This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)

Expressions in a language, whether words, phrases, or sentences, have meanings. So it seems reasonable to suppose that there are meanings that expressions have. Of course, it is fashionable in some philosophical circles to deny this.

' I heartily recommend it to any philosopher of language interested in the issues. [] Logicians, of course, will want to savour the whole thing.' Australian Journal of Philosophy, 71:3 (1993).

In this paper, I offer a view beyond that which would narrowly reduce the role of parents in medical decision making to acting as custodians of the best interests of children and toward an account of family authority and family autonomy. As a fundamental social unit, the good of the family is usually appreciated, at least in part, in terms of its ability successfully to instantiate its core moral and cultural understandings as well as to pass on such commitments to (...) future generations. The putative rights of children to expression, information, freedom of thought, conscience, religion, and to freedom of association with others are, in this essay, assessed from the perspective of those conditions necessary for the family to function as a moral community. In so doing, I respond to the move to liberate children from parental authority and to effect the transformation of the family as implied by the United Nations’ "Convention on the Rights of the Child" and the pediatric bioethics it supports. (shrink)

The paper considers the question of when the operator L of necessity in modal logic can be expressed in terms of the operator meaning it is non-contingent that.

Semantic Indexicality shows how a simple syntax can be combined with a propositional language at the level of logical analysis. It is the adoption of such a base language which has not been attempted before, and it is this which constitutes the originality of the book. Cresswell's simple and direct style makes this book accessible to a wider audience than the somewhat specialized subject matter might initially suggest.

Adverbial modification is probably one of the least understood areas of linguistics. The essays in this volume all address the problem of how to give an analysis of adverbial modifiers within truth-conditional semantics. Chapters I-VI provide analyses of particular modifiers within a possible worlds framework, and were written between 1974 and 1981. Original publication details of these chapters may be found on p. vi. Of these, all but Chapter I make essential use of the idea that the time reference involved (...) in tensed sentences should be a time interval rather than a single instant. The final chapter (Chapter VII) was written especially for this volume and investigates the question of how the 'situation semantics' recently devised by Jon Barwise and John Perry, as a rival to possible-worlds semantics, might deal with adverbs. In addition I have included an appendix to Chapter III and an introduction which links all the chapters together. (shrink)

I distinguish between sentences like(1) Last Thursday we drove from Wellington to Waikanae and (2) Last Thursday my copy of Aspects of the Theory of Syntax remained on my bookshelf. Sentence (2) has the subinterval property. If it is true at an interval t it is true at every subinterval of t. (1) lacks this property. (1) reports an event. (2) reports a state. Events do not have the subinterval property but states do have it, and so do objects. If (...) something is a linguist at an interval t then that person is a linguist at all subintervals of t. I argue that exists applies to things which have the subdinterval property, and occurs applies to things which lack it. (shrink)

In this study, we present a cost-sharing rule for cost-sharing problems. This rule prescribes the same allocations in a problem and in its dual one. Moreover, in some specific problems it gives the same allocations as the serial cost-sharing rule (Moulin and Shenker, Econometrica, 60, 1009–1037, 1992) does in a related problem. That is why we call it as the self-dual serial cost-sharing rule. We give two axiomatizations of this new rule and another one for the serial cost-sharing rule.

Over a longer period than I sometimes care to contemplate I have worked on possible-worlds semantics. The earliest work was in modal logic, to which I keep returning, but a sabbatical in 1970 took me to UCLA, there to discover the work of Richard Montague in applying possible-worlds semantics to natural lan guage. My own version of this appeared in Cresswell (1973) and was followed up in a number of articles, most of which were collected in Cresswell (1985b). A central (...) problem for possible worlds semantics is how to accommodate propositional attitudes. This problem was addressed in Cresswell (1985a), and the three books mentioned so far represent a reasonably complete picture of my positive views on formal semantics. I have regarded the presentation of a positive view as more important than the criticism of alternatives, although the works referred to do contain many passages in which I have tried to defend my own views against those of others. But such criticism is important in that a crucial element in establishing the content of a theory is that we be able to evaluate it in relation to its com petitors. It is for that reason that I have collected in this volume a number of articles in which I attempt to defend the positive semantical picture I favour against objections and competing theories. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

A (normal) system of propositional modal logic is said to be complete iff it is characterized by a class of (Kripke) frames. When we move to modal predicate logic the question of completeness can again be raised. It is not hard to prove that if a predicate modal logic is complete then it is characterized by the class of all frames for the propositional logic on which it is based. Nor is it hard to prove that if a propositional modal (...) logic is incomplete then so is the predicate logic based on it. But the interesting question is whether a complete propositional modal logic can have an incomplete extension. In 1967 Kripke announced the incompleteness of a predicate extension of S4. The purpose of the present article is to present several such systems. In the first group it is the systems with the Barcan Formula which are incomplete, while those without are complete. In the second group it is those without the Barcan formula which are incomplete, while those with the Barcan Formula are complete. But all these are based on propositional systems which are characterized by frames satisfying in each case a single first-order sentence. (shrink)

While not taking St. Anselm’s ontological argument in the Proslogion to be valid, this paper shows that the dismissal of the thesis by both St. Thomas Aquinas and Kant does less than justice to St. Anselm’s text. In Chapter II of the Proslogion Anselm defines God as ‘something than which nothing greater can be thought’, claiming that this notion ‘exists in the mind’. The question is does its subject, God, exist ‘in re’. Can one proceed from the mental existence to (...) real existence given that to exist in re is greater than to exist notionally? This paper sets out several of Anselm’s premises from which he concludes that the notional existence of God defined by Anselm entails God’s actual existence, Aquinas dismissed Anselm’s arguments – possibly not having Anselm’s full text at hand. Anselm maintains that if ‘something than which nothing greater can be thought’ can be conceived, then to deny its existence in re constitutes a self-contradiction. The present paper examines in detail the elements of which Anselm’s elegant arguments are composed: q.v. Reference is made to Anselm’s Reply to Gaunilo, and to Anselm’s ontology set out in Monologion. Much, for the modern reader, turns on the topical logic of ‘perfection’ and of ‘greatness’. Again: much turns on the Kantian question ‘Is existence a predicate?’ And on the question: what kinds of things can be the subject of predicates? The comparison which Anselm is making between real and conceptual existence is not like any other comparison. This may be the flaw in his arguments. (shrink)

The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.