David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Foundations of Science 14 (1-2):136-152 (2009)
In this paper, I assume, perhaps controversially, that translation into a language of formal logic is not the method by which mathematicians assess mathematical reasoning. Instead, I argue that the actual practice of analyzing, evaluating and critiquing mathematical reasoning resembles, and perhaps equates with, the practice of informal logic or argumentation theory. It doesn’t matter whether the reasoning is a full-fledged mathematical proof or merely some non-deductive mathematical justification: in either case, the methodology of assessment overlaps to a large extent with argument assessment in non-mathematical contexts. I demonstrate this claim by considering the assessment of axiomatic or deductive proofs, probabilistic evidence, computer-aided proofs, and the acceptance of axioms. I also consider Jody Azzouni’s ‘derivation indicator’ view of proofs because it places derivations—which may be thought to invoke formal logic—at the center of mathematical justificatory practice. However, when the notion of ‘derivation’ at work in Azzouni’s view is clarified, it is seen to accord with, rather than to count against, the informal logical view I support. Finally, I pose several open questions for the development of a theory of mathematical argument.
|Keywords||Argumentation Proof Mathematics Argument schemes Dialectic Informal logic Azzouni Rav|
|Categories||categorize this paper)|
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
Irving M. Copi (2008). Introduction to Logic. Pearson/Prentice Hall.
Douglas Walton & Erik C. W. Krabbe (1995). Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning. State University of New York Press.
Imre Lakatos (ed.) (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Douglas N. Walton (2006). Fundamentals of Critical Argumentation. Cambridge University Press.
Citations of this work BETA
Andrew Aberdein (2013). Mathematical Wit and Mathematical Cognition. Topics in Cognitive Science 5 (2):231-250.
Uwe Riss (2011). Objects and Processes in Mathematical Practice. Foundations of Science 16 (4):337-351.
Similar books and articles
Andrew Aberdein (2011). The Dialectical Tier of Mathematical Proof. In Frank Zenker (ed.), Argumentation: Cognition & Community. Proceedings of the 9th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 18--21, 2011. OSSA
Jody Azzouni (2004). The Derivation-Indicator View of Mathematical Practice. Philosophia Mathematica 12 (2):81-106.
Jody Azzouni (2009). Why Do Informal Proofs Conform to Formal Norms? Foundations of Science 14 (1-2):9-26.
Jean Paul van Bendegem & Bart van Kerkhove (2009). Mathematical Arguments in Context. Foundations of Science 14 (1-2):45-57.
Mark McEvoy (2012). Platonism and the 'Epistemic Role Puzzle'. Philosophia Mathematica 20 (3):289-304.
Jean Paul Van Bendegem (2005). Proofs and Arguments: The Special Case of Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
Brendan Larvor (2012). How to Think About Informal Proofs. Synthese 187 (2):715-730.
Andrew Aberdein (2006). The Informal Logic of Mathematical Proof. In Reuben Hersh (ed.), 18 Unconventional Essays About the Nature of Mathematics. Springer-Verlag 56-70.
Marianna Antonutti Marfori (2010). Informal Proofs and Mathematical Rigour. Studia Logica 96 (2):261-272.
Yehuda Rav (2007). A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices. Philosophia Mathematica 15 (3):291-320.
Added to index2009-01-28
Total downloads53 ( #63,571 of 1,725,867 )
Recent downloads (6 months)12 ( #56,105 of 1,725,867 )
How can I increase my downloads?