Rigour and Proof

Tatton-Brown, Oliver

doi:10.1017/s1755020320000398

Cited by 5 publications

(2 citation statements)

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“…18 In the following, we shall often identify a hl-rule with its associated verification process, and talk freely of hl-rules as verification processes. 19 On the importance of taking into account the mathematical training of the agents when analyzing how proofs are judged to be rigorous in mathematical practice, see also Tatton-Brown (2019).…”

Section: The Set Of Verification Processesmentioning

confidence: 99%

Mathematical Rigor and Proof

Hamami

2019

The Review of Symbolic Logic

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Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowledge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous? According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary mathematicians, and is endorsed by many logicians and philosophers, but it has also been heavily criticized in the philosophy of mathematics literature. Progress on the debate between the proponents and opponents of the standard view is, however, currently blocked by a major obstacle, namely, the absence of a precise formulation of it. To remedy this deficiency, I undertake in this paper to provide a precise formulation and a thorough evaluation of the standard view of mathematical rigor. The upshot of this study is that the standard view is more robust to criticisms than it transpires from the various arguments advanced against it, but that it also requires a certain conception of how mathematical proofs are judged to be rigorous in mathematical practice, a conception that can be challenged on empirical grounds by exhibiting rigor judgments of mathematical proofs in mathematical practice conflicting with it.

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Section: The Set Of Verification Processesmentioning

confidence: 99%

Mathematical Rigor and Proof

Hamami

2019

The Review of Symbolic Logic

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“…A philosopher in the Rav tendency might argue thus: mathematicians formalise, but the art of it is tacit knowledge. It is not a summatively assessed part of mathematical training (seeTatton-Brown (2020) for an account of how it is learned). Mathematicians who have entirely internalised the art of formalisation may feel that they're doing almost nothing, something 'routine', rather as a virtuoso jazz musician might insist that they're not thinking about music theory or technique while improvising.…”

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confidence: 99%