Abstract
We argue that two well-known examples (strawberry distribution and Konigsberg bridges) generally considered genuine cases of distinctively mathematical explanation can also be understood as cases of distinctively generic explanation. The latter answer resemblance questions (e.g., why did neither person A nor B manage to cross all bridges) by appealing to ‘generic task laws’ instead of mathematical necessity (as is done in distinctively mathematical explanations). We submit that distinctively generic explanations derive their explanatory force from their role in ontological unification. Additionally, we argue that distinctively generic explanations are better seen as standardly mathematical instead of distinctively mathematical. Finally, we compare and contrast our proposal with the work of Christopher Pincock on abstract explanations in science and the views of Michael Strevens on abstract causal event explanations.
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Notes
It is not clear to us what ‘constitutive of the explanandum’ means. In any case, we think that both [1] and [2] deserve discussion. We focus on [2] here because of the variations it leads to. Explanandum [1] is discussed in Sect. 7.
We agree with Strevens on how explanatory asymmetry can be guaranteed. Differences between our assessment of explanations in the strawberry distribution case and Strevens’ view are discussed in Sect. 7.
The opposite is not true: some Hempelian explanations are not suited for being used in unification attempts because they contain irrelevant premises and/or accidental generalisations.
By emphasizing the importance of an ontic component that relates to causation we avoid the problems that counterfactual accounts of explanation face if you want to go beyond causation (see Lange 2021). Our position also implies that DGEs can be fitted into Woodward’s framework directly, without extending it beyond the domain of causation. This differs from the approach in Woodward 2018.
In our examples we have assumed (as is traditionally done) that it is human who attempts to perform the tasks. However, the specific and more generic task regularities and laws also apply if e.g. a robot tries to distribute the strawberries or books within the same restrictions.
We call an explanation ‘non-mathematical’ if it contains no mathematical derivation. A non-mathematical explanation can use mathematical concepts (e.g. numbers) but no mathematical knowledge that supports derivations.
General anaesthesia refers to a combination of four features: unconsciousness, amnesia, analgesia and muscle relaxation.
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Acknowledgements
The research of Kristian González Barman for this paper was supported by FWO (Research Foundation Flanders) through grant G047017N. The research of Thijs De Coninck was supported by a PhD fellowship of FWO (grant 1167619N).
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Weber, E., Barman, K.G. & De Coninck, T. Distinctively generic explanations of physical facts. Synthese 203, 102 (2024). https://doi.org/10.1007/s11229-024-04486-2
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DOI: https://doi.org/10.1007/s11229-024-04486-2