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  1. Towards a theory of abduction based on conditionals.Rolf Pfister - 2022 - Synthese 200 (3):1-30.
    Abduction is considered the most powerful, but also the most controversially discussed type of inference. Based on an analysis of Peirce’s retroduction, Lipton’s Inference to the Best Explanation and other theories, a new theory of abduction is proposed. It considers abduction not as intrinsically explanatory but as intrinsically conditional: for a given fact, abduction allows one to infer a fact that implies it. There are three types of abduction: Selective abduction selects an already known conditional whose consequent is the given (...)
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  • Dialogue Types, Argumentation Schemes, and Mathematical Practice: Douglas Walton and Mathematics.Andrew Aberdein - 2021 - Journal of Applied Logics 8 (1):159-182.
    Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.
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