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  1. Viewing-as Explanations and Ontic Dependence.William D’Alessandro - 2020 - Philosophical Studies 177 (3):769-792.
    According to a widespread view in metaphysics and philosophy of science, all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewing-as explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first part of the paper defends this claim (...)
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  2. Explicitism About Truth in Fiction.William D’Alessandro - 2016 - British Journal of Aesthetics 56 (1):53-65.
    The problem of truth in fiction concerns how to tell whether a given proposition is true in a given fiction. Thus far, the nearly universal consensus has been that some propositions are ‘implicitly true’ in some fictions: such propositions are not expressed by any explicit statements in the relevant work, but are nevertheless held to be true in those works on the basis of some other set of criteria. I call this family of views ‘implicitism’. I argue that implicitism faces (...)
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  3. Arithmetic, Set Theory, Reduction and Explanation.William D’Alessandro - 2018 - Synthese 195 (11):5059-5089.
    Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...)
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    Mathematical Explanation Beyond Explanatory Proof.William D’Alessandro - 2017 - British Journal for the Philosophy of Science 71 (2):581-603.
    Much recent work on mathematical explanation has presupposed that the phenomenon involves explanatory proofs in an essential way. I argue that this view, ‘proof chauvinism’, is false. I then look in some detail at the explanation of the solvability of polynomial equations provided by Galois theory, which has often been thought to revolve around an explanatory proof. The article concludes with some general worries about the effects of chauvinism on the theory of mathematical explanation. 1Introduction 2Why I Am Not a (...)
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