Erkenntnis 76 (2):263-278 (2012)

Authors
Joe Morrison
Queen's University, Belfast
Abstract
The indispensability argument is a method for showing that abstract mathematical objects exist. Various versions of this argument have been proposed. Lately, commentators seem to have agreed that a holistic indispensability argument will not work, and that an explanatory indispensability argument is the best candidate. In this paper I argue that the dominant reasons for rejecting the holistic indispensability argument are mistaken. This is largely due to an overestimation of the consequences that follow from evidential holism. Nevertheless, the holistic indispensability argument should be rejected, but for a different reason —in order that an indispensability argument relying on holism can work, it must invoke an unmotivated version of evidential holism. Such an argument will be unsound. Correcting the argument with a proper construal of evidential holism means that it can no longer deliver mathematical Platonism as a conclusion: such an argument for Platonism will be invalid. I then show how the reasons for rejecting the holistic indispensability argument importantly constrain what kind of account of explanation will be permissible in explanatory versions
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s10670-011-9300-4
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,319
Through your library

References found in this work BETA

Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford University Press.
Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.
Pursuit of Truth.W. V. QUINE - 1990 - Harvard University Press.

View all 34 references / Add more references

Citations of this work BETA

Good Weasel Hunting.Robert Knowles & David Liggins - 2015 - Synthese 192 (10):3397-3412.
Platonic Relations and Mathematical Explanations.Robert Knowles - forthcoming - The Philosophical Quarterly.

View all 12 citations / Add more citations

Similar books and articles

Isn’T the Indispensability Argument Necessarily Analogical?Woosuk Park - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:13-18.
Indispensability Without Platonism.Anne Newstead & James Franklin - 2012 - In Alexander Bird, Brian Ellis & Howard Sankey (eds.), Properties, Powers, and Structures: Issues in the Metaphysics of Realism. New York, USA: Routledge. pp. 81-97.
Indispensability and Holism.Jacob Busch - 2011 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 42 (1):47-59.
A Truthmaker Indispensability Argument.Sam Baron - 2013 - Synthese 190 (12):2413-2427.
Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.
In Defence of Indispensability.Mark Colyvan - 1998 - Philosophia Mathematica 6 (1):39-62.
Indispensability Arguments and Instrumental Nominalism.Richard Pettigrew - 2012 - Review of Symbolic Logic 5 (4):687-709.
Numbers Without Science.Russell Marcus - 2007 - Dissertation, The Graduate School and University Center of the City University of New York

Analytics

Added to PP index
2011-05-17

Total views
125 ( #85,170 of 63,273 )

Recent downloads (6 months)
7 ( #97,523 of 63,273 )

How can I increase my downloads?

Downloads

My notes