The syntactic priority thesis (henceforth SP) asserts that the truth of appropriate sentential contexts containing what are, by syntactic criteria, singular terms, is sufficient to justify the attribution of objectual reference to such terms (Wright, 1983, 24). One consequence that the neo-Fregean draws from SP is that it is through an analysis of the syntactic structure of true statements that 'ontological questions are to be understood and settled' (Wright, 1983, 25). Despite the significant literature on SP, little consideration has been given to this bold meta-ontological claim.1 My concern here is accordingly not with specific applications of SP to debates in the philosophy of mathematics, but rather with the neo-Fregean's claim that SP can constitute a decision-procedure in relation to substantive ontological disputes. I argue that the explanatory power of SP is limited to an account of what 'there are' sentences are true and does not extend as far as substantive ontology. In section II, I examine alternative interpretations of SP with a view to arriving at the version which best fits with Hale and Wright's intentions. [End Page 149] Section III then demonstrates why, even on the most charitable interpretation, SP cannot settle disputes about the existence of numbers or deliver on the stronger meta-ontological claims made on behalf of it by the neo-Fregean more generally. Although my focus is on SP and neo-Fregeanism, the paper raises broader problems associated with the attempt to establish ontological theses through logical and linguistic analysis.
One of the more ambitious claims made by neo-Fregeanism is that SP constitutes a decision-procedure in relation to substantive ontological disputes. In order to assess this claim, it is first necessary to establish the precise role played by SP in neo-Fregean arguments for the existence of abstract objects. My aim in this section is to provide such clarification, while also pointing to some key conditions that would need to be met for SP to constitute an ontological decision-procedure.
SP is a thesis ultimately derived from the application of Fregean logical syntax to ontological problems. It says that prior distinctions concerning syntactic types of expression such as singular term and predicate can explain distinctions concerning non-linguistic types of entity such as object and concept. In conformity with Frege's principle that a word only has meaning in the context of a sentence, being a singular term is not a property of an expression in isolation, but rather depends upon its functioning in a certain way in complete sentences. As a consequence, it is regarded as a sufficient (but not necessary) condition for the existence of objects of some given kind that there are true statements in which expressions of the appropriate sort function as singular terms. Hence, according to Wright:
When it has been established ... that a given class of terms are functioning as singular terms, and when it has been verified that certain appropriate sentences containing them are, by ordinary criteria, true, then it follows that those terms do genuinely refer.(1983, 14)
On this basis, the neo-Fregean attempts to prove the existence of numbers and other abstract entities through abstraction principles of the form:
[End Page 150]
Principles of this form serve as stipulative implicit definitions of the Σ-operator and in so doing also of the new kind of term introduced by means of it with the corresponding sortal concept (Hale and Wright, 2009, 179). According to Hale and Wright, abstraction principles thereby allow us to overcome concerns about our epistemic access to abstract objects by giving an account of the 'truth conditions of Σ identities as coincident with those of a kind of statement we already understand' (2009, 179). We can exploit this prior understanding so as to establish our knowledge of the referents of the Σ-terms, referents whose status as genuine objects is guaranteed by the truth of the identity statements by means of which we gain access to them.
This explanatory model is dependent upon the link between truth and objectual reference. It is this link that is supposed to justify the move from facts...