My ultimate goal in this paper is to illuminate, from a naturalistic point of view, the significance of the application of mathematics in the natural sciences for the practice of contemporary set theory.

Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...

I examine various claims to the effect that Cantor's Continuum Hypothesis and other problems of higher set theory are ill-posed questions. The analysis takes into account the viability of the underlying philosophical views and recent mathematical developments.

This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.

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.

Quine was one of the foremost philosophers of the Twentieth century. In this outstanding overview of Quine's philosophy, Peter Hylton shows why Quine is so important and how his philosophical naturalism has been so influential within analytic philosophy. Beginning with an overview of Quine's philosophical background in logic and mathematics and the role of Rudolf Carnap's influence on Quine's thought, he goes on to discuss Quine's famous analytic-synthetic distinction and his arguments concerning the nature of the a priori. He also (...) discusses Quine's philosophy of language and epistemology, his celebrated theory of the indeterminacy of translation and his broader views of ontology and modality. This book is essential reading for anyone interested in Quine, twentieth century philosophy and the philosophy of language. (shrink)