British Journal for the Philosophy of Science 42 (4):469-489 (1991)
Philosophers have recently expressed interest in accounting for the usefulness of mathematics to science. However, it is certainly not a new concern. Putnam and Quine have each worked out an argument for the existence of mathematical objects from the indispensability of mathematics to science. Were Quine or Putnam to disregard the applicability of mathematics to science, he would not have had as strong a case for platonism. But I think there must be ways of parsing mathematical sentences which account for applicability of mathematics and also do not require us to believe in entities we have no evidence for, other than through reading these sentences literally. We will explore a particular way to interpret sentences of arithmetic which promises to account for their applicability without bringing in metaphysics not also brought in by science. The investigation will be limited to the arithmetic of cardinal numbers. The general strategy is to argue for the analogy between arithmetic and science, rather than to argue for one case having a particular characteristic independently of the other.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Structuralism and the Applicability of Mathematics.Jairo José Silvdaa - forthcoming - Axiomathes.
Lost on the Way From Frege to Carnap: How the Philosophy of Science Forgot the Applicability Problem.Torsten Wilholt - 2006 - Grazer Philosophische Studien 73 (1):69-82.
The Applicability of Mathematics as a Scientific and a Logical Problem.Feng Ye - 2009 - Philosophia Mathematica 18 (2):144-165.
Kant's Theory of Arithmetic: A Constructive Approach? [REVIEW]Kristina Engelhard & Peter Mittelstaedt - 2008 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245 - 271.
On Representing the Relationship Between the Mathematical and the Empirical.Otávio Bueno, Steven French & James Ladyman - 2002 - Philosophy of Science 69 (3):497-518.
The Indispensability Argument and Multiple Foundations for Mathematics.Alan Baker - 2003 - Philosophical Quarterly 53 (210):49–67.
Quine, Putnam, and the 'Quine-Putnam' Indispensability Argument.David Liggins - 2007 - Erkenntnis 68 (1):113 - 127.
Added to index2009-01-28
Total downloads13 ( #340,219 of 2,143,803 )
Recent downloads (6 months)1 ( #387,257 of 2,143,803 )
How can I increase my downloads?
There are no threads in this forum
Nothing in this forum yet.