Lange on Mathematical Explanation, Grounding, and the Divergence Thesis
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Mark Lange ha defendido la opinión de que la explicación matemática y la explicación basada en fundamentación divergen. En este artículo sostengo que al menos un tipo de relación de fundamentación es inmune a sus críticas. Tras introducir una teoría separatista mínima de la fundamentación, muestro que sus argumentos dependen en gran medida de otra tesis sobre la fundamentación (a la cual llamaré “tesis de fundamentación atómica”), que carece de respaldo. Además, un segundo intento utilizando la pureza no resulta completamente satisfactorio.
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Ahlfors, Lars, 1979, Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, McGraw-Hill Education.
Davis, Philip J., 1981, “Are There Coincidences in Mathematics?”, The American Mathematical Monthly, vol. 88, no. 5, pp. 311–320.
Detlefsen, Michael, 2008a, “Proof: Its Nature and Significance”, in Bonnie Gold and Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy, Spectrum. Mathematical Association of America, pp. 3–32.
Detlefsen, Michael, 2008b, “Purity as an Ideal of Proof”, in Paolo Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford University Press, pp. 179–197.
Detlefsen, Michael and Andrew Arana, 2011, “Purity of Methods”, Philosophers’ Imprint, p. 11.
Diamond, Harold G., 1982, “Elementary Methods in the Study of the Distribution of Prime Numbers”, Bulletin of the American Mathematical Society, vol. 7, no. 3, pp. 553–589.
D’Alessandro, William, 2020, “Viewing-as Explanations and Ontic Dependence”, Philosophical Studies, vol. 177, no. 3, pp. 769–792.
D’Alessandro, William, 2017, “Mathematical Explanation beyond Explanatory Proof”, British Journal for the Philosophy of Science, vol. 71, no. 2, pp. 581–603.
Fine, Kit, 2012, “A Guide to Ground”, in Fabrice Correia and Benjamin Schnieder (eds.), Metaphysical Grounding, Cambridge University Press, pp. 37–80.
Glazier, Martin, 2020, “Explanation”, in Michael J. Raven (ed.), Routledge Handbook of Metaphysical Grounding, pp. 121–132.
Hafner, Johannes and Paolo Mancosu, 2008, “Beyond Unification”, in Paolo Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford University Press, pp. 151–178.
Hodges, Wilfrid, 2022, “Model Theory”, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University, Spring 2022 edition.
Kitcher, Philip, 1989, “Explanatory Unification and the Causal Structure of the World”, in Philip Kitcher and Wesley Salmon (eds.), Scientific Explanation, University of Minnesota Press, Minneapolis, pp. 410–505.
Kovacs, David Mark, 2020, “Four Questions of Iterated Grounding”, Philosophy and Phenomenological Research, vol. 101, no. 2, pp. 341–364.
Krämer, Stephan, 2018, “Towards a Theory of Ground-Theoretic Content”, Synthese, vol. 195, no. 2, pp. 785–814.
Lang, Serge, 2005, Algebra, Graduate Texts in Mathematics, Springer, New York.
Lange, Marc, 2022, “Bolzano, the Parallelogram of Forces, and Scientific Explanation”, in Stefan Roski, and Benjamin Schnieder (eds.), Bolzano’s Philosophy of Grounding: Translations and Studies, Oxford University Press.
Lange, Marc, 2019, “Ground and Explanation in Mathematics”, Philosophers’ Imprint, vol. 19, no. 33.
Lange, Marc, 2018, “Mathematical Explanations that Are Not Proofs”, Erkenntnis, vol. 83, no. 6, pp. 1285–1302.
Lange, Marc, 2014, “Aspects of Mathematical Explanation: Symmetry, Unity, and Salience”, Philosophical Review, vol. 123, no. 4, pp. 485–531.
Lange, Marc, 2010, “What are Mathematical Coincidences?”, Mind, vol. 119, no. 474, pp. 307–340.
Litland, Jon Erling, 2023, “Ground First: Against the Proof-Theoretic Definition of Ground”, Synthese, vol. 201, no. 1, p. 28.
Mancosu, Paolo, 2011, “Explanation in Mathematics”, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
Mancosu, Paolo, 2001, “Mathematical Explanation: Problems and Prospects”, Topoi, vol. 20, no. 1, pp. 97–117.
Mancosu, Paolo, 2000, “On Mathematical Explanation”, in Grosholz Emily and Breger Herbert (eds.), The Growth of Mathematical Knowledge, Springer, Dordrecht, pp. 103–119.
Marker, David, 2002, Model Theory: An Introduction. Graduate Texts in Mathematics, Springer, New York.
Pincock, Christopher, 2015, “The Unsolvability of the Quintic: A Case Study in Abstract Mathematical Explanation”, Philosophers’ Imprint, vol. 15, no. 3.
Poggiolesi, Francesca, 2023, “Mathematical Explanations: An Analysis Via Formal Proofs and Conceptual Complexity”, Philosophia Mathematica, vol. 2, no. 2, pp. 145–176.
Poggiolesi, Francesca and Francesco Genco, 2023, “Conceptual (and Hence Mathematical) Explanation, Conceptual Grounding and Proof”, Erkenntnis, vol. 88, no. 4, pp. 1481–1507.
Raven, Michael J., 2015, “Ground”, Philosophy Compass, vol. 10, no. 5, pp. 322–333.
Roski, Stefan, 2021, “In Defence of Explanatory Realism”, Synthese, vol. 199, no. 5, pp. 14121–14141.
Rusnock, Paul, 2022, “Grounding in Practice Bolzano’s Purely Analytic Proof in Light of the Contributions”, in Stefan Roski and Benjamin Schnieder (eds.), Bolzano’s Philosophy of Grounding: Translations and Studies, Oxford University Press.
Schaffer, Jonathan, 2016, “Grounding in the Image of Causation”, Philosophical Studies, vol. 173, no. 1, pp. 49–100.
Schnieder, Benjamin, 2020, “Dependence”, in Michael J. Raven (ed.), Routledge Handbook of Metaphysical Grounding, pp. 107–120.
Sjölin Wirling, Ylwa, 2020, “Is Backing Grounding?”, Ratio, vol. 33, no. 3, pp. 129–137.
Skiles, Alexander, 2020, “Necessity”, in Michael J. Raven (ed.), Routledge Handbook of Metaphysical Grounding, pp. 148–163.
Skiles, Alexander and Kelly Trogdon, 2021, “Should Explanation Be a Guide to Ground?”, Philosophical Studies, vol. 178, no. 12, pp. 4083–4098.
Steiner, Mark, 1978, “Mathematical Explanation”, Philosophical Studies, vol. 34, no. 2, pp. 135–151.
Trogdon, Kelly, 2018, “Grounding-Mechanical Explanation”, Philosophical Studies, vol. 175, no. 6, pp. 1289–1309.
Zagier, Don, 1977, “The First 50 Million Prime Numbers”, The Mathematical Intelligencer, 1(Suppl 1), pp. 7–19.

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