Lexical Flexibility, Natural Language, and Ontology

The Realist that investigates questions of ontology by appeal to the quantificational structure of language assumes that the semantics for the privileged language of ontology is externalist. I argue that such a language cannot be (some variant of) a natural language, as some Realists propose. The flexibility exhibited by natural language expressions noted by Chomsky and others cannot obviously be characterized by the rigid models available to the externalist. If natural languages are hostile to externalist treatments, then the meanings of natural language expressions serve as poor guides for ontological investigation, insofar as their meanings will fail to determine the referents of their constituents. This undermines the Realist’s use of natural languages to settle disputes in metaphysics

Tetrahedral curves via graphs and Alexander duality

A tetrahedral curve is a (usually nonreduced) curve in P^3 defined by an unmixed, height two ideal generated by monomials. We characterize when these curves are arithmetically Cohen-Macaulay by associating a graph to each curve and, using results from combinatorial commutative algebra and Alexander duality, relating the structure of the complementary graph to the Cohen-Macaulay property.Comment: 15 pages; minor revisions to v. 1 to improve clarity; to appear in JPA