The article develops and extends the theory of Glenn Kessler (Frege, Mill and the foundations of arithmetic, Journal of Philosophy 77, 1980) that a (cardinal) number is a relation between a heap and a unit-making property that structures the heap. For example, the relation between some swan body mass and "being a swan on the lake" could be 4.

This is a book of philosophy, written by a philosopher and intended for anyone who knows enough philosophy to have been seriously injured, antagonised, mystified or intoxicated by it. Stove is passionately polemical, a philosophical counterpart to Tom Wolfe. Setting out to deflate a few philosophical reputations, he lambastes both the dead and the living. Yet he says things that need to be said, and that others often lack the courage to say.

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...) She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

This book espouses an innovative theory of scientific realism in which due weight is given to mathematics and logic. The authors argue that mathematics can be understood realistically if it is seen to be the study of universals, of properties and relations, of patterns and structures, the kinds of things which can be in several places at once. Taking this kind of scientific platonism as their point of departure, they show how the theory of universals can account for probability, laws (...) of nature, causation, and explanation, and explore the consequences in all these fields. This will be an important book for all philosophers of science, logicians, and metaphysicians, and their graduate students. The readership will also include those outside philosophy interested in the interrelationship of philosophy and science. (shrink)

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.