Confronting Existential Angst

Paul Pietroski (Rutgers)


Davidson (1967) connected two old ideas: action reports are understood as existential generalizations over events; and in the scope of existential generalizations, conjunct reduction is a valid form of inference. This turned out to be the tip of an iceberg. The symbols ‘∃’ and ‘&’ regularly appear in posited logical forms for sentences that do not contain corresponding overt analogs (e.g., ‘some’ or ‘and’). But this raises questions about the sources of the existential and conjunctive implications. One can posit covert constituents, combinatorial operations that are not logically innocent, or both. Thinking about the options raises further questions about which departures from innocence are warranted if our goal is to explain how expressions are understood, as opposed to characterizing “semantic values” for expressions. Should we agree that ‘Caesar died in March’ implies a death—and try to figure out how the English sentence could be understood as having this implication—but then not worry if our theory says that ‘Caesar saw every senator’ implies a set of senators, a set of things Caesar saw, and perhaps functions that map each thing to a truth value? If so, how do we tell which implications of our theories matter for purposes of (dis)confirmation? I think that all implications matter, that combinatorial operations are not logically innocent, and that we need to rethink familiar accounts of quantification.