In part one, I give an (unsystematic) overview of the development of logical tools which have been employed in the course of the analysis of referring expressions, i.e. definite and (specific) indefinite singular terms, of natural language. I present Russell's celebrated theory of definite descriptions which I see as an attempt to explain definite reference in terms of unique existence (and reference in general in terms of existence simpliciter); and I present Hilbert's E-calculus as an attempt to explain existence in (...) terms of choice. Then I turn to contemporary, dynamic approaches to the analysis of singular terms and point out that only within a dynamic framework can the Russellian and Hilbertian ideas yield a truly satisfactory analysis of singular terms, and consequently of reference and coreference. I call attention to the fact that current results of formal semantics demonstrate the advantages of viewing singular terms as denoting updates, i.e. as a means of changing the context (information state), and especially that part of the context which I call the individually. (shrink)

The epsilon calculus improves upon the predicate calculus by systematically providing complete individual terms. Recent research has shown that epsilon terms are therefore the “logically proper names” Russell was not able to formalize, but their use improves upon Russell’s theory of descriptions not just in that way. This paper details relevant formal aspects of the epsilon calculus before tracing its extensive application not just to the theory of descriptions, but also to more general problems with anaphoric reference. It ends by (...) contrasting a Meinongian account of cross-reference in intensional constructions with the epsilon account. (shrink)

Cantor’s abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor’s proposal based upon the set theoretic framework of Bourbaki—called BK—which is a First-order set theory extended with Hilbert’s \-operator. Moreover, it is argued that the BK system and the \-operator provide a faithful reconstruction of Cantor’s insights on cardinal numbers. I will introduce first (...) the axiomatic setting of BK and the definition of cardinal numbers by means of the \-operator. Then, after presenting Cantor’s abstractionist theory, I will point out two assumptions concerning the definition of cardinal numbers that are deeply rooted in Cantor’s work. I will claim that these assumptions are supported as well by the BK definition of cardinal numbers, which will be compared to those of Zermelo–von Neumann and Frege–Russell. On the basis of these similarities, I will make use of the BK framework in meeting Frege’s objections to Cantor’s proposal. A key ingredient in the defence of Cantorian abstraction will be played by the role of representative sets, which are arbitrarily denoted by the \-operator in the BK definition of cardinal numbers. (shrink)

In this paper I revive two important formal approaches to the interpretation of natural language, that of Montague and that of Karttunen and Peters. Armed with insights from dynamic semantics (Heim, Krifka) the two turn out to stand up against age-old criticisms in an orthodox fashion. The plan is mainly methodological, as I only want to illustrate the technical feasibility of the revived proposals. Even so, there are illuminating and welcome empirical consequences on the subject of scope islands (as discussed (...) by Abusch and Kratzer, among many others), as well as unintended theoretical implications in the contextualist debate (Grice, Recanati, Simons, Stanley, and many others again). (shrink)

This paper describes a prototype implementation of a Labelled Deduction System for natural language interpretation, where interpretation is taken to be the process of understanding a natural language utterance. The implementation models the process of understanding wh-gap dependencies in questions and relative clauses for a fragment of English. The paper is divided in three main sections. In Section 1, we introduce the basic architecture of the system. Section 2 outlines a prototype implementation of wh-binding and indicates its potential for explanation (...) of linguistic phenomena, and in Section 3 we briefly set the model within a large theoretical perspective, comparing it to other type-logical approaches to natural language analysis. (shrink)

Criticisms have been aired before about the fear of certain Platonic abstract objects, propositions. That criticism extends to the widespread preference for an operator analysis of expressions like ‘It is true, known, obligatory that p’ as opposed to the predicative analysis in their equivalents ‘That p is true, known, obligatory’. The criticism in the present work also concerns Prior’s attitude to Platonic entities of a certain kind: not propositions, i.e., the referents of ‘that’-clauses, but individuals, i.e., the referents of Russell’s (...) ‘logically proper names’. Prior had a close knowledge of theories of individuals, including that of Russell. However, when Prior formulated his tense logic Q he presumed a non-Russellian, pre-suppositional account of individuals, such that they might exist at one time but not at another, and when they did not exist no statement could be made about them. This paper examines the correctness of such a pre-suppositional account of individuals, showing there are features of natural language it cannot account for. It is shown that the required features can be formalised in Hilbert’s epsilon calculus, and that using that calculus substantiates a Russellian understanding of ‘logically proper names’. (shrink)