This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

A transcript of three lectures, given at Princeton University in 1970, which deals with (inter alia) debates concerning proper names in the philosophy of language.

It follows from Humean principles of plenitude, I argue, that island universes are possible: physical reality might have 'absolutely isolated' parts. This makes trouble for Lewis's modal realism; but the realist has a way out. First, accept absolute actuality, which is defensible, I argue, on independent grounds. Second, revise the standard analysis of modality: modal operators are 'plural', not 'individual', quantifiers over possible worlds. This solves the problem of island universes and confers three additional benefits: an 'unqualified' principle of compossibility (...) can be accepted; the possibility of nothing can be accommodated; and the identity of indiscernible worlds can be decisively refuted. (shrink)

Preface In these days, an anthology on the topic of possible worlds hardly needs justification. No issue has given rise to as much literature in the past ...

The foregoing set of theorems forms an effective foundation for the theory of situations and worlds. All twenty-five theorems seem to be basic, reasonable principles that structure the domains of properties, relations, states of affairs, situations, and worlds in true and philosophically interesting ways. They resolve 15 of the 19 choice points defined in Barwise (1989) (see Notes 22, 27, 31, 32, 35, 36, 39, 43, and 45). Moreover, important axioms and principles stipulated by situation theorists are derived (see Notes (...) 33, 37, and 38). This is convincing evidence that the foregoing constitutes a theory of situations. Note that worlds are just a special kind of situation, and that the basic theorems of world theory, which were derived in previous work, can still be derived in this situation-theoretic setting. So there seems to be no fundamental incompatibility between situations and worlds — they may peacably coexist in the foundations of metaphysics. The theory may therefore reconcile two research programs that appeared to be heading off in different directions. And we must remind the reader that the general metaphysical principles underlying our theory were not designed with the application to situation theory in mind. This suggests that the general theory and the underlying distinction have explanatory power, for they seem to relate and systematize apparently unrelated phenomena. (shrink)

Relevantism, as a matter of definition, rejects classical logic as incorrect and adopts instead a relevant logic as encapsulating correct inference. It rejects classical logic on the grounds that the rule of Material Detachment, from A and not A or B to infer B,, sometimes leads from truth to falsity. Relevantism — although promoted by some relevant logicians, and an integral part of ultralogic — has recently encountered heavy, but interesting, criticism from relevance logicians themselves.

In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...) volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006. (shrink)

A realist theory of truth for a class of sentences holds that there are entities in virtue of which these sentences are true or false. We call such entities ‘truthmakers’ and contend that those for a wide range of sentences about the real world are moments (dependent particulars). Since moments are unfamiliar, we provide a definition and a brief philosophical history, anchoring them in our ontology by showing that they are objects of perception. The core of our theory is the (...) account of truthmaking for atomic sentences, in which we expose a pervasive ‘dogma of logical form’, which says that atomic sentences cannot have more than one truthmaker. In contrast to this, we uphold the mutual independence of logical and ontological complexity, and the authors outline formal principles of truthmaking taking account of both kinds of complexity. (shrink)

Vann McGee; XIII*—Two Problems with Tarski's Theory of Consequence, Proceedings of the Aristotelian Society, Volume 92, Issue 1, 1 June 1992, Pages 273–292, htt.

What is the logic of entailment? The latter half of the twentieth century has seen, for even the simplest languages, a proliferation of distinct formal entailment systems, each having those willing to defend its status as the answer. Among those defenders, and among the most adamant and mutually critical, are the champions of strict implication and relevance logic. To an outsider, this debate must seem singularly odd. Here we have a group of philosophers who cannot agree on the validity of (...) a simple, easily comprehensible inference scheme. They seem to think that they are not talking past one another---that there is some reality each seeks to describe---for they continue to write articles declaring that the opposing view is wrong. Yet they cannot seem to convince the other side that their view is even remotely plausible, thus leading some to an instrumentalist dismissal of the whole debate.I argue that the defenders of the two systems are right to suggest that something deeper is at issue between them than mere usefulness in particular applied contexts. Once we see what this is, however, we will see that they are, after all, talking past one another. When we succeed in clarifying the crucial underlying issue, we can then succeed in clarifying the crucial distinction between two dimensions of the underlying concept. Both the classicalist and the relevantist, then, will be seen to have accurately captured one dimension of the root concept. (shrink)

What is the logic of entailment? The latter half of the twentieth century has seen, for even the simplest languages, a proliferation of distinct formal entailment systems, each having those willing to defend its status as the answer. Among those defenders, and among the most adamant and mutually critical, are the champions of strict implication and relevance logic. To an outsider, this debate must seem singularly odd. Here we have a group of philosophers who cannot agree on the validity of (...) a simple, easily comprehensible inference scheme. They seem to think that they are not talking past one another---that there is some reality each seeks to describe---for they continue to write articles declaring that the opposing view is wrong. Yet they cannot seem to convince the other side that their view is even remotely plausible, thus leading some to an instrumentalist dismissal of the whole debate.I argue that the defenders of the two systems are right to suggest that something deeper is at issue between them than mere usefulness in particular applied contexts. Once we see what this is, however, we will see that they are, after all, talking past one another. When we succeed in clarifying the crucial underlying issue, we can then succeed in clarifying the crucial distinction between two dimensions of the underlying concept. Both the classicalist and the relevantist, then, will be seen to have accurately captured one dimension of the root concept. (shrink)

Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR.

Following Moore, I use ‘P entails Q’ as a convenient shorthand for ‘Q can be deduced logically from P’, ‘From P, Q follows logically’, ‘There is a logically valid argument with P as sole premise and Q as conclusion’, and the like.1 Apart from a minor point to be raised in Section XVI, distinctions within this cluster do not matter for present purposes. An analysis of the concept of entailment is answerable to careful, educated uses of expressions such as those. (...) An analysis which condemned nearly everything we say about what follows from what simply would not be an analysis of the common concept of entailment. If the concept were inconsistent, some common uses of it would be condemned; but only by standards established by the others. C. I. Lewis maintained this: to say that P entails Q is to say that it is logically impossible that (P & ¬Q).2 If Quine is right, then ‘entails’ and ‘impossible’ are as suspect as all other intensional terms. So perhaps they are; but their uses are not wholly without structure, and there are wrong ways of interrelating them. Lewis’s contention is about the internal geography of the intensional area, not its relations to the surrounding conceptual territory: it is an attempted analysis of one intensional expression in terms of another. I shall argue that Lewis was right, and also - by implication - that his thesis is helpful and clarifying - that is, that it is a genuine analysis. As is well known, Lewis’s analysis implies that each impossible proposition entails every proposition. Accepting the analysis, I accept this result. For one thing, Lewis has an argument for it (I use ‘→’ to abbreviate ‘entails’): (1) P & ¬P.. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...) students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...) will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)

We are pluralists about logical consequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity. Our pluralism starts with our analysis of consequence. This analysis of consequence is not idiosyncratic. We agree with Richard Jeffrey, and with many other philosophers of logic about how logical consequence is to be defined. To quote Jeffrey.

This paper uses the strengthened liar paradox as a springboard to illuminate two more general topics: i) the negation operator and the speech act of denial among speakers of English and ii) some ways the potential for acceptable language change is constrained by linguistic meaning. The general and special problems interact in reciprocally illuminating ways. The ultimate objective of the paper is, however, less to solve certain problems than to create others, by illustrating how the issues that form the topic (...) of this paper are more intricate than previously realised, and that they are related in delicate and somewhat surprising ways. (shrink)

In this note I respond to Hartley Slater's argument 12 to the e ect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt to show that the negation of paraconsistent logics is merely a subcontrary forming operator and not one which forms contradictories. I will show that Slater's argument fails, for two distinct reasons. Firstly, the argument does not consider the position of non-dialethic paraconsistency which rejects the possible truth (...) of any contradictions. Against this position Slater's argument has no bite at all. Secondly, while the argument does show that for dialethic paraconsistency according to which contradictions can be true, certain other contradictions must be true, I show that this need not deter the dialethic paraconsistentist from their position. (shrink)