Motivated proofs: What they are, why they matter and how to write them

Review of Symbolic Logic 13 (1):23-46 (2020)
  Copy   BIBTEX

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,642

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2019-11-08

Downloads
19 (#190,912)

6 months
71 (#224,364)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Rebecca Morris
Independent Scholar

References found in this work

Scientific Explanation.P. Kitcher & W. C. Salmon - 1992 - British Journal for the Philosophy of Science 43 (1):85-98.
Mathematical explanation.Mark Steiner - 1978 - Philosophical Studies 34 (2):135 - 151.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
Purity of Methods.Michael Detlefsen & Andrew Arana - 2011 - Philosophers' Imprint 11.
Modularity in mathematics.Jeremy Avigad - 2020 - Review of Symbolic Logic 13 (1):47-79.

View all 18 references / Add more references