Five theories of reasoning: Interconnections and applications to mathematics

Logic and Logical Philosophy 20 (1-2):7-57 (2011)

Andrew Aberdein
Florida Institute of Technology
The last century has seen many disciplines place a greater priority on understanding how people reason in a particular domain, and several illuminating theories of informal logic and argumentation have been developed. Perhaps owing to their diverse backgrounds, there are several connections and overlapping ideas between the theories, which appear to have been overlooked. We focus on Peirce’s development of abductive reasoning [39], Toulmin’s argumentation layout [52], Lakatos’s theory of reasoning in mathematics [23], Pollock’s notions of counterexample [44], and argumentation schemes constructed by Walton et al. [54], and explore some connections between, as well as within, the theories. For instance, we investigate Peirce’s abduction to deal with surprising situations in mathematics, represent Pollock’s examples in terms of Toulmin’s layout, discuss connections between Toulmin’s layout and Walton’s argumentation schemes, and suggest new argumentation schemes to cover the sort of reasoning that Lakatos describes, in which arguments may be accepted as faulty, but revised, rather than being accepted or rejected. We also consider how such theories may apply to reasoning in mathematics: in particular, we aim to build on ideas such as Dove’s [13], which help to show ways in which the work of Lakatos fits into the informal reasoning community
Keywords Lakatos  mathematics  informal reasoning  argumentation
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DOI 10.12775/LLP.2011.002
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References found in this work BETA

Two Dogmas of Empiricism.W. V. O. Quine - 1951 - [Longmans, Green].
The Uses of Argument.Stephen E. Toulmin - 1958 - Cambridge University Press.
Collected Papers of Charles Sanders Peirce.Charles S. Peirce - 1931 - Cambridge: Harvard University Press.
Non-Standard Analysis.A. Robinson - 1961 - North-Holland Publishing Co..

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Citations of this work BETA

Mathematical Wit and Mathematical Cognition.Andrew Aberdein - 2013 - Topics in Cognitive Science 5 (2):231-250.
The Parallel Structure of Mathematical Reasoning.Andrew Aberdein - 2012 - In Alison Pease & Brendan Larvor (eds.), Proceedings of the Symposium on Mathematical Practice and Cognition Ii: A Symposium at the Aisb/Iacap World Congress 2012. Society for the Study of Artificial Intelligence and the Simulation of Behaviour. pp. 7--14.

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