Philosophers' Imprint (forthcoming)

Authors
Silvia De Toffoli
Princeton University
Abstract
Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear.
Keywords Mathematical Diagram  Visualization  Justification  Proof  Notational Systems
Categories (categorize this paper)
Options
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

Languages of Art.Nelson Goodman - 1970 - Philosophy and Rhetoric 3 (1):62-63.
What Metaphors Mean.Donald Davidson - 2010 - In Darragh Byrne & Max Kölbel (eds.), Critical Inquiry. Routledge. pp. 31.
What Metaphors Mean.Donald Davidson - 1978 - Critical Inquiry 5 (1):31-47.
Rigor and Structure.John P. Burgess - 2015 - Oxford, England: Oxford University Press UK.
The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.

View all 26 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

The Role of Diagrams in Mathematical Arguments.David Sherry - 2008 - Foundations of Science 14 (1-2):59-74.
Groundwork for a Fallibilist Account of Mathematics.Silvia De Toffoli - 2021 - Philosophical Quarterly 7 (4):823-844.
Diagrams as Sketches.Brice Halimi - 2012 - Synthese 186 (1):387-409.
Proof, Logic and Formalization.Michael Detlefsen (ed.) - 1992 - London, England: Routledge.
Diagrams and Proofs in Analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.
Mathematical Rigor and Proof.Yacin Hamami - forthcoming - Review of Symbolic Logic:1-41.

Analytics

Added to PP index
2021-12-30

Total views
149 ( #74,072 of 2,463,174 )

Recent downloads (6 months)
149 ( #3,886 of 2,463,174 )

How can I increase my downloads?

Downloads

My notes