Philosophia Mathematica - Advance Access

Exploring the Boundaries of Conceptual Evaluation

Pincock, C. — Thu, 05 Nov 2009 06:26:10 PST

BRUNO DE FINETTI. Philosophical Lectures on Probability. Collected, edited, and annotated by Alberto Mura. Translated by Hykel Hosni. Synthese Library; 340

Williamson, J. — Thu, 05 Nov 2009 03:19:22 PST

ANDREW D. IRVINE. Philosophy of Mathematics. (Handbook of the Philosophy of Science)

Thu, 05 Nov 2009 03:19:21 PST

Whitehead and Russell on Points

Bostock, D. — Thu, 05 Nov 2009 03:19:21 PST

This paper considers the attempts put forward by A.N. Whitehead and by Bertrand Russell to ‘construct’ points (and temporal instants) from what they regard as the more basic concept of extended ‘regions’. It is shown how what they each say themselves will not do, and how it should be filled out and amended so that the ‘construction’ may be regarded as successful. Finally there is a brief discussion of whether this ‘construction’ is worth pursuing, or whether it is better—as in today’s mathematics—to prefer a ‘construction’ that goes the other way round, i.e., to view a region as a set of points.

DAVID BOSTOCK. Philosophy of Mathematics: An Introduction

Brown, J. R. — Thu, 05 Nov 2009 03:19:20 PST

PETER SMITH. An Introduction to Godel's Theorems

Smorynski, C. — Thu, 01 Oct 2009 01:47:28 PDT

The Applicability of Mathematics as a Scientific and a Logical Problem

Ye, F. — Wed, 30 Sep 2009 09:14:25 PDT

This paper explores how to explain the applicability of classical mathematics to the physical world in a radically naturalistic and nominalistic philosophy of mathematics. The applicability claim is first formulated as an ordinary scientific assertion about natural regularity in a class of natural phenomena and then turned into a logical problem by some scientific simplification and abstraction. I argue that there are some genuine logical puzzles regarding applicability and no current philosophy of mathematics has resolved these puzzles. Then I introduce a plan for resolving the logical puzzles of applicability.

Ontology and the Word 'Exist': Uneasy Relations

Azzouni, J. — Wed, 26 Aug 2009 01:11:35 PDT

An extensive exploration of the special properties of ‘exist’ is here undertaken. Two of several results are: Denying that `exist’ has associated with it a set of necessary and sufficient conditions has seemed to a number of philosophers to imply metaphysical nihilism. This is because it has seemed that without such conditions the target domain of `existence’ is arbitrarily open. I show this is wrong. Second, my analysis sheds light on the puzzling question of what we are asking when we ask of something, `Does it exist?’ and mean that question in an ontically relevant way.

Mathematical Nominalism and Measurement

Rizza, D. — Mon, 29 Jun 2009 02:20:50 PDT

In this paper I defend mathematical nominalism by arguing that any reasonable account of scientific theories and scientific practice must make explicit the empirical non-mathematical grounds on which the application of mathematics is based. Once this is done, references to mathematical entities may be eliminated or explained away in terms of underlying empirical conditions. I provide evidence for this conclusion by presenting a detailed study of the applicability of mathematics to measurement. This study shows that mathematical nominalism may be regarded as a methodological approach to applicability, illuminating the use of mathematics in science.