ZDM 51 (5):825-834 (2019)

Andrew Aberdein
Florida Institute of Technology
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning.
Keywords argument  argumentation schemes  derivation  evidence  proof
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

Intuition.Elijah Chudnoff - 2013 - Oxford University Press.
The Uses of Argument.Stephen E. Toulmin - 1958 - Cambridge University Press.
The Uses of Argument.Stephen E. Toulmin - 1958 - Cambridge University Press.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.

View all 31 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Towards a Theory of Mathematical Argument.Ian J. Dove - 2009 - Foundations of Science 14 (1-2):136-152.
Mathematical Wit and Mathematical Cognition.Andrew Aberdein - 2013 - Topics in Cognitive Science 5 (2):231-250.
Formalizing Informal Logic.Douglas Walton & Thomas F. Gordon - 2015 - Informal Logic 35 (4):508-538.
A Dialogical Theory of Presumption.Douglas Walton - 2008 - Artificial Intelligence and Law 16 (2):209-243.


Added to PP index

Total views
141 ( #63,760 of 2,340,261 )

Recent downloads (6 months)
25 ( #26,900 of 2,340,261 )

How can I increase my downloads?


My notes