This volume offers a selection of the most interesting and important work from recent years in the philosophy of mathematics, which has always been closely linked to, and has exerted a significant influence upon, the main stream of analytical philosophy. The issues discussed are of interest throughout philosophy, and no mathematical expertise is required of the reader. Contributors include W.V. Quine, W.D. Hart, Michael Dummett, Charles Parsons, Paul Benacerraf, Penelope Maddy, W.W. Tait, Hilary Putnam, George Boolos, Daniel Isaacson, Stewart Shapiro, (...) and Hartry Field. (shrink)

Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy by excellent philosophers up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, (...) mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy. (shrink)

This study is an unusual contribution to the philosophy of mind in that it argues for the sometimes unfashionable view of dualism: that mind and matter are distinct and separate entities as Descartes believed. The author takes as his point of departure the imaginative hypothesis of disembodiment, which establishes the possibility of the mind's being a quite non-material thing. There are clear casual correlations between what is physical and what is mental, and the most serious issue confronting dualism since Descartes (...) has been how such an interaction is possible. Dr Hart sets out to answer this question by showing that the issue is as much about the nature of causation as it is about the natures of mind and matter. (shrink)

Keith Hossack's thesis is that knowledge is a conceptually primitive and metaphysically fundamental relation between a mind and a fact. He argues that in terms of the simple relation of knowledge we can analyze central notions of epistemology , of semantics , of modality and a priori knowledge , of psychology , and of linguistics . He does so in a framework that includes a fairly rich faculty psychology and that stresses causation: knowledge can be caused by belief, but because (...) knowledge is simple, it is not any kind of belief. He regards his enterprise as metaphysics, and he proceeds in a rather grand manner. The beginning of his Preface might remind one of the opening paragraphs of Leibniz's The Monadology.If knowledge is a simple relation between minds and facts, then we want to know a bit about facts. Hossack takes facts to consist in universals being instantiated among things. He favours a view of universals as respects in which things resemble each other , but his theory is at least officially silent about which universals exist, leaving that as a matter for scientific inquiry . But he takes metaphysics to be a science . Here he is being coy, and it is worth making out how. Hossack uses multigrade relations; these are relations of no fixed polyadicity that for any natural number n may be instantiated by n things. Vectors are bearers of such relations. The relation among working men of uniting to form a union is a multigrade relation, and the founders of the International Workers of the World are a vector bearing this relation. (shrink)

Hume's Principle requires the existence of the finite cardinals and their cardinal, but these are the only cardinals the Principle requires. Were the Principle an analysis of the concept of cardinal number, it would already be peculiar that it requires the existence of any cardinals; an analysis of bachelor is not expected to yield unmarried men. But that it requires the existence of some cardinals, the countable ones, but not others, the uncountable, makes it seem invidious; it is as if (...) an analysis of people required that there be men but not women, or whites but not blacks. If we deprive the Principle of existential commitments, it will cease to yield Dedekind's axioms for the natural numbers and so fail a good test of material adequacy. But since there are cardinals no second-order theory guarantees, neither can the Principle be beefed up to require all cardinals. (shrink)