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Marianna Antonutti: Detlefsen on Mathematical Proof



According the common view of proof (CVP) a rigorous proof is a proof which (i) does not conceal nonlogical information, and (ii) whose inferences can be seen as valid solely in virtue of purely logical relations between concepts (Detlefsen, 2009: 16-7). The idea is that every mathematical proof should be converted into a formal derivation in a suitable formal system. 1 On this view, rigor is a necessary feature of proof, and formalizability is a necessary condition of rigor. 2 CVP has emerged out the foundational crisis at the beginning of the 20 th century as a guarantee that theorems were flawlessly deduced from axioms. Foundational concerns produced a shift in mathematical epistemology, which ceased to be concerned with the actual ways of acquiring mathematical knowledge by individuals and started focussing on mathematical subdisciplines as axiomatized bodies of mathematical knowledge. 3 In this context, mathematical proof is not aimed at capturing the ways in which mathematical reasoning proceeds, nor providing mathematical understanding or suggesting ideas for new proofs, but was conceived as an essential justificatory device. Detlefsen (2009) takes the main challenges made to our understanding of the notion of proof to come from two sources, namely the epistemic status of computerbased proofs, and the role of visual reasoning in mathematics. In this paper, I look at proof as the justification for a mathematical statement. My aim is that of clarifying different ways of addressin

Year: 2011
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