Review of Symbolic Logic 13 (1):23-46 (2020)
Authors |
|
Abstract |
Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such qualities. However, mathematicians frequently draw attention to another desirable proof quality: being motivated. Intuitively, motivated proofs contain no "puzzling" steps, but they have received little further analysis. In this paper, I begin a philosophical investigation into motivated proofs. I suggest that a proof is motivated if and only if mathematicians can identify (i) the tasks each step is intended to perform; and (ii) where each step could have reasonably come from. I argue that motivated proofs promote understanding, convey new mathematical resources and stimulate new discoveries. They thus have significant epistemic benefits and directly contribute to the efficient dissemination and advancement of mathematical knowledge. Given their benefits, I also discuss the more practical matter of how we can produce motivated proofs. Finally I consider the relationship between motivated proofs and proofs which are explanatory, beautiful and fitting.
|
Keywords | No keywords specified (fix it) |
Categories | (categorize this paper) |
DOI | 10.1017/s1755020319000583 |
Options |
![]() ![]() ![]() ![]() |
Download options
References found in this work BETA
Scientific Explanation.P. Kitcher & W. C. Salmon - 1992 - British Journal for the Philosophy of Science 43 (1):85-98.
View all 18 references / Add more references
Citations of this work BETA
Philosophy of Mathematical Practice: A Primer for Mathematics Educators.Yacin Hamami & Rebecca Morris - forthcoming - ZDM Mathematics Education.
Plans and Planning in Mathematical Proofs.Yacin Hamami & Rebecca Lea Morris - forthcoming - Review of Symbolic Logic:1-40.
Increasing Specialization: Why We Need to Make Mathematics More Accessible.Rebecca Lea Morris - 2020 - Social Epistemology 35 (1):37-47.
Similar books and articles
Probabilistic Proofs and Transferability.Kenny Easwaran - 2009 - Philosophia Mathematica 17 (3):341-362.
On the Status of Proofs by Contradiction in the Seventeenth Century.Paolo Mancosu - 1991 - Synthese 88 (1):15 - 41.
A Problem with the Dependence of Informal Proofs on Formal Proofs.Fenner Tanswell - 2015 - Philosophia Mathematica 23 (3):295-310.
The Nature and Relation of the Three Proofs of God's Existence in Descates' Meditations.David N. Stamos - unknown
Mathematicians Writing for Mathematicians.Line Edslev Andersen, Mikkel Willum Johansen & Henrik Kragh Sørensen - 2019 - Synthese 198 (Suppl 26):6233-6250.
Strategic Maneuvering in Mathematical Proofs.Erik C. W. Krabbe - 2008 - Argumentation 22 (3):453-468.
Normal Natural Deduction Proofs (in Classical Logic).Wilfried Sieg & John Byrnes - 1998 - Studia Logica 60 (1):67-106.
Aspects of Mathematical Explanation: Symmetry, Unity, and Salience.Marc Lange - 2014 - Philosophical Review 123 (4):485-531.
Phallocentrism in Bergson: Life and Matter.Rebecca Hill - 2008 - Deleuze and Guatarri Studies 2 (Suppl):123-136.
Analytics
Added to PP index
2019-11-08
Total views
38 ( #300,959 of 2,519,807 )
Recent downloads (6 months)
2 ( #270,824 of 2,519,807 )
2019-11-08
Total views
38 ( #300,959 of 2,519,807 )
Recent downloads (6 months)
2 ( #270,824 of 2,519,807 )
How can I increase my downloads?
Downloads