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  1. Mathematics and Explanatory Generality: Nothing but Cognitive Salience.Juha Saatsi & Robert Knowles - 2019 - Erkenntnis 86 (5):1119-1137.
    We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content to key (...)
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  • Mathematical Representation and Explanation: Structuralism, the Similarity Account, and the Hotchpotch Picture.Ziren Yang - 2020 - Dissertation, University of Leeds
    This thesis starts with three challenges to the structuralist accounts of applied mathematics. Structuralism views applied mathematics as a matter of building mapping functions between mathematical and target-ended structures. The first challenge concerns how it is possible for a non-mathematical target to be represented mathematically when the mapping functions per se are mathematical objects. The second challenge arises out of inconsistent early calculus, which suggests that mathematical representation does not require rigorous mathematical structures. The third challenge comes from renormalisation group (...)
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  • Asymmetry as a Challenge to Counterfactual Accounts of Non-Causal Explanation.Marc Lange - 2019 - Synthese 198 (4):3893-3918.
    This paper examines some recent attempts that use counterfactuals to understand the asymmetry of non-causal scientific explanations. These attempts recognize that even when there is explanatory asymmetry, there may be symmetry in counterfactual dependence. Therefore, something more than mere counterfactual dependence is needed to account for explanatory asymmetry. Whether that further ingredient, even if applicable to causal explanation, can fit non-causal explanation is the challenge that explanatory asymmetry poses for counterfactual accounts of non-causal explanation. This paper argues that several recent (...)
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  • Universality Caused: The Case of Renormalization Group Explanation.Emily Sullivan - 2019 - European Journal for Philosophy of Science 9 (3):36.
    Recently, many have argued that there are certain kinds of abstract mathematical explanations that are noncausal. In particular, the irrelevancy approach suggests that abstracting away irrelevant causal details can leave us with a noncausal explanation. In this paper, I argue that the common example of Renormalization Group explanations of universality used to motivate the irrelevancy approach deserves more critical attention. I argue that the reasons given by those who hold up RG as noncausal do not stand up to critical scrutiny. (...)
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  • Distinguishing Topological and Causal Explanation.Lauren N. Ross - 2021 - Synthese 198 (10):9803-9820.
    Recent philosophical work has explored the distinction between causal and non-causal forms of explanation. In this literature, topological explanation is viewed as a clear example of the non-causal variety–it is claimed that topology lacks temporal information, which is necessary for causal structure. This paper explores the distinction between topological and causal forms of explanation and argues that this distinction is not as clear cut as the literature suggests. One reason for this is that some explanations involve both topological and causal (...)
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  • Unification and mathematical explanation in science.Sam Baron - forthcoming - Synthese:1-25.
    Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda and physical explananda are unified under a common explanation within science, then we have good reason to believe that mathematics is explanatory in its own right. The argument motivates the search for a new kind of scientific case study, a case in which pure mathematical facts and physical facts are explanatorily unified. I argue (...)
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  • The Prospects for a Monist Theory of Non-Causal Explanation in Science and Mathematics.Alexander Reutlinger, Mark Colyvan & Karolina Krzyżanowska - forthcoming - Erkenntnis:1-21.
    We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation (CTE) for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us (...)
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  • Manipulation is Key: On Why Non-Mechanistic Explanations in the Cognitive Sciences Also Describe Relations of Manipulation and Control.Lotem Elber-Dorozko - 2018 - Synthese 195 (12):5319-5337.
    A popular view presents explanations in the cognitive sciences as causal or mechanistic and argues that an important feature of such explanations is that they allow us to manipulate and control the explanandum phenomena. Nonetheless, whether there can be explanations in the cognitive sciences that are neither causal nor mechanistic is still under debate. Another prominent view suggests that both causal and non-causal relations of counterfactual dependence can be explanatory, but this view is open to the criticism that it is (...)
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  • A Pluralist Account of Non-Causal Explanation in Science and Mathematics: Marc Lange: Because Without Cause: Non-Causal Explanation in Science and Mathematics. Oxford: Oxford University Press, 2017, Xxii+489pp, $74.00 HB.Juha Saatsi - 2018 - Metascience 27 (1):3-9.
    Contribution to a review symposium on Marc Lange's Because without cause: Non-causal explanation in science and mathematics. Oxford: Oxford University Press, 2017.
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  • Unifying the Debates: Mathematical and Non-Causal Explanations.Daniel Kostić - 2019 - Perspectives on Science 27 (1):1-6.
    In the last couple of years a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the questions what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences sometimes take a form of the question what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue of what they are explanatory. These questions raise further issues about (...)
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  • Counterfactuals and Explanatory Pluralism.Kareem Khalifa, Gabriel Doble & Jared Millson - 2020 - British Journal for the Philosophy of Science 71 (4):1439-1460.
    Recent literature on non-causal explanation raises the question as to whether explanatory monism, the thesis that all explanations submit to the same analysis, is true. The leading monist proposal holds that all explanations support change-relating counterfactuals. We provide several objections to this monist position. 1Introduction2Change-Relating Monism's Three Problems3Dependency and Monism: Unhappy Together4Another Challenge: Counterfactual Incidentalism4.1High-grade necessity4.2Unity in diversity5Conclusion.
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  • Realism and the Limits of Explanatory Reasoning.Juha Saatsi - 2018 - In The Routledge Handbook of Scientific Realism. London: Routledge. pp. 200-211.
    This chapter examines issues surrounding inference to the best explanation, its justification, and its role in different arguments for scientific realism, as well as more general issues concerning explanations’ ontological commitments. Defending the reliability of inference to the best explanation has been a central plank in various realist arguments, and realists have drawn various ontological conclusions from the premise that a given scientific explanation best explains some phenomenon. This chapter stresses the importance of thinking carefully about the nature of explanation (...)
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  • Realism and Explanatory Perspectivism.Juha Saatsi - forthcoming - In Michela Massimi & C. D. McCoy (eds.), Understanding Perspectivism: Scientific Challenges and Methodological Prospects. New York: Routledge.
    This chapter defends a (minimal) realist conception of progress in scientific understanding in the face of the ubiquitous plurality of perspectives in science. The argument turns on the counterfactual-dependence framework of explanation and understanding, which is illustrated and evidenced with reference to different explanations of the rainbow.
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  • Emergence Without Limits: The Case of Phonons.Alexander Franklin & Eleanor Knox - 2018 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 64:68-78.
    Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence that does not fit into this narrative: the case of phonons. These quasi-particles have some claim to be emergent, not least because the way in which they relate to the underlying crystal is almost precisely analogous to the way in which quantum particles relate to the underlying quantum field theory. But there (...)
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  • Searching for Noncausal Explanations in a Sea of Causes.Alisa Bokulich - 2018 - In Alexander Reutlinger & Juha Saatsi (eds.), Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations. Oxford University Press.
    In the spirit of explanatory pluralism, this chapter argues that causal and noncausal explanations of a phenomenon are compatible, each being useful for bringing out different sorts of insights. After reviewing a model-based account of scientific explanation, which can accommodate causal and noncausal explanations alike, an important core conception of noncausal explanation is identified. This noncausal form of model-based explanation is illustrated using the example of how Earth scientists in a subfield known as aeolian geomorphology are explaining the formation of (...)
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  • Varieties of Difference-Makers: Considerations on Chirimuuta’s Approach to Non-Causal Explanation in Neuroscience.Abel Wajnerman Paz - 2019 - Manuscrito 42 (1):91-119.
    Causal approaches to explanation often assume that a model explains by describing features that make a difference regarding the phenomenon. Chirimuuta claims that this idea can be also used to understand non-causal explanation in computational neuroscience. She argues that mathematical principles that figure in efficient coding explanations are non-causal difference-makers. Although these principles cannot be causally altered, efficient coding models can be used to show how would the phenomenon change if the principles were modified in counterpossible situations. The problem is (...)
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  • Mathematical Explanation and Indispensability.Vineberg Susan - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):233-247.
    This paper discusses Baker’s Enhanced Indispensability Argument for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not (...)
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  • On the Renormalization Group Explanation of Universality.Alexander Franklin - 2018 - Philosophy of Science 85 (2):225-248.
    It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to (...)
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