An Essay on Mathematical Instrumentalism M. Detlefsen. THE PHILOSOPHICAL FUNDAMENTALS OF HILBERT'S PROGRAM 1. INTRODUCTION In this chapter I shall attempt to set out Hilbert's Program in a way that is more revealing than ...

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.

This volume which was compiled as a festschrift on the occasion of Russell's ninety-fifth birthday, contains a well-chosen combination of articles dealing with Russell's personality, political life, and influence upon public issues; as well as some rather more technical papers concerning Russell's theory of knowledge, sense-perception, his contribution to logical theory, and ontology. Of the popular and semi-popular pieces in the first half of this volume, many good things might be said; but especially worthwhile are I. F. Stone's moving article, (...) "To Oppose the Stream," an appreciation of Russell's courage and intellectual integrity, and Linus Pauling's bone chilling apocalyptic arithmetic in "Would Civilization Survive a Nuclear War?" It should also be added that Schoenman's introduction to the volume may be an important document in itself. The articles by Dana Scott and Georg Kreisel will be accessible only to readers with considerable training in logic and set theory, but will be of utmost interest to such specialists, as they concern the philosophically significant issues of improper descriptions, existence statements, and the extent to which logic can serve as "foundations" for mathematics. Putnam argues against the traditional logicist view and bases a good deal of his criticism upon the occurrence of impredicative definitions in Principia-type systems. The one sour note in the book is Quine's article on Russell's ontology, which occupies eleven rather insubstantial pages. Surely, this important facet of Russell's work deserves a more detailed exposition and analysis.—H. P. K. (shrink)