Federal University of Rio de Janeiro
A Semantic Criterion for Existential Import
19 December 2017, 16:00
Faculdade de Letras de Lisboa
Abstract: In his book Logic and How It Gets That Way, Jacquette (2010) presents ‘the formalization paradox’ which emerges from the attempt to formalize a sentence like ‘Some monkey devours every craisin’, where craisins are imaginary non-existent fruits. From this paradox Jacquette concludes the expressive inadequacy of classical predicate quantificational logic. In this paper I analyze the three assumptions made in the emergence of the paradox, viz.: (i) colloquial expressions of the same logical form can and should be formally symbolized by applying the same symbolization schema; (ii) ‘Some monkey devours every raisin’ is correctly translated as ∃x (Mx ∧ ∀y (Ry ® Dxy)); (iii) uninstantiated predicates can legitimately enter into (meaningful, true or false) predicate-quantificational symbolizations. I fully accept (iii), but reject both (i) and (ii). I argue, firstly, that (i) has at first glance two possible interpretations, one trivial and one false. So, I try to establish a third and more reasonable interpretation. Based on this interpretation I argue that ∃x (Mx ∧ ∀y (Ry ® Dxy)) is not the adequate formalization of ‘Some monkey devours every raisin’. My basic claim is based on a generalization of Russell’s theory of descriptions: just as most sentences of natural language which contain definite descriptions are viewed as entailing existential force which must be made explicit in formalization, so do we also consider many, although not all, sentences which contain general terms. A criterion will be presented and defended for deciding in each possible case if a sentence entails existential force.