Platonism by the Numbers

Abstract

In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.

Categories

Keywords

Reprint years

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

My notes

Similar books and articles

Mathematical Platonism.Massimo Pigliucci - 2011 - Philosophy Now 84:47-47.
Necessary Existence and A Priori Knowledge.Colin Cheyne - unknown
Problems with profligate platonism.Colin Cheyne - 1999 - Philosophia Mathematica 7 (2):164-177.
Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
Platonism and anti-Platonism in mathematics.Mark Balaguer - 1998 - New York: Oxford University Press.
Learning natural numbers is conceptually different than learning counting numbers.Dwight Read - 2008 - Behavioral and Brain Sciences 31 (6):667-668.
Counting systems and the First Hilbert problem.Yaroslav Sergeyev - 2010 - Nonlinear Analysis Series A 72 (3-4):1701-1708.
Uwagi o platonizmie matematycznym.Anna Lemańska - 2012 - Filozofia Nauki 20 (2).
Getting in touch with numbers: Intuition and mathematical platonism.Colin Cheyne - 1997 - Philosophy and Phenomenological Research 57 (1):111-125.
What numbers could be (and, hence, necessarily are).Mark Eli Kalderon - 1996 - Philosophia Mathematica 4 (3):238-255.
The epistemic significance of numerals.Jan Heylen - 2014 - Synthese 198 (Suppl 5):1019-1045.
Platonism in the Philosophy of Mathematics.Øystein Linnebo - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
Is there a good epistemological argument against platonism?David Liggins - 2006 - Analysis 66 (2):135–141.
Platonism and anti‐Platonism: Why worry?Mary Leng - 2005 - International Studies in the Philosophy of Science 19 (1):65 – 84.
Counting and the natural numbers.Jeffrey F. Sicha - 1970 - Philosophy of Science 37 (3):405-416.

Analytics

Added to PP
2014-07-23

Downloads
362 (#56,369)

6 months
71 (#68,953)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Steven Merle Duncan
Bellevue Community College

Citations of this work

Add more citations

References found in this work

No references found.

Add more references