Contemporary argumentation theory tends to steer away from traditional formal logic. In the case of argumentation theory applied to mathematics, though, it is proper for argumentation theory to revisit formal logic owing to the in-principle formalizability of mathematical arguments. Completely formal proofs of substantial mathematical arguments suffer from well-known problems. But practical formalizations of substantial mathematical results are now available, thanks to the help provided by modern automated reasoning systems. In-principle formalizability has become in-practice formalizability. Such efforts are a resource for argumentation theory applied to mathematics because topics that might be thought to be essentially informal reappear in the computer-assisted, formal setting, prompting a fresh appraisal.
Keywordformal logic mathematical practice mathematical proof natural deduction proof analysis proof checking proof reconstruction
Both authors were partially supported by the ESF research project Dialogical Foundations of Semantics within the ESF Eurocores programme ‘LogICCC’, LogICCC/0001/2007, and the project ‘The Notion of Mathematical Proof’, PTDC/MHC-FIL/5363/2012, both funded by the Portuguese Science Foundation FCT. Alama’s research was conducted in part as a visiting fellow at the Isaac Newton Institute for the Mathematical Sciences, Cambridge, in the programme ‘Semantics & Syntax’. Kahle was partially supported by the FCT project ‘Hilbert’s Legacy in the Philosophy of Mathematics’, PTDC/FIL-FCI/109991/2009.
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