Proofs and rebuttals: Applying Stephen Toulmin's layout of arguments to mathematical proof

In Marta Bílková & Ondřej Tomala (eds.), The Logica Yearbook 2005. Filosofia. 11-23 (2006)
Abstract
This paper explores some of the benefits informal logic may have for the analysis of mathematical inference. It shows how Stephen Toulmin’s pioneering treatment of defeasible argumentation may be extended to cover the more complex structure of mathematical proof. Several common proof techniques are represented, including induction, proof by cases, and proof by contradiction. Affinities between the resulting system and Imre Lakatos’s discussion of mathematical proof are then explored.
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