Functional explanation in mathematics

Synthese:1-24 (forthcoming)

Authors
Matthew Inglis
Loughborough University
Abstract
Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s suggestion that explanations are those sorts of things that generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore argue that the explanatory criteria offered by earlier accounts can all be thought of as features that make it more likely that a mathematical proof will generate understanding. On the functional account, features such as characterising properties, unification, and salience correlate with explanatoriness, but they do not define explanatoriness.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1007/s11229-019-02234-5
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 46,179
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

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Explanation in Mathematical Practice.David Sandborg - 1997 - Dissertation, University of Pittsburgh
Can Intentional and Functional Explanations of Actions Coexist?Rob Vanderbeeken - 2006 - The Proceedings of the Twenty-First World Congress of Philosophy 9:143-147.
Systems Biology and the Integration of Mechanistic Explanation and Mathematical Explanation.Ingo Brigandt - 2013 - Studies in History and Philosophy of Biological and Biomedical Sciences 44 (4):477-492.
“Looking Up” and “Looking Down”: On the Dual Character of Mechanistic Explanations.Kari L. Theurer - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (3):371-392.
Can Intentional and Functional Explanations of Actions Coexist?Rob Vanderbeeken - 2006 - The Proceedings of the Twenty-First World Congress of Philosophy 9:143-147.
Causal Patterns and Adequate Explanations.Angela Potochnik - 2015 - Philosophical Studies 172 (5):1163-1182.
Viability Explanation.Arno Wouters - 1995 - Biology and Philosophy 10 (4):435-457.
Against Mathematical Explanation.Mark Zelcer - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):173-192.
Mechanism or Bust? Explanation in Psychology.Lawrence A. Shapiro - 2017 - British Journal for the Philosophy of Science 68 (4):1037-1059.

Analytics

Added to PP index
2019-05-22

Total views
11 ( #729,319 of 2,285,434 )

Recent downloads (6 months)
2 ( #578,621 of 2,285,434 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature