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)|
References found in this work BETA
Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning.Douglas Walton & Erik C. W. Krabbe - 1995 - State University of New York Press.
Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos (ed.) - 1976 - Cambridge University Press.
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Mathematical Wit and Mathematical Cognition.Andrew Aberdein - 2013 - Topics in Cognitive Science 5 (2):231-250.
Objects and Processes in Mathematical Practice.Uwe Riss - 2011 - Foundations of Science 16 (4):337-351.
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