The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio (...) ad absurdum is needed. Thus our main goal is to derive results on the existence (or nonexistence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments. (shrink)

This chapter contains sections titled: Introduction Pronouns and Variables Anaphoric Pronouns in Generative Grammar Phonetic Form and Logical Form Binding and Scope The Binding Theory Aphonic Pronouns Pronouns as Determiners A Unified Account of Binding Bound and Free Discourse Anaphora Unselective Binding and Donkey Problems Notes.

Some philosophers, notably Professors Quine and Geach, have stressed the analogies they see between pronouns of the vernacular and the bound variables of quantification theory. Geach, indeed, once maintained that ‘for a philosophical theory of reference, then, it is all one whether we consider bound variables or pronouns of the vernacular'. This slightly overstates Geach's positition since he recognizes that some pronouns of ordinary language do function differently from bound variables; he calls such pronouns ‘pronouns of laziness'. Geach's characterisation of (...) pronouns of laziness has varied from time to time, but the general idea should be clear from a paradigm example: A man who sometimes beats his wife has more sense than one who always gives in to her.The pronouns ‘one’ and ‘her’ go proxy for a noun or a noun phrase in the sense that the pronoun is replaceable in paraphrase by simple repetition of its antecedent. (shrink)

I first show that most authors who developed Plural Quantification Logic (PQL) argued it could capture various features of natural language better than can other logic systems. I then show that it fails to do so: it radically departs from natural language in two of its essential features; namely, in distinguishing plural from singular quantification and in its use of an relation. Next, I sketch a different approach that is more adequate than PQL for capturing plural aspects of natural language (...) semantics and logic. I conclude with a criticism of the claim that PQL should replace natural language for specific philosophical or scientific purposes. (shrink)

I show that the contemporary dominant analysis of natural language quantifiers that are one-place determiners by means of binary generalized quantifiers has failed to explain why they are, according to it, conservative. I then present an alternative, Geachean analysis, according to which common nouns in the grammatical subject position are plural logical subject-terms, and show how it does explain that fact and other features of natural language quantification.

This is a reply to H. Ben-Yami, 'Generalized quantifiers, and beyond' (this journal, 2009), where he argues that standard GQ theory does not explain why natural language quantifiers have a restricted domain of quantification. I argue, on the other hand, that although GQ theory gives no deep explanation of this fact, it does give a sort of explanation, whereas Ben-Yami's suggested alternative is no improvement.