A doctoral thesis by Ian Underwood
Within linguistics, the dominant truth-conditional approach to semantics belongs to the Tarskian, model-theoretic tradition. Theories in this tradition offer an abstract, mathematical description of the truth conditions of natural language expressions in terms of their correspondence with the world. This thesis takes issue with existing model-theoretic accounts of quantification on the basis that the specific abstract relations that they describe could not plausibly be models of natural language-to-world relations.
Recent decades have seen much philosophical interest in naturalistic theories of reference and mental content. In one sense, these theories address the above concern by trying to identify something naturalistic for semantic correspondence to consist in, such as causal-historical chains or ceteris paribus laws. In another sense, they fail to address the problem, since no account is given of either the semantic structure or the truth conditions of even the tiniest fragment of a natural language. Crucially, it is far from clear that model-theoretic semantics, in anything like its present form, can accommodate the solutions proposed by naturalistic theories of content. If correspondence truth and naturalism are both to be retained, a new theory is needed.
I begin by arguing that the class nominalism underlying model-theoretic semantics is unsuited to this naturalistic project, and propose that a variant of Armstrong's realist metaphysic, incorporating Donald Baxter's theory of aspects, provides the ideal ontology. I revise and extend Baxter's theory for a more complete and precise account of the instantiation of properties and relations, and show that the theory of aspects allows for an appealing treatment of both numbers and general facts.
Against the background of this realist metaphysic, and drawing on insights from naturalistic theories of mental content, I propose an original theory of mentally represented semantic structures and their truth-conditional analysis. Within this framework, I treat the core semantic phenomena of predication, negation, conjunction, and disjunction, and devote considerable attention to relations. I also develop a detailed theory of quantification, which includes a fully naturalistic account of both universal quantification and numerals.