The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

This paper argues in favor of two claims: (a) that Scope Shifting Operations (Quantifier Raising and Quantifier Lowering) are restricted by economy considerations, and (b) that the relevant economy considerations compare syntactic derivations that end up interpretively identical. These ideas are shown to solve several puzzles having to do with the interaction of scope with VP ellipsis, coordination, and the interpretation of bare plurals. Further, the paper suggests a way of dealing with the otherwise puzzling clause-boundedness of Quantifier Raising.

Recent developments in the semantics of natural language seem to lead to a genuine synthesis of ideas from linguistics and logic, producing novel concepts and questions of interest to both parent disciplines. This book is a collection of essays on such new topics, which have arisen over the past few years. Taking a broad view, developments in formal semantics over the past decade can be seen as follows. At the beginning stands Montague's pioneering work, showing how a rigorous semantics can (...) be given for complete fragments of natural language by creating a suitable fit between syntactic categories and semantic types. This very enterprise already dispelled entrenched prejudices concerning the separation of linguistics and logic. Having seen the light, however, there is no reason at all to stick to the letter of Montague's proposals, which are often debatable. Subsequently, then, many improvements have been made upon virtually every aspect of the enterprise. More sophisticated grammars have been inserted (lately, lexical-functional grammar and generalized phrase structure grammar), more sensitive model structures have been developed (lately, 'partial' rather than 'total' in their com position), and even the mechanism of interpretation itself may be fine-tuned more delicately, using various forms of 'representations' mediating between linguistic items and semantic reality. In addition to all these refinements of the semantic format, descriptive coverage has extended considerably. (shrink)

Chapter. 1. Logical. Form. as. a. Level. of. Linguistic. Representation. What is the relation of a sentence's syntactic form to its logical form? This issue has been of central concern in modern inquiry into the semantic properties of natural ...

Argues against a Gillon-style covers-based analysis of plural noun phrases.

Questions on Form and Interpretation PdR Press Publications in Philosophy of Language.

Argues for an assimilation of sentential and predicate conjunction to collective conjunction, based on modification of predicates by adverbs such as 'alternately'.

In the spring of 1978, one of the authors of this book was sitting in on a course in logic for linguists given by the other author. In attempting to present some of Montague's insights in an elementary way, the authors began dis cussions aimed towards the construction of a simple model-theoretical semantic apparatus which could be applied directly to a small English-like language and used to illustrate the methods of formal logical interpretation. In these discussions two points impressed themselves (...) on us. First, our task could be simplified by using boolean algebras and boolean homomorphisms in the models; and second, the boolean approach we were developing had much more widespread relevance to the logical structure of English than we first thought. During the summer and fall of 1978 we continued work on the system, proving the more fundamental theorems and outlining the way in which an intensional interpretation scheme could be developed which made use of the boolean approach. We presented our findings in a monograph which the UCLA Linguistics Department kindly published as part of their series called Occa sional Papers in Linguistics; one of the authors also presented the system at a colloquium held at the Winter Meeting of the Linguistic Society of America in December 1978. (shrink)