Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

Pease, Alison; Smaill, Alan; Colton, Simon; Lee, John Y.K.

doi:10.1007/s10699-008-9150-y

Cited by 8 publications

(3 citation statements)

References 22 publications

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“…However, Furse (1990) had already called into question the robustness of approaches to modelling mathematical creativity that only model a solitary creative individual. Pease et al (2009) describe an implementation effort that made use of a multi-agent approach, drawing on argumentation theory concepts and a Lakatosian model of dialogue. However, the mathematical applications of that system were limited to straightforward computational aspects of number theory and group theory, which suggests a "knowledge bottleneck" Moens, 2018).…”

Section: Discussionmentioning

confidence: 99%

Argumentation Theory for Mathematical Argument

et al. 2019

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To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport's structured proofs.

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Section: Discussionmentioning

confidence: 99%

Argumentation Theory for Mathematical Argument

et al. 2019

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“…And such an acceptance itself rests on some informal reasoning (Krabbe 2008). Mathematical proofs very often involve informal considerations (Dove 2009) (Pease et al 2009). And even the probative force of the formal part of the proof rests on some confidence in this kind of reasoning, which results itself from "intuitions" partly made of learned habits (Tappenden 2005) (Longo 2010).…”

Section: The Dichotomy Between Logic Of Discovery and Logic Of Justifmentioning

confidence: 99%

Iconic virtues of diagrams

Leclercq

2019

signata

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“…who use 'expla*' and 'underst*' as explanation indicators.6 Dutilh Novaes (2019, p. 73) argues that, "In an explanatory proof, there should be no surprises: each step in the proof must be clear and evident, eliciting immediate understanding in whoever inspects the proof, thus ruling out unexpected 'turns'." 7 For more on the relationship between philosophy of mathematics and argumentation theory, seePease et al (2009). Ashton and Mizrahi (2018a) use a similar methodology and the tools of data science to investigate appeals to intuition in philosophy.…”

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Proof, Explanation, and Justification in Mathematical Practice

Mizrahi

2020

J Gen Philos Sci

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In this paper, I propose that applying the methods of data science to "the problem of whether mathematical explanations occur within mathematics itself" (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of this empirical study suggest that mathematical explanations do occur in research articles published in mathematics journals, as indicated by the occurrence of explanation indicators. When compared with the use of justification indicators, however, the data suggest that justifications occur much more frequently than explanations in scholarly mathematical practice. The results also suggest that justificatory proofs occur much more frequently than explanatory proofs, thus suggesting that proof may be playing a larger justificatory role than an explanatory role in scholarly mathematical practice.

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Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

Cited by 8 publications

References 22 publications

Argumentation Theory for Mathematical Argument

Argumentation Theory for Mathematical Argument

Iconic virtues of diagrams

Proof, Explanation, and Justification in Mathematical Practice

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