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  1. added 2018-11-15
    The Applicability of Mathematics to Physical Modality.Nora Berenstain - 2017 - Synthese 194 (9):3361-3377.
    This paper argues that scientific realism commits us to a metaphysical determination relation between the mathematical entities that are indispensible to scientific explanation and the modal structure of the empirical phenomena those entities explain. The argument presupposes that scientific realism commits us to the indispensability argument. The viewpresented here is that the indispensability of mathematics commits us not only to the existence of mathematical structures and entities but to a metaphysical determination relation between those entities and the modal structure of (...)
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  2. added 2018-08-31
    Mathematical Explanations and the Piecemeal Approach to Thinking About Explanation.Gabriel Târziu - forthcoming - Logique Et Analyse.
    A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...)
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  3. added 2018-04-30
    Tuples All the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.
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  4. added 2017-12-31
    Review of Marc Lange, Because Without Cause: Non-Causal Explanations in Science and Mathematics. [REVIEW]Mark Povich & Carl F. Craver - forthcoming - Philosophical Review.
    Lange’s collection of expanded, mostly previously published essays, packed with numerous, beautiful examples of putatively non-causal explanations from biology, physics, and mathematics, challenges the increasingly ossified causal consensus about scientific explanation, and, in so doing, launches a new field of philosophic investigation. However, those who embraced causal monism about explanation have done so because appeal to causal factors sorts good from bad scientific explanations and because the explanatory force of good explanations seems to derive from revealing the relevant causal (or (...)
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  5. added 2017-12-31
    The Directionality of Distinctively Mathematical Explanations.Carl F. Craver & Mark Povich - 2017 - Studies in History and Philosophy of Science Part A 63:31-38.
    In “What Makes a Scientific Explanation Distinctively Mathematical?” (2013b), Lange uses several compelling examples to argue that certain explanations for natural phenomena appeal primarily to mathematical, rather than natural, facts. In such explanations, the core explanatory facts are modally stronger than facts about causation, regularity, and other natural relations. We show that Lange's account of distinctively mathematical explanation is flawed in that it fails to account for the implicit directionality in each of his examples. This inadequacy is remediable in each (...)
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  6. added 2017-10-16
    Taking Reductionism to the Limit: How to Rebut the Antireductionist Argument From Infinite Limits.Juha Saatsi & Alexander Reutlinger - 2017 - Philosophy of Science (3):455-482.
    This paper analyses the anti-reductionist argument from renormalisation group explanations of universality, and shows how it can be rebutted if one assumes that the explanation in question is captured by the counterfactual dependence account of explanation.
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  7. added 2017-05-21
    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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  8. added 2016-09-05
    Explanatory Abstractions.Lina Jansson & Juha Saatsi - 2016 - British Journal for the Philosophy of Science:axx016.
    A number of philosophers have recently suggested that some abstract, plausibly non-causal and/or mathematical, explanations explain in a way that is radically dif- ferent from the way causal explanation explain. Namely, while causal explanations explain by providing information about causal dependence, allegedly some abstract explanations explain in a way tied to the independence of the explanandum from the microdetails, or causal laws, for example. We oppose this recent trend to regard abstractions as explanatory in some sui generis way, and argue (...)
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  9. added 2015-11-21
    Complements, Not Competitors: Causal and Mathematical Explanations.Holly Andersen - 2017 - British Journal for the Philosophy of Science:axw023.
    A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. There (...)
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  10. added 2015-10-26
    Mathematical Representation: Playing a Role.Kate Hodesdon - 2014 - Philosophical Studies 168 (3):769-782.
    The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Non-eliminative structuralism attributes these features to the particular ontology of mathematics. I argue that attributing the features to an ontology of structural objects conflicts with claims often made by structuralists to the effect that their structuralist theses are versions of Quine’s ontological relativity or Putnam’s internal realism. I describe and argue for an alternative explanation for these features which instead explains the (...)
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  11. added 2015-10-07
    Argument and Explanation in Mathematics.Michel Dufour - 2013 - In Dima Mohammed and Marcin Lewiński (ed.), Virtues of Argumentation. Proceedings of the 10th International Conference of the Ontario Society for the Study of Argumentation (OSSA), 22-26 May 2013. pp. pp. 1-14..
    Are there arguments in mathematics? Are there explanations in mathematics? Are there any connections between argument, proof and explanation? Highly controversial answers and arguments are reviewed. The main point is that in the case of a mathematical proof, the pragmatic criterion used to make a distinction between argument and explanation is likely to be insufficient for you may grant the conclusion of a proof but keep on thinking that the proof is not explanatory.
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  12. added 2015-05-29
    On Explanations From 'Geometry of Motion'.Juha Saatsi - 2018 - British Journal for the Philosophy of Science 69 (1):253–273.
    This paper examines explanations that turn on non-local geometrical facts about the space of possible configurations a system can occupy. I argue that it makes sense to contrast such explanations from "geometry of motion" with causal explanations. I also explore how my analysis of these explanations cuts across the distinction between kinematics and dynamics.
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  13. added 2014-05-12
    Multi-Level Selection and the Explanatory Value of Mathematical Decompositions.Christopher Clarke - 2016 - British Journal for the Philosophy of Science 67 (4):1025-1055.
    Do multi-level selection explanations of the evolution of social traits deepen the understanding provided by single-level explanations? Central to the former is a mathematical theorem, the multi-level Price decomposition. I build a framework through which to understand the explanatory role of such non-empirical decompositions in scientific practice. Applying this general framework to the present case places two tasks on the agenda. The first task is to distinguish the various ways of suppressing within-collective variation in fitness, and moreover to evaluate their (...)
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