On the Innocence and Determinacy of Plural Quantification

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. Both assumptions are problematic, as is shown by providing a Henkin-style semantics for plural logic that does not resort to sets but takes a plural term to have plural reference. This semantics gives rise to a generalized notion of ontological commitment, which is used to develop some ideas of earlier critics of the alleged ontological innocence of plural logic.

The Semantics of Plurals

Plural logic provides an appealing framework for the regimentation of natural language plurals. However, the choice of a regimenting language leaves wide open the semantic question of how this language should be interpreted. One option is to interpret a plural term as denoting a non-empty set. Another is to embrace plurals in the metalanguage and take a plural term to have plural reference. A detailed comparison of the options reveals that there is no simple solution to the problem of choosing among them.

Are there any collective nouns among lexical plurals in English?

The grammatical tradition has excluded lexical plurals from the category of collective nouns on the sole basis of their morphology (no discrepancy between singular form and so-called plural reference); but this criterion has led to hesitations, some linguists including, for instance,cattleorpeople. This study therefore considers other, semantic, criteria to establish more convincingly whether lexical plurals that denote pluralities of entities may be collective nouns. Relying on distinctions between meronymy and (non-taxonomic) hyperonymy, collectiveness and cohesion, and(a) crew(collective sense) /(several) crew(uninflected plural), it concludes that they are definitely not collective nouns, but aggregate nouns (or senses of nouns). Two sets are established. Some, mainly denoting humans, typically originate in the collective sense of the noun through a coercion mechanism; the others, mainly denoting objects, result from an operation of abstraction. For some of these, the notion of “hyperonyms of plural classes” is put forward.

One Act, Several Conceptual Parts

The chapter clarifies the conclusion of Brentano’s Duplication Argument. On Brentano’s view, a conscious mental act is directed on two objects, one of them being the act itself, but its plural reference is primitive, not due to the fact that the mental act has parts which each have reference on their own. Because of the plural reference the act can be brought under different partial concepts that are arrived at by abstraction. Brentano’s view is compared with contemporary versions of self-representationalism and shown not to admit of higher orders, double presentations, or indirect presentation of complexes. Brentano’s Duplication Argument makes plausible that awareness of perceiving can’t be such a complex that integrates independently existing mental acts; instead one simple act can have multiple objects.