Properhood

A history of the notion of PROPERHOOD in philosophy and linguistics is given. Two long-standing ideas, (i) that proper names have no sense, and (ii) that they are expressions whose purpose is to refer to individuals, cannot be made to work comprehensively while PROPER is understood as a subcategory of linguistic units, whether of lexemes or phrases. Phrases of the type the old vicarage, which are potentially ambiguous with regard to properhood, encourage the suggestion that PROPER is best understood as mode of reference contrasting with SEMANTIC reference; in the former, the intension/sense of any lexical items within the referring expression, and any entailments they give rise to, are canceled. PROPER NAMES are all those expressions that refer nonintensionally. Linguistic evidence is given that this opposition can be grammaticalized, speculation is made about its neurological basis, and psycholinguistic evidence is adduced in support. The PROPER NOUN,asa lexical category, is argued to be epiphenomenal on proper names as newly defined. Some consequences of the view that proper names have no sense in the act of reference are explored; they are not debarred from having senses (better: synchronic etymologies) accessible during other (meta)linguistic activities

On the Convergence of Gromov-Witten Potentials and Givental's Formula

Let X be a smooth projective variety. The Gromov-Witten potentials of X are generating functions for the Gromov-Witten invariants of X: they are formal power series, sometimes in infinitely many variables, with Taylor coefficients given by Gromov-Witten invariants of X. It is natural to ask whether these formal power series converge. In this paper we describe and analyze various notions of convergence for Gromov-Witten potentials. Using results of Givental and Teleman, we show that if the quantum cohomology of X is analytic and generically semisimple then the genus-g Gromov-Witten potential of X converges for all g. We deduce convergence results for the all-genus Gromov-Witten potentials of compact toric varieties, complete flag varieties, and certain non-compact toric varieties.Comment: 38 pages, 1 figure, v2: corrected several error