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.

The titile essay of this collection suggests that Bertrand Russell's lifelong preoccupation: the disentanglement, with ever-increasing precision, of what is subjective or intellectualy cloudy from what is objective or capable of logical demonstration. The first five essays he calls 'entirely popular': they include two on the revolutionary changes in mathematics in the last hundred years, and one on the value of science in human culture. The last five, 'somewhat more technical', are concerned with particular problems of philosophy: the ultimate nature (...) of matter, the connection between the sense-data and physics, the problem of casuality and different ways of knowing. In these one can see the Russell method in operation, intellectual analysis dissecting the problem to its bare bones. (shrink)

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work ...

This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

1 Meaning and Truth Objection to propositions Propositions as information Diffuseness of empirical meaning Propositions dismissed Truth and semantic ascent Tokens and eternal sentences 2 Grammar Grammar by recursion Categories Immanence and transcendence Grammarian's goal reexamined Logical grammar Redundant devices Names and functors Lexicon, particle, and name Criterion of lexicon Time, events, adverbs Attitudes and modality 3 Truth Truth and satisfaction Satisfaction by sequences Tarski's definition of truth Paradox in the object language Resolution in set theory 4 Logical Truth In (...) terms of structure In terms of substitution In terms of models Adequacy of substituteon In terms of proof In terms of grammar 5 The Scope of Logic Affinities of identity Identity reduced Set theory Set theory in sheep's clothing Logic in wolf's clothing Scope of the virtual theory Simulated class quantification Other simulated quantification Annexes 6 Deviant Login Change of logic, change of subject Logic in translation Law of excluded middle Debate about the dichotomy Intuitionism Branched quantifiers Substitutional quantification Its strength 7 The Ground of Logical Truth The semblance of a theory An untenable dualism The place of logic For Further Reading Index. (shrink)

This brief paperback is designed for symbolic/formal logic courses. It features the tree method proof system developed by Jeffrey. The new edition contains many more examples and exercises and is reorganized for greater accessibility.

This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...

Many topics have not been covered, in most cases because I don't know quite what to say about them. Would it be possible to add a decidability predicate to the language? What about stronger connectives, like exclusion negation or Lukasiewicz implication? Would an expanded language do better at expressing its own semantics? Would it contain new and more terrible paradoxes? Can the account be supplemented with a workable notion of inherent truth (see note 36)? In what sense does stage semantics (...) lie “between” fixed point and stability semantics? In what sense, exactly, are our semantical rules inconsistent? In what sense, if any, does their inconsistency resolve the problem of the paradoxes?The ideals of strength, grounding, and closure together define an intuitively appealing conception of truth. Nothing would be gained by insisting that it was the intuitive conception of truth, and in fact recent developments make me wonder whether such a thing exists. However that may be, until the alternatives are better understood it would be foolish to attempt to decide between them. Truth gives up her secrets slowly and grudgingly, and loves to confound our presumptions. (shrink)

Recasting important questions about truth and objectivity in new and helpful terms, his book will become a focus in the contemporary debates over realism, and ...

We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...) KF and conjectured that the detour through classical logic in KF is dispensable. We refute Reinhardt's Conjecture, and provide a direct axiomatization PKF of Kripke's theory in partial logic. We argue that any natural axiomatization of Kripke's theory in Strong Kleene logic has the same proof-theoretic strength as PKF, namely the strength of the system RA< ωω ramified analysis or a system of Tarskian ramified truth up to ωω. Thus any such axiomatization is much weaker than Feferman's axiomatization KF in classical logic, which is equivalent to the system RA<ε₀ of ramified analysis up to ε₀. (shrink)

Bas C. van Fraassen presents an original exploration of how we represent the world.

Roy Sorenson offers a unique exploration of an ancient problem: vagueness. Did Buddha become a fat man in one second? Is there a tallest short giraffe? According to Sorenson's epistemicist approach, the answers are yes! Although vagueness abounds in the way the world is divided, Sorenson argues that the divisions are sharp; yet we often do not know where they are. Written in Sorenson'e usual inventive and amusing style, this book offers original insight on language and logic, the way world (...) is, and our understanding of it. (shrink)

In this collection of original papers, leading international authorities turn their attention to one of the most important questions in theoretical philosophy: ...

This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B⁺ and B. We show that the simplified semantics can also be used for a large number of extensions of the positive base logic B⁺, and then add the dualising '*' operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.

An text for introducing both formal and philosophical logic.

A logic is said to be contraction free if the rule from A→(A→B) to A→B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there is another contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to be robustly contraction free if (...) there is no such operator expressible in its language. We show that a large class of finitely valued logics are each not robustly contraction free, and demonstrate that some other contraction free logics fail to be robustly contraction free. Finally, the sublogics of Łω (with the standard connectives) are shown to be robustly contraction free. (shrink)

The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.

I argue that there is nothing about truth as such that prevents contradictions from being true. I argue this by considering the main standard accounts of truth, and showing that they are quite compatible with the existence of true contradictions. Indeed, in many cases, they are actually friendly to the idea.

It is known that a semantically closed theory with description may well be trivial if the principles concerning denotation and descriptions are formulated in certain ways, even if the underlying logic is paraconsistent. This paper establishes the nontriviality of a semantically closed theory with a natural, but non-extensional, description operator.

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)

In In Contradiction, Graham Priest shows, as clearly as anything like this can be shown, that it is coherent to maintain that some sentences can be both true and false at the same time. As a consequence, some contradictions are true, and an appreciation of this possibility advances our understanding of the nature of logic and language.