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)

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)

(1996). Knowledge elicitation using a multi‐modal approach. World Futures: Vol. 47, Unity and Diversity in Contemporary Systems Tinking: Systematic Pictures at an Exhibition, pp. 93-101.

Interest in the metaphysics and logic of possible worlds goes back at least as far as Aristotle, but few books address the history of these important concepts. This volume offers new essays on the theories about the logical modalities held by leading philosophers from Aristotle in ancient Greece to Rudolf Carnap in the twentieth century. The story begins with an illuminating discussion of Aristotle's views on the connection between logic and metaphysics, continues through the Stoic and mediaeval traditions, and then (...) moves to the early modern period with particular attention to Locke and Leibniz. The views of Kant, Peirce, C. I. Lewis and Carnap complete the volume. Many of the essays illuminate the connection between the historical figures studied, and recent or current work in the philosophy of modality. The result is a rich and wide-ranging picture of the history of the logical modalities. (shrink)

' 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).

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)

Following Fine [3], p. 20, we say that a normal propositional modal logic is canonical i all its theorems are valid on the frame of its canonical model . In this paper we prove that K1:1, i.e. S4+ J1 L p) p is not canonical y . We say that two points x and y in a frame are co-accessible i xRy; yRx, but x =6 y. Our proof proceeds by showing that A. The canonical model for K1:1 contains a (...) pair of co-accessible points; and B. J1 is not valid on any frame with a pair of co-accessible points. Clearly our result follows immediately from A and B. (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)

The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only 'real' time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of first-order predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the (...) other. I shew that this translation is preserved at the metalinguistic level, so that equivalent truth conditions can be defined in a tensed metalanguage or an indexical metalanguage. I then make some remarks about the connection between proofs of relative consistency and metaphysical truth; and some historical remarks about Arthur Prior's use of formal logic in expressing his presentist views. (shrink)

The most common way of proving decidability in propositional modal logic is to shew that the system in question has the finite model property. This is not however the only way. Gabbay in [4] proves the decidability of many modal systems using Rabin's result in [8] on the decidability of the second-order theory of successor functions. In particular [4, pp. 258-265] he is able to prove the decidability of a system which lacks the finite model property. Gabbay's system is however (...) complete, in the sense of being characterized by a class of frames, and the question arises whether there is a decidable modal logic which is not complete. Since no incomplete modal logic has the finite model property [9, p. 33], any proof of decidability must employ some such method as Gabbay's. In this paper I use the Gabbay/Rabin technique to prove the decidability of a finitely axiomatized normal modal propositional logic which is not characterized by any class of frames. I am grateful to the referee for suggesting improvements in substance and presentation.The terminology I am using is standard in modal logic. By aframeis understood a pair 〈W, R〉 in whichWis a class (of “possible worlds”) andR⊆W2. To avoid confusion in what follows, a frame will henceforth be referred to as aKripkeframe. By contrast, ageneral frameis a pair 〈,Π〉 in whichis a Kripke frame andΠis a collection of subsets ofWclosed under the Boolean operations and satisfying the condition that ifAis inΠthen so isR−1“A. A model on a frame (of either kind) is obtained by adding a functionVwhich assigns sets of worlds to propositional variables. In the case of a general frame we require thatV(p) ∈Π. (shrink)

This paper explores a modal analogue of Hugh Mellor''s version of McTaggart''s argument against the reality of tense. I show that if Mellor''s argument succeeds in showing that the present moment cannot be any more real than any other moment then it also shows that the actual world cannot be any more real than any other possible world.

In Book Γ of the Metaphysics Aristotle states and attempts to prove what he calls the basic principle of the science of being as being: the law of non‐contradiction. In this paper I defend an interpretation of his proof, inspired by Elizabeth Anscombe's 1961 essay in ‘Three Philosophers’, though some of its features were remarked on by Lukasiewicz in 1910, according to which Aristotle is proving this principle only for substance predicates, and that it is to be understood as the (...) basic principle of metaphysics rather than of logic. It is the principle that every substance has an essential nature, and if it is of the essential nature of x to be F then it cannot be of the essential nature of x to be not‐F since then x's being F and x's being not‐F would be the same. He puts it by saying that in such a case F and not‐F would ‘signify the same’ for x. Since they do not, x cannot be both. (shrink)

In this paper I shall look at the application of the ltration technique to omnitemporal logic . The principal result of the paper will be that the system BSeg of [3] has the nite model property; but I shall also make a few remarks about the system B+ of [2].

In this note we sketch a decision procedure for S3.51 based on reduction to conjunctive normal form. Using the following theorem of S3.5: and its dual for M over a conjunction, any formula can be reduced by standard methods (as in S52) to a conjunction of disjunctions of the form where Í is (p ⊃ p), 0 is ∼(p ⊃ p) and α — λ are all PC-wffs (i.e. they contain no modal operators).

Does Duns Scotus identify the natural will with the affectio commodi ? This identifica- tion has become the standard view. In this paper, I will challenge this view through an analysis of some key texts. The main thesis of the paper is that Scotus allows for two scenarios related to the will’s dual affections. The first is the real situation of the created will: the will is a free potency and possesses two affections. The second is a hypothetical case; Scotus (...) suggests the fictive case of a will that only possesses the affectio commodi. Accordingly, it can be concluded that: (i ) when considering the will in its real condi- tion, both affections belong to the will’s free appetite; (ii) in the hypothetical case the natural will, the intellectual appetite and the affectio commodi are all identified; (iii ) in the real condition of the will, the natural will is a passive inclination to receive perfection. (shrink)

Thomas Aquinas's vision of atonement is generally considered more conceptually expansive than Anselm of Canterbury's. Where Aquinas's multipartite account of Christ's passion incorporates a variety of biblical motifs, Anselm appears to narrow the focus to satisfactory debt-repayment alone. This article proposes two approaches for reframing the comparison between the two accounts. I argue first that both Anselm and Aquinas considered debt-repayment necessary but not sufficient in itself to accomplish all that is needed for the remittance of sin and the restoration (...) of humanity. For Anselm, as for Aquinas, Christ must also liberate captives, defeat the devil, amend Adam's sin by recapitulation and win merit in which his members participate. The first reframing thus locates Anselm in much closer proximity to Aquinas than has generally been supposed. The second reframing throws light on a significant divergence between the two. I argue that the kenotic trajectory of abasement and ascent, pictured in the Philippian hymn, is put to strikingly different use by each theologian. This second reframing throws into sharp relief Aquinas's emphasis on Christ's suffering as a theological priority which Anselm does not share. Looking to Anselm's Benedictine context, I contend, yields one possible means of accounting for this departure. (shrink)

It is a matter of some irony that psychiatry's most trenchant critic for over four decades is himself a psychiatrist. I refer to Thomas S. Szasz. Szasz's core thesis may be succinctly rendered: mental illness is a “myth”, a “metaphor” which serves only to obscure the social and ethical “problems in living” we face as human beings. This paper reconsiders the conceptual bases of Szasz's assault on psychiatry and assesses recent counter-arguments of his critical interlocutors. It presents a defence of (...) the Szaszian conception and emphasises the continuing relevance of his earliest work. Additionally, the paper discusses Szasz's thesis in light of the work of the influential French philosopher of medicine, Georges Canguilhem. (shrink)

I discuss three ways of responding to the logical omniscience problems faced by traditional ‘possible worlds’ epistemic logics. Two of these responses were put forward by Hintikka and the third by Cresswell; all three have been influential in the literature on epistemic logic. I show that both of Hintikka's responses fail and present some problems for Cresswell’s. Although Cresswell's approach can be amended to avoid certain unpalatable consequences, the resulting formal framework collapses to a sentential model of (...) knowledge, which defenders of the ‘possible worlds’ approach are frequently critical of. (shrink)

My 1998: 78–81 contains an argument against tensed facts, like the fact that it’s raining now, which exist at some times like 1 January 2010 and not others. ‘Facts’ here means truthmakers, not facts in the trivial sense defined by the equivalence principle EP: For all P, P is a fact iff the proposition ‘P’ is true, in which no one can deny the existence of tensed facts. The argument, which I’ll call TA, may be summarized as follows, where a (...) B-theory of time is one that says there are not, and an A-theory one that says there are, tensed truthmakers. B- theory: Any tensed ‘P’ is made true at any time t by the tenseless fact P-at- t. So: ‘P’ has as many truthmakers as there are times. A-theory: ‘P’ is made true by the tensed fact P, which exists at some but not all t. So: ‘P’ has only one truthmaker, P. So: P makes all tokens of ‘P’ true now. So: P makes tokens of ‘P’ at times when P didn’t exist true now, which is absurd. TA: So: P only makes present tokens of ‘P’ true. So: tokens of ‘P’ at any time t are true iff P exists at t, i.e. ‘P’ is made true at any time t by the tenseless fact P-at- t. So: there are no tensed facts. Max Creswell and Adriane Rini have now produced a modal analogue of TA, which I’ll call MA, whose conclusion is that there are no contingent facts, like the fact that I live in Cambridge, and which may be summarized as follows: Modal realism: Any contingent ‘P’ is made true in any world …. (shrink)

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)

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)

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.

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)