A Structured Argumentation Framework for Modeling Debates in the Formal Sciences

Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (2):219-241 (2020)
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Abstract

Scientific research in the formal sciences comes in multiple degrees of formality: fully formal work; rigorous proofs that practitioners know to be formalizable in principle; and informal work like rough proof sketches and considerations about the advantages and disadvantages of various formal systems. This informal work includes informal and semi-formal debates between formal scientists, e.g. about the acceptability of foundational principles and proposed axiomatizations. In this paper, we propose to use the methodology of structured argumentation theory to produce a formal model of such informal and semi-formal debates in the formal sciences. For this purpose, we propose ASPIC-END, an adaptation of the structured argumentation framework ASPIC+ which can incorporate natural deduction style arguments and explanations. We illustrate the applicability of the framework to debates in the formal sciences by presenting a simple model of some arguments about proposed solutions to the Liar paradox, and by discussing a more extensive—but still preliminary—model of parts of the debate that mathematicians had about the Axiom of Choice in the early twentieth century.

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Formal Models of Scientific Inquiry in a Social Context: An Introduction.Dunja Šešelja, Christian Straßer & AnneMarie Borg - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (2):211-217.

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