The Necessity of Mathematics

&
Noûs 52 (3):549-577 (2018)
  Copy   BIBTEX

Abstract

Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.

Categories

Keywords

Reprint years

DOI

10.1111/nous.12268

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Mathematical necessity and reality.James Franklin - 1989 - Australasian Journal of Philosophy 67 (3):286 – 294.
Metaphysical modality and essentiality.Robert Michels - 2013 - Dissertation, University of Geneva
On a derivation of the necessity of identity.John P. Burgess - 2014 - Synthese 191 (7):1-19.
Metaphysical necessity is not logical necessity.Robert Farrell - 1981 - Philosophical Studies 39 (2):141 - 153.
The extent of metaphysical necessity.Daniel Nolan - 2011 - Philosophical Perspectives 25 (1):313-339.
Towards an Institutional Account of the Objectivity, Necessity, and Atemporality of Mathematics.Julian C. Cole - 2013 - Philosophia Mathematica 21 (1):9-36.
The Metaphysics of Modality: A Study in the Foundations of Necessity.Scott A. Shalkowski - 1984 - Dissertation, University of Michigan
Natural necessity as grounded in natural essence: towards a homogeneous essentialist account of modality.Hireche Salim - 2016 - Dissertation, University of Geneva
Using Aristotle's Philosophy of Mathematics to Understand the Scope of Hypothetical and Simple Necessity in His Philosophy of Biology.David Clair Williams - 2000 - Dissertation, The University of Utah
Necessity and Language.Morris Lazerowitz & Alice Ambrose - 2016 - Routledge.
Why essentialism requires two senses of necessity.Stephen K. McLeod - 2006 - Ratio 19 (1):77–91.
Necessity, Possibility and Determinism in Stoic Thought.Vanessa de Harven - 2016 - In Max Cresswel, Edwin Mares & Adriane Rini (eds.), Logical Modalities from Aristotle to Carnap: The Story of Necessity. Cambridge: Cambridge University Press. pp. 70-90.
The Necessity of Contingency or Contingent Necessity: Meillassoux, Hegel, and the Subject.John Van Houdt - 2011 - Cosmos and History : The Journal of Natural and Social Philosophy 7 (1):128-141.
Varieties of Necessity.Kit Fine - 2002 - In Tamar Szabo Gendler & John Hawthorne (eds.), Conceivability and Possibility. Oxford Up. pp. 253-281.
Physical and metaphysical necessity.Stephen Leeds - 2007 - Pacific Philosophical Quarterly 88 (4):458–485.

Analytics

Added to PP
2017-12-25

Downloads
869 (#16,215)

6 months
152 (#20,102)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Juhani Yli-Vakkuri
Australian Catholic University
John Hawthorne
Australian Catholic University

Citations of this work

Counterpossibles.Alexander W. Kocurek - 2021 - Philosophy Compass 16 (11):e12787.
Epistemic Autonomy and Externalism.J. Adam Carter - 2020 - In Kirk Lougheed & Jonathan Matheson (eds.), Epistemic Autonomy. London: Routledge.
How can necessary facts call for explanation.Dan Baras - 2020 - Synthese 198 (12):11607-11624.
Metaphysical Nihilism and Modal Logic.Ethan Brauer - 2022 - Philosophical Studies 179 (9):2751-2763.
Are Counterpossibles Epistemic?Daniel Dohrn - 2021 - Pacific Philosophical Quarterly 102 (1):51-72.

View all 7 citations / Add more citations

References found in this work

Writing the Book of the World.Theodore Sider - 2011 - Oxford, England: Oxford University Press.
Demonstratives: An Essay on the Semantics, Logic, Metaphysics and Epistemology of Demonstratives and other Indexicals.David Kaplan - 1989 - In Joseph Almog, John Perry & Howard Wettstein (eds.), Themes From Kaplan. Oxford University Press. pp. 481-563.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Knowledge of Language: Its Nature, Origin, and Use.Noam Chomsky - 1986 - Prager. Edited by Darragh Byrne & Max Kölbel.

View all 57 references / Add more references