A Quick Argument for Property Realism
Property realism is the view that objects instantiate properties independently of mind or language. A standard argument for this view is that objects could have properties in the absence of mind and language. The anti-realist about properties must deny this, and sometimes he is sanguine in that denial. If there is nothing more to property talk than concepts and predicates, then objects have their properties in virtue of the existence of concepts and predicates—which depend upon psychological subjects. The anti-realist accepts a kind of idealism about properties: they are, if they are anything, projections from psychological and linguistic reality. Being square, say, is satisfying the concept square or falling under the predicate “square”. Must we conclude that there is a stalemate here, given that an idealist view of properties seems viable?
No, because there is this point: concepts and predicates themselves have properties. A concept has psychological properties and a predicate has linguistic properties. So the anti-realist is suggesting reducing properties to things with properties. A concept has properties like intentionality and compositionality; a predicate has properties like shape or sound (or whatever exactly a word is). The question must then arise as to what it is for such properties to be instantiated, and there is an obvious dilemma: either these properties are possessed in virtue of concepts and predicates or they are not. If they are not, then we have abandoned conceptualism and nominalism for these properties; but if they are, then we need another concept or predicate to which they reduce. But this too will have properties of some sort, so the same dilemma will arise again. There will be an infinite regress of properties and concepts (or predicates) as we move to a new concept (or predicate). Every new concept or predicate we introduce will have its own properties that cry out for reduction. So it can’t be that every property is possessed in virtue of a concept or predicate, because concepts and predicates also have properties. And if they have irreducible properties, then why should properties of objects be any different? If an object is square in virtue of the applicability of “square” to it, then in virtue of what does “square” possess six letters? Not in virtue of the predicate “has six letters” applying to it, because the same question arises with respect to that predicate—in virtue of what does that predicate consist of thirteen letters? And so in turn for the predicate “has thirteen letters”.
 There is no problem with an idealism that declares all properties to be psychological; the vicious regress arises when we try to explain psychological properties in terms of concepts or words, since these just introduce further properties.