A powerful challenge to some highly influential theories, this book offers a thorough critical exposition of modal realism, the philosophical doctrine that many possible worlds exist of which our own universe is just one. Chihara challenges this claim and offers a new argument for modality without worlds.

This book, one of the first full-length studies of the modalities to emerge from the debate to which Saul Kripke, David Lewis, Ruth Marcus, and others are contributing, is an exploration and defense of the notion of modality de re, the idea that objects have both essential and accidental properties. Plantinga develops his argument by means of the notion of possible worlds and ranges over such key problems as the nature of essence, transworld identity, negative existential propositions, and the existence (...) of unactual objects in other possible worlds. He also applies his logical theories to the elucidation of two problems in the philosophy of religion: the problem of evil and the ontological argument. (shrink)

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...) many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. (shrink)

It seems to be an obvious truth that There could be something that doesn't actually exist. That is, it seems to be obiously true that ◊∃×). It is sufficient for the truth of that there could be more people, or trees, or cars, than there actually are. It is also sufficient for the truth of that there could be some pepole, or trees, or cars that are distinct from all those that actually exist. Do and suchlike statements involve a commitment (...) to possibilia, to things that possibly exist, but do not actually exist? If not, why not? And if so, what is the nature of the possibilia to which and its ilk commit us? These simple little questions are at the tip of an iceberg. (shrink)

This volume succeeds the same authors' well-known An Introduction to Modal Logic and A Companion to Modal Logic. We designate the three books and their authors NIML, IML, CML and H&C respectively. Sadly, George Hughes died partway through the writing of NIML.

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)

The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of non-classical systems of logic, including many-valued logics, (...) fuzzy logic, moddal and tense logics, and relevance logics. Persupposing only an elementary knowledge of formal logic, this book includes many useful summary tables and diagrams, as well as a helpful glossary of technical terms. Wide-ranging, informative, and eminently readable, this book has proven a valuable resource for generations of students and scholars in a variety of disciplines outside philosophy needing guidance on the philosophy of logic. (shrink)

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.

I discuss ways in which the linguistic form of mathimatics helps us think mathematically.

a collection of articles by philosophers of mathematics on themes associated with the work of Paul Benacceraf.

In the mathematical documents which have come down to us from these peoples, there are no theorems or demonstrations, and the fundamental concepts of ...

It seems to be an obvious truth that There could be something that doesn't actually exist.That is, it seems to be obiously true that ◊∃×).It is sufficient for the truth of that there could be more people, or trees, or cars, than there actually are. It is also sufficient for the truth of that there could be some pepole, or trees, or cars that are distinct from all those that actually exist. Do and suchlike statements involve a commitment to possibilia, (...) to things that possibly exist, but do not actually exist? If not, why not? And if so, what is the nature of the possibilia to which and its ilk commit us? These simple little questions are at the tip of an iceberg. (shrink)