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)

Modal propositional logic; Modal predicate logic; A survey of modal logic.

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.

Originally published in 1973, this book shows that methods developed for the semantics of systems of formal logic can be successfully applied to problems about the semantics of natural languages; and, moreover, that such methods can take account of features of natural language which have often been thought incapable of formal treatment, such as vagueness, context dependence and metaphorical meaning. Parts 1 and 2 set out a class of formal languages and their semantics. Parts 3 and 4 show that these (...) formal languages are rich enought to be used in the precise description of natural languages. Appendices describe some of the concepts discussed in the text. (shrink)

Normal propositional modal systems This first chapter has two main aims. One is to give a general account of the propositional modal systems that we shall ...

' 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).

Is what could have happened but never did as real as what did happen? What did happen, but isn't happening now, happened at another time. Analogously, one can say that what could have happened happens in another possible world. Whatever their views about the reality of such things as possible worlds, philosophers need to take this analogy seriously. Adriane Rini and Max Cresswell exhibit, in an easy step-by-step manner, the logical structure of temporal and modal discourse, and show that every (...) temporal construction has an exact parallel that requires a language that can refer to worlds, and vice versa. They make precise, in a way which can be articulated and tested, the claim that the parallel is at work behind even ordinary talk about time and modality. The book gives metaphysicians a sturdy framework for the investigation of time and modality - one that does not presuppose any particular metaphysical view. (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)

David Lewis's modal realism claims that nothing can exist in more than one world or time, and that statements about how something would have been are to be analysed in terms of its counterpart. I first explain why the counterpart relation depends on de re modal statements in an intensional language, so that intuitive properties of similarity relations cannot be used to show that the counterpart relation is not an equivalence relation. I then look at test sentences in (the intensional) (...) natural language, and show that none of them provide compelling evidence that a counterpart semantics is needed. (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)

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)

Truth of x (independently of any description of x) that it is f. A property f which holds of x but is not per se of x is said to hold per accidens of x. The essence of an individual is the sum of its per se properties. We can formulate the following: doctrine a: concrete individuals do not have essences though abstract entities do. Doctrine b: concrete individuals have essences but they do not individuate, whereas abstract entities have essences (...) which do individuate. Assumption i: we shall say that a thing exists insofar as it has an essence. Assumption ii: we shall say that we know a thing when we know what its per se properties are. We argue that plato held doctrine a and aristotle doctrine b (with assumptions i and ii). (edited). (shrink)

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)

In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices as (...) multiple indexing or quantification over times. (shrink)

This article discusses the argument we cannot have knowledge of abstract entities because they are not part of the causal order. The claim of this article is that the argument fails because of equivocation. Assume that the “causal order” is concerned with contingent facts involving time and space. Even if the existence of abstract entities is not contingent and does not involve time or space it does not follow that no truths about abstract entities are contingent or involve time or (...) space. I argue that it is the latter which is required to obtain the desired conclusion. (shrink)

The paper investigates interpretations of propositional and firstorder logic in which validity is defined in terms of partial indices; sometimes called possibilities but here understood as non-empty subsets of a set W of possible worlds. Truth at a set of worlds is understood to be truth at every world in the set. If all subsets of W are permitted the logic so determined is classical first-order predicate logic. Restricting allowable subsets and then imposing certain closure conditions provides a modelling for (...) intuitionistic predicate logic. The same semantic interpretation rules are used in both logics for all the operators. (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.