Switch to: References

Add citations

You must login to add citations.
  1. Platonism and Intra-mathematical Explanation.Sam Baron - forthcoming - Philosophical Quarterly.
    I introduce an argument for Platonism based on intra-mathematical explanation: the explanation of one mathematical fact by another. The argument is important for two reasons. First, if the argument succeeds then it provides a basis for Platonism that does not proceed via standard indispensability considerations. Second, if the argument fails it can only do so for one of three reasons: either because there are no intra-mathematical explanations, or because not all explanations are backed by dependence relations, or because some form (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Plumbing metaphysical explanatory depth.Nicholas Emmerson - forthcoming - Philosophical Studies:1-22.
    Recent years have seen increasing interest in interventionist analyses of metaphysical explanation. One area where interventionism traditionally shines, is in providing an account of explanatory depth; the sense in which explanation comes in degrees. However, the literature on metaphysical explanation has left the notion of depth almost entirely unexplored. In this paper I shall attempt to rectify this oversight by motivating an interventionist analysis of metaphysical explanatory depth (MED), in terms of the range of interventions under which a metaphysically explanatory (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Can Non-Causal Explanations Answer the Leibniz Question?Jens Lemanski - 2022 - Metaphysica 23 (2):427-443.
    Leibniz is often cited as an authority when it comes to the formulation and answer strategy of the question “Why is there something rather than nothing?” Yet much current research assumes that Leibniz advocates an unambiguous question and strategy for the answer. In this respect, one repeatedly finds the argument in the literature that alternative explanatory approaches to this question violate Leibniz’s intention, since he derives the question from the principle of sufficient reason and also demands a causal explanation to (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • A Defence of Manipulationist Noncausal Explanation: The Case for Intervention Liberalism.Nicholas Emmerson - 2023 - Erkenntnis 88 (8):3179-3201.
    Recent years have seen growing interest in modifying interventionist accounts of causal explanation in order to characterise noncausal explanation. However, one surprising element of such accounts is that they have typically jettisoned the core feature of interventionism: interventions. Indeed, the prevailing opinion within the philosophy of science literature suggests that interventions exclusively demarcate causal relationships. This position is so prevalent that, until now, no one has even thought to name it. We call it “intervention puritanism” (I-puritanism, for short). In this (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • The Automated Laplacean Demon: How ML Challenges Our Views on Prediction and Explanation.Sanja Srećković, Andrea Berber & Nenad Filipović - 2021 - Minds and Machines 32 (1):159-183.
    Certain characteristics make machine learning a powerful tool for processing large amounts of data, and also particularly unsuitable for explanatory purposes. There are worries that its increasing use in science may sideline the explanatory goals of research. We analyze the key characteristics of ML that might have implications for the future directions in scientific research: epistemic opacity and the ‘theory-agnostic’ modeling. These characteristics are further analyzed in a comparison of ML with the traditional statistical methods, in order to demonstrate what (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist.Fabio Sterpetti - 2021 - Foundations of Science 27 (3):1073-1105.
    This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Challenges Facing Counterfactual Accounts of Explanation in Mathematics.Marc Lange - 2022 - Philosophia Mathematica 30 (1):32-58.
    Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory asymmetry, and fails to specify why (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Counter Countermathematical Explanations.Atoosa Kasirzadeh - 2021 - Erkenntnis 88 (6):2537-2560.
    Recently, there have been several attempts to generalize the counterfactual theory of causal explanations to mathematical explanations. The central idea of these attempts is to use conditionals whose antecedents express a mathematical impossibility. Such countermathematical conditionals are plugged into the explanatory scheme of the counterfactual theory and—so is the hope—capture mathematical explanations. Here, I dash the hope that countermathematical explanations simply parallel counterfactual explanations. In particular, I show that explanations based on countermathematicals are susceptible to three problems counterfactual explanations do (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • A Counterfactual Approach to Explanation in Mathematics.Sam Baron, Mark Colyvan & David Ripley - 2020 - Philosophia Mathematica 28 (1):1-34.
    ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.
    Download  
     
    Export citation  
     
    Bookmark   19 citations