Journal of Humanistic Mathematics 7 (2):355-378 (2017)

James Franklin
University of New South Wales
The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.
Keywords Discrete  Continuous  Philosophy of mathematics  infinitesimals
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Analogue Magnitude Representations: A Philosophical Introduction.Jacob Beck - 2015 - British Journal for the Philosophy of Science 66 (4):829-855.
Analog and Digital, Continuous and Discrete.Corey J. Maley - 2011 - Philosophical Studies 155 (1):117-131.
Analog and Digital.David K. Lewis - 1971 - Noûs 5 (3):321-327.

View all 13 references / Add more references

Citations of this work BETA

Finitism in Geometry.Jean-Paul Van Bendegem - 2002 - Stanford Encyclopedia of Philosophy.
The Idea of Continuity as Mathematical-Philosophical Invariant.Eldar Amirov - 2019 - “Metafizika” Journal 2 (8):p. 87-100.

Add more citations

Similar books and articles

Can Discrete Time Make Continuous Space Look Discrete?Claudio Mazzola - 2014 - European Journal for Philosophy of Science 4 (1):19-30.
Mathematics: Essential Tensions. [REVIEW]Roman Duda - 1997 - Foundations of Science 2 (1):11-19.
Prices in Financial Markets.Michael U. Dothan - 1990 - Oxford University Press USA.
Discrete Mathematics.S. K. Chakraborty & B. K. Sarkar - 2011 - Oxford University Press India.
Potential Continuity of Colorings.Stefan Geschke - 2008 - Archive for Mathematical Logic 47 (6):567-578.
Anticipatory Timing of Continuous and Discrete Responses.Jack A. Adams & Lyle R. Creamer - 1962 - Journal of Experimental Psychology 63 (1):84.
On What There is—Infinitesimals and the Nature of Numbers.Jens Erik Fenstad - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):57-79.


Added to PP index

Total views
449 ( #16,050 of 2,421,634 )

Recent downloads (6 months)
58 ( #13,297 of 2,421,634 )

How can I increase my downloads?


My notes