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A Logical Framework for Understanding Why

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Selected Reflections in Language, Logic, and Information (ESSLLI 2019)

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Abstract

Epistemic logic pays barely any attention to the notion of understanding, which stands in total contrast to the current situation in epistemology and in philosophy of science. This paper studies understanding why in an epistemic-logic-style. It is generally acknowledged that understanding why moves beyond knowing why. Inspired by philosophical ideas, we consider whereas knowing why requires knowing horizontal explanations, understanding why additionally requires vertical explanations. Based on justification logic and existing logical work for knowing why, we build up a framework by introducing vertical explanations, and show it could accommodate different philosophical viewpoints via adding conditions to the models. A sound and complete axiomatization for the most general case is given.

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Notes

  1. 1.

    See, for instance [16, 20, 22, 31] etc. All mentions of “understanding” in their work should be read as concerning “understanding why”. And the author of [20] refers to understanding why as a narrow conception of understanding.

  2. 2.

    For example, see [3] and the bibliographies therein.

  3. 3.

    As mentioned by an anonymous review, both the knowing why logic by [33] and the understanding why logic introduced in this paper could be seen as a sub-logic of some kind of justification logic with existential quantifiers and knowledge operators. Some work corresponding to the full logic have been formalized in the literature. For example, the authors of [6] propose an axiomatization of a justification logic with operators \(\exists r\varphi ,~B\varphi ,\) and \(r:\varphi \) to capture the notion of reason-based belief.

  4. 4.

    Note that the notions of knowing why and understanding why in Pritchard’s work are particularly to do with causal matters. The paper [19], to be mentioned later, also follows this restriction for simplicity.

  5. 5.

    In actual fact it is a question in justification logics for justification application as well, as remarked in [8].

  6. 6.

    For more details about these two notions the reader is referred to [26] and the bibliographies therein.

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Acknowledgements

The author wishes to thank Fernando Velazquez Quesada, Sonja Smets and Yanjing Wang for their patient guidance and helpful suggestions on this project. The research was also supported by CSC, which made my visit to ILLC possible. I’m grateful to the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially. Many thanks to Qiang Wang for her inspired comments and careful inspection. Last but not least, the support from Shanghai Pujiang Program (Grant No. 22PJC034) is acknowledged.

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Authors and Affiliations

  1. Department of Philosophy, East China Normal University, Shanghai, China

    Yu Wei

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  1. Yu Wei
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Correspondence to Yu Wei .

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Editors and Affiliations

  1. Institute of Logic and Computation, TU Wien, Vienna, Austria

    Alexandra Pavlova

  2. Department of Information Science and Media Studies, University of Bergen, Bergen, Norway

    Mina Young Pedersen

  3. University of Trento, Rovereto, Italy

    Raffaella Bernardi

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Wei, Y. (2024). A Logical Framework for Understanding Why. In: Pavlova, A., Pedersen, M.Y., Bernardi, R. (eds) Selected Reflections in Language, Logic, and Information. ESSLLI 2019. Lecture Notes in Computer Science, vol 14354. Springer, Cham. https://doi.org/10.1007/978-3-031-50628-4_13

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  • DOI: https://doi.org/10.1007/978-3-031-50628-4_13

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  • Print ISBN: 978-3-031-50627-7

  • Online ISBN: 978-3-031-50628-4

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