Quine is well known for his aversion to universals – his ontology of existential quantification rules out commitment to the existence of universls such as redness, tallness, etc. For Quine, first-order existential quantifier is ontologically committing, and it is this quantifer which quantifies over objects, of which properteis are predicated. Thus, to use a stock example, if we say ‘Socrates is mortal’, we can ‘quine’t it by translating it into a formal logic sentence – ∃x M(x), where M is mortal and x is Socrates – which tells us just what we are ontologically committed to. In this sentence, the domain of the existential quantifier includes x, therefore, we are ontologically committed to x. Thus, we can predicate properties of objects without being ontologically committed to universals.
A closely related debate is whether abstract objects exist, and interestingly enough, Quine is ontologically committed to abstract objects – in this context, numbers. What’s also somewhat interesting is that, as I read Quine, it’s his ontological sparseness that is the driving force behind his commitment to abstract objects. His (also Putnam’s, but for present purposes I’ll refer to it as just Quine’s) indispensability argument for mathematics appears to be what does most of the work here:
‘(P1) We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories.
(P2) Mathematical entities are indispensable to our best scientific theories.
(C) We ought to have ontological commitment to mathematical entities.’
Now, historically, a rejection of universals falls within the large family of positions known as nominalism, but one could reject universals without a rejection of abstract objects being entailed. It becomes somewhat difficult to see, however, if it’s not entailed just why we shouldn’t accept the existence of universals. There is a wiff of circularity here, as Roger Scruton points out (this particular selection is in the context of Quine’s thesis on analytic-icity and the a priori but the point remains valid here):
‘The problem is that, if you accept Quine’s conclusion, you find yourself drawn to nominalism, pragmatism, and a highly scientistic worldview. Yet, if you look closely at his arguments, you will find those positions built into the premises, and so protected from their much-deserved interrogation.’ (‘Modern Philosophy’, p. 167)
As it stands, Scruton appears to be onto something. It appears that the Quinean position looks something like this: the conclusions lead to ontological sparseness because ontological sparseness is an assumption of Quine’s entire philosophy. Stated differently, Quine ends up being a semi-platonist for nominalist reasons. Two questions arise here: why should we accept the nominalism that seems to be driving his arguments? and if we are committed to the existence of abstract objects, why, other than an a priori commitment to nominalism, should we reject the existence of universals?