class of red things. Similarly, there are many more classes that exist than there are properties. Property-talk tends to see being a cat as a separate property from being red, and would state that if you had a red cat, it has the property of redness and the property of being a cat. This split is usually made with reference to our common modal intuitions - you can imagine something being red without being a cat and something being a cat but not being red. There are, then, a class of classes that are essentially arbitrary and a class of classes that are non-arbitrary - the real properties. Class nominalism seems to fail to account for this common intuition about properties.

Coextensive classes also provide a problem for class nominalist theories - the classic example in philosophy is of the properties is cordate (has a heart) and is renate (has a liver). One can grant that the class of cordates is coextensive with the class of renates, but state that the properties are different. One can solve problems of this sort with an appeal to modal realism, but many wish to avoid this on Ockhamist grounds. Since relations are just classes-of-classes, the coextension problem can apply to relations also.

Similarly, negations of properties can have classes, but we don't generally talk of something being "not red".

Natural class nominalism
A modified form of class nominalism held by Anthony Quinton posits that certain classes are natural classes, classes which have naturally go together.

A natural class is unanalyzable, but is a class which we would naturally pick out. If one put a number of bottles on a table and asked people to sort them into rough sets, they may do so on the basis of colour, shape, material, whether they are corked or capped, or even the type or brand of the contents within. The classes which are thus constructed would be natural classes, while some kind of "grue"-like category of bottles that are either brown ale bottles or have not been uncorked is not natural, and thus not a property. Those sceptical of the natural class position need only point out that this is an unnecessary epistemological intrusion into an ontological debate.

Resemblance nominalism
Resemblance nominalism is a position that holds that general terms and predicates ground their meaning in the resemblance between instances. What makes sentences using the word "hairy" meaningful is the resemblance that exists between all hairy things - between cats, dogs, humans, and other animals that are hairy, as well as wigs and bearskin rugs. A resemblance, then, is a relational property that exists between two objects, and a term can refer to a web of such close relations. Of the non-trope nominalist theories, D. M. Armstrong considers this the strongest.