Linked bibliography for the SEP article "Explanation in Mathematics" by Paolo Mancosu

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Andersen, H., 2014, “A Field Guide to Mechanisms: Part I”, Philosophy Compass, 9(4): 274–283. (Scholar)
–––, 2016, “Complements, Not Competitors: Causal and Mathematical Explanations”, British Journal for the Philosophy of Science, first online 17 August 2016. doi: 10.1093/bjps/axw023 (Scholar)
Arana, A., and P. Mancosu, 2012, “On the Relationship between Plane and Solid Geometry”, The Review of Symbolic Logic, 5: 294–353. (Scholar)
Aristotle, [BWA], 1941, The Basic Works of Aristotle, ed. by R. McKeon, New York: Random House. (Scholar)
–––, [CWA], 1984, The Complete Works of Aristotle, ed. by J. Barnes, Princeton: Princeton University Press. (Scholar)
Asbaugh, M. S., C. C. Chicone, and R. H. Cushman, 1991, “The Twisting Tennis Racket”, Journal of Dynamics and Differential Equations, 3 (1): 67–85. (Scholar)
Avigad, J., 2008, “Understanding Proof”, in P. Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford: Oxford University Press, 317–353. (Scholar)
Baker, A., 2005, “Are there Genuine Mathematical Explanations of Physical Phenomena?”, Mind, 114: 223–238. (Scholar)
–––, 2009a, “Mathematical Explanation in Science”, British Journal for the Philosophy of Science, 60: 611–633. (Scholar)
–––, 2009b, “Mathematical Induction and Explanation”, Analysis, 70: 681–690. (Scholar)
–––, 2009c, “Mathematical Accidents and the End of Explanation”, in O. Bueno and Ø. Linnebo (eds.), New Waves in Philosophy of Mathematics, London: Palmgrave, MacMillan, 137–159. (Scholar)
–––, 2012, “Science-Driven Mathematical Explanation”, Mind, 121: 243–267. (Scholar)
–––, 2015, “Mathematical Explanation in Biology”, in P.-A. Braillard and C. Malaterre (eds.), Explanation in Biology., Dordrecht: Springer, 229–247. (Scholar)
–––, 2016, “Parsimony and Inference to the Best Mathematical Explanation”, Synthese, 193: 333–350. (Scholar)
–––, 2017a, “Mathematics and Explanatory Generality”, Philosophia Mathematica, 25: 194–209. (Scholar)
–––, 2017b, “Mathematical Spandrels”, Australasian Journal of Philosophy, 95: 779–793. (Scholar)
Baker, A., and M. Colyvan, 2011, “Indexing and Mathematical Explanation”, Philosophia Mathematica, 19 (3): 323–334. (Scholar)
Baldwin, J., 2016, “Foundations of Mathematics: Reliability AND Clarity: The Explanatory Role of Mathematical Induction”, in J. Väänänen et al. (eds.), Logic, Language, Information, and Computation, Lecture Notes in Computer Science, Berlin/Heidelberg: Springer, 68–82. (Scholar)
Bangu, S. I., 2008, “Inference to the Best Explanation and Mathematical Realism”, Synthese, 160: 13–20. (Scholar)
–––, 2012, The Applicability of Mathematics in Science: Indispensability and Ontology, London: Palmgrave, MacMillan. (Scholar)
–––, 2013, “Indispensability and Explanation”, British Journal for the Philosophy of Science, 64: 225–277. (Scholar)
Baracco, F., 2017, “Explanatory Proofs in Mathematics: Noneism, Someism, and Allism”, Logique et Analyse, 60 (237): 67–86. (Scholar)
Baron, S., 2014, “Optimization and Mathematical Explanation: Doing the Lévy Walk”, Synthese, 191: 459–479. (Scholar)
–––, 2015, “Mathematical Explanation and Epistemology: Please Mind the Gap”, Ratio, 29: 149–167. (Scholar)
–––, 2016a, “Explaining Mathematical Explanation”, The Philosophical Quarterly, 66 (264): 458–480. (Scholar)
–––, 2016b, “The Explanatory Dispensability of Idealizations”, Synthese, 193 (2): 365–386. (Scholar)
–––, 2017, “Mathematical Explanation by Law”, British Journal for the Philosophy of Science, first online 28 November 2017. doi: 10.1093/bjps/axx062 (Scholar)
Baron, S., and M. Colyvan, 2016, “Time Enough for Explanation”, Journal of Philosophy, 113 (2): 61–88. (Scholar)
Baron, S., M. Colyvan, and D. Ripley, 2017, “How Mathematics Can Make a Difference”, Philosophers’ Imprint, 17 (3): 1–29. (Scholar)
Batterman, R., 2002, The Devil in the Details. Asymptotic Reasoning in Explanation, Reduction, and Emergence, Oxford: Oxford University Press. (Scholar)
–––, 2005, “Critical Phenomena and Breaking Drops: Infinite Idealizations in Physics”, Studies in History and Philosophy of Modern Physics B, 36 (2): 225–244. (Scholar)
–––, 2009, “Idealization and Modeling”, Synthese, 169 (3): 427–446. (Scholar)
–––, 2010a, “On the Explanatory Role of Mathematics in Empirical Science”, British Journal for the Philosophy of Science, 61: 1–25. (Scholar)
–––, 2010b, “Mathematical Reduction and Renormalization”, in A. Hüttemann and G. Ernst (eds.), Time, Chance, and Reduction: Philosophical Aspects of Statistical Mechanics, Cambridge: Cambridge University Press, 159–179. (Scholar)
–––, 2011, “Emergence, Singularities, and Symmetry Breaking”, Foundations of Physics, 61: 1031–1050. (Scholar)
Batterman, R., and C. Rice, 2014, “Minimal Model Explanations”, Philosophy of Science, 81: 349–376. (Scholar)
Belot, G., 2005, “Whose Devil? Which Details?”, Philosophy of Science, 72: 128–153. (Scholar)
Betti, A., 2010, “Explanation in Metaphysics and Bolzano’s Theory of Ground and Consequence”, Logique et Analyse, 56 (211): 281–316. (Scholar)
Bokulich, A., 2008, “Can Classical Structures Explain Quantum Phenomena?”, British Journal for the Philosophy of Science, 59 (2): 217–235. (Scholar)
–––, 2011, “How Scientific Models Can Explain”, Synthese, 180: 33–45. (Scholar)
Brigandt, I., 2013, “Systems Biology and the Integration of Mechanistic Explanation and Mathematical Explanation”, Studies in History and Philosophy of Biological and Biomedical Sciences, 44 (4): 477–492. (Scholar)
Brumfiel, G., 1979, Partially Ordered Rings and Semi-algebraic Geometry, Cambridge: Cambridge University Press. (Scholar)
Bueno, O., 2012, “An Easy Road to Nominalism”, Mind, 121: 967–982. (Scholar)
Bueno, O. and M. Colyvan, 2011, “An Inferential Conception of the Application of Mathematics”, Noûs, 45: 345–374. (Scholar)
Bueno, O. and S. French, 2012, “Can Mathematics Explain Physical Phenomena?”, British Journal for the Philosophy of Science, 63 (1): 85–113. (Scholar)
Busch, O., 2011, “Scientific Realism and the Indispensability Argument for Mathematical Realism: A Marriage Made in Hell”, International Studies in the Philosophy of Science, 121: 967–982. (Scholar)
Busch, O., and J. Morrison, 2016, “Should Scientific Realists be Platonists?”, Synthese, 25 (4): 307–325. (Scholar)
Cartwright, N., 1989, Nature’s Capacities and Their Measurement, Oxford: Clarendon Press. (Scholar)
Castel, L., 1734, Vrai Système de Physique Générale de M. Isaac Newton, Paris. (Scholar)
Cellucci, C., 2008, “The Nature of Mathematical Explanation”, Studies in History and Philosophy of Science, 39: 202–210. (Scholar)
–––, 2014, “Mathematical Beauty, Understanding, Discovery”, Foundations of Science, 20: 339–355. (Scholar)
–––, 2017, Rethinking Knowledge, Cham: Springer. (Scholar)
Chirimuuta, M., 2014, “Minimal Models and Canonical Neural Computations: The Distinctness of Computational Explanation in Neuroscience ”, Synthese, 191: 127–153. (Scholar)
–––, 2017, “Explanation in Computational Neuroscience: Causal and Non-causal”, The British Journal for the Philosophy of Science, first online 14 March 2017. doi: 10.1093/bjps/axw034 (Scholar)
–––, 2018, “The Development and Application of Efficient Coding Explanation in Neuroscience”, in A. Reutlinger and J. Saatsi (eds.), Explanation beyond Causation, Oxford: Oxford University Press, 164–184. (Scholar)
Clarke, C., 2016, “Multi-Level Selection and the Explanatory Value of Mathematical Decompositions”, British Journal for the Philosophy of Science, 67: 1025–1055. (Scholar)
Colyvan, M., 2001, The Indispensability of Mathematics, Oxford: Oxford University Press. (Scholar)
–––, 2002, “Mathematics and Aesthetic Considerations in Science”, Mind, 11: 69–78. (Scholar)
–––, 2006, “Scientific Realism and Mathematical Nominalism: A Marriage made in Hell”, in C. Cheyne and J. Warral (eds.), Rationality and Reality: Essays in Honour of Alan Musgrave, Dordrecht: Kluwer, 225–237. (Scholar)
–––, 2010, “There is No Easy Road to Nominalism”, Mind, 119: 285–306. (Scholar)
–––, 2012a, “Road Work Ahead: Heavy Machinery on the Easy Road”, Mind, 121: 1031–1045. (Scholar)
–––, 2012b, Introduction to the Philosophy of Mathematics, Cambridge: Cambridge University Press. (Scholar)
Colyvan, M., J. Cusberg, and K. McQueen, 2018, “Two Flavours of Mathematical Explanation”, in A. Reutlinger and J. Saatsi (eds.), Explanation beyond Causation, Oxford: Oxford University Press, 231–249. (Scholar)
Correia, F., and B. Schneider, eds., 2012, Metaphysical Grounding: Understanding the Structure of Reality, Cambridge: Cambridge University Press. (Scholar)
Cournot, A., 1851, Essai sur les fondements de nos connaissances philosophiques et sur le caractère de la critique philosophique, in Oeuvres complètes, Volume II, J.C. Pariente (ed.), Paris: Vrin, 1981. English translation by M. H. Moore in A. Cournot, An Essay on the Foundations of our Knowledge, The Liberal Arts Press, New York, 1956. (Scholar)
Craver, C. F., and M. Povich, 2017, “The Directionality of Distinctively Mathematical Explanations”, Studies in History and Philosophy of Science, 63: 31–38. (Scholar)
Craver, C. F., and J. Tabery, 2016, “Mechanisms in Science”, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2016/entries/sciencemechanisms/> (Scholar)
D’Alessandro, W., 2017, “Arithmetic, Set theory, Reduction and Explanation”, Synthese, first online 26 May 2017. doi: 10.1007/s11229-017-1450-8 (Scholar)
–––, 2018, “Mathematical Explanation beyond Explanatory Proof”, British Journal for the Philosophy of Science, first online 16 January 2018. doi: 10.1093/bjps/axy009 (Scholar)
Daly, C., and S. Langford, 2009, “Mathematical Explanation and Indispensability Arguments”, The Philosophical Quarterly, 59: 641–658. (Scholar)
Darrason, M., 2018, “Mechanistic and Topological Explanation in Medicine: The Case of Medical Genetics and Network Medicine”, Synthese, 195 (1): 967–982. (Scholar)
Delarivière, S., J. Frans, and B. van Kerkhove, 2017, “Mathematical Explanation: A Contextual Approach”, Journal of the Indian Council for Philosophical Research, 34: 309–329. (Scholar)
Detlefsen, M., and A. Arana, 2011, “Purity of Methods”, Philosophers’ Imprint, 11, published online. (Scholar)
De Regt, H., 2009, “The Epistemic Value of Understanding ”, Philosophy of Science, 76: 585–597. (Scholar)
–––, 2017, Understanding Scientific Understanding, Oxford: Oxford University Press. (Scholar)
De Regt, H., and D. Diecks, eds., 2005, “A Contextual Approach to Scientiﬁc Understanding”, Synthese, 144: 137–170. (Scholar)
De Regt, H., S. Leonelli, and K. Eigner, eds., 2013, Scientific Understanding: Philosophical Perspectives, Oxford: Oxford University Press, 164–184. (Scholar)
Dorato, M., 2017, “Dynamical versus structural explanations in scientific revolutions”, Synthese, 194 (7): 2307–2327. (Scholar)
Dorato, M., and L. Felline, 2010a, “Scientific Explanation and Scientific Structuralism”, in V. Petkov (ed.), Space, Time, and Spacetime: Physical and Philosophical Implications of Minkowski’s Unification of Space and Time, Berlin: Springer, 161–177. (Scholar)
Dorato, M., and L. Felline, 2010b, “Structural Explanations in Minkowski Spacetime: Which Account of Models?”, in A. Bokulich and A. Bokulich (eds.), Scientific Structuralism, Dordrecht: Springer, 193–209. (Scholar)
Dougherty, J., 2017, “What Inductive Explanations Could Not Be”, Synthese, first online 05 June 2017. doi: 10.1007/s11229-017-1457-1 (Scholar)
Dutilh Novaes, C., 2018, “A Dialogical Conception of Explanation in Mathematical Proofs”, in P. Ernest (ed.), Philosophy of Mathematics Education Today, Berlin: Springer, forthcoming. (Scholar)
Felline, L., 2010, “Remarks on a Structural Account of Scientific Explanation”, in in M. Suàrez, M. Dorato, and M. Redei (eds.), EPSA Philosophical Issues in the Sciences: Launch of the European Philosophy, vol. 2, Dordrecht: Springer, 43–54. (Scholar)
Felline, L., 2018, “Mechanisms meet Structural Explanation”, Synthese, 195 (1): 99–114. (Scholar)
Field, H., 1980, Science without Numbers: A Defence of Nominalism, Oxford: Blackwell; second edition (with a new lengthy introduction), 2016. (Scholar)
–––, 1989, Realism, Mathematics, and Modality, Oxford: Blackwell. (Scholar)
Frans, J. and E. Weber, 2014, “Mechanistic Explanation and Explanatory Proof in Mathematics”, Philosophia Mathematica, 22: 231–248. (Scholar)
French, S. and J, Saatsi, 2018, “Symmetries and Explanatory Dependencies in Physics”, in A. Reutlinger and J. Saatsi (eds.), Explanation beyond Causation, Oxford: Oxford University Press, 185–205. (Scholar)
Friedman, M., 1974, “Explanation and Scientific Understanding”, The Journal of Philosophy, 71: 5–19. (Scholar)
Friend, M., and D. Molinini, 2015, “Using Mathematics to Explain a Scientific Theory”, Philosophia Mathematica, 24: 185–213. (Scholar)
Gijsbers, V., 2017, “A Quasi-Interventionist Theory of Mathematical Explanation”, Logique et Analyse, 60 (237): 47–66. (Scholar)
Giaquinto, M., 2016, “Mathematical Proofs: The Beautiful and the Explanatory”, Journal of Humanistic Mathematics, 6 (1): 56–72. (Scholar)
Gingras, Y., 2001, “What did Mathematics do to Physics?”, History of Science, 39: 383–416. (Scholar)
Hafner, J. and P. Mancosu, 2005, “The Varieties of Mathematical Explanation”, in P. Mancosu et al. (eds.), Visualization, Explanation and Reasoning Styles in Mathematics, Berlin: Springer, 215–250. (Scholar)
–––, 2008, “Beyond Unification”, in P. Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford: Oxford University Press, 151–178. (Scholar)
Hales, T., 2000, “Cannonballs and Honeycombs”, Notices of the American Mathematical Society, 47: 440–449. (Scholar)
–––, 2001, “The Honeycomb Conjecture”, Discrete and Computational Geometry, 25: 1–22. (Scholar)
Hanna, G., H. N. Jahnke, and H. Pulte, eds., 2010, Explanation and Proof in Mathematics. Philosophical and Educational Perspectives, New York: Springer. (Scholar)
Harari, O., 2008, “Proclus’ Account of Explanatory Demonstrations in Mathematics and its Context”, Archiv für Geschichte der Philosophie, 90: 137–164. (Scholar)
Hoeltje, M., B. Schnieder, and A. Steinberg, 2013, “Explanation by Induction?”, Synthese, 190: 509–524. (Scholar)
Hughes, R. I. G., 1989, “Bell’s Theorem, Ideology, and Structural Explanation”, in J. Cushing and E. McMullin (eds.), Philosophical Consequences of Quantum Theory: Reflections on Bell’s Theorem, Notre Dame, IN: University of Notre Dame Press, 195–207. (Scholar)
Huneman, P., 2010, “Topological Explanations and Robustness in Biological Sciences”, Synthese, 177: 213–245. (Scholar)
Huneman, P., 2018, “Diversifying the Picture of Explanations in Biological Sciences: Ways of Combining Topology with Mechanisms”, Synthese, 195 (1): 115–146. (Scholar)
Hunt, J., 2016, “Indispensability and the Problem of Compatible Explanations”, Synthese, 193: 451–467. (Scholar)
Inglis, M., and A. Aberdein, 2015, “Beauty is not Simplicity: An Analysis of Mathematicians’ Proof Appraisals”, Philosophia Mathematica, 23 (1): 87–109. (Scholar)
Jackson, F., and P. Pettit, 1990, “Program Explanation: A General Perspective”, Analysis, 50 (2): 107–117. (Scholar)
Jansson, L., and J. Saatsi, 2017, “Explanatory Abstractions”, British Journal for the Philosophy of Science, first online 30 November 2017, doi: 10.1093/bjps/axx016 (Scholar)
Jones, N., 2014, “Bowtie Structures, Pathway Diagrams and Topological Explanation”, Synthese, 79: 1135–1155. (Scholar)
Kim, J., 1994, “Explanatory Knowledge and Metaphysical Dependence”, Philosophical Issues, 5: 51–69. (Scholar)
Kitcher, P., 1975, “Bolzano’s Ideal of Algebraic Analysis”, Studies in History and Philosophy of Science, 6: 229–269. (Scholar)
–––, 1981, “Explanatory Unification”, Philosophy of Science, 48: 507–531. (Scholar)
–––, 1984, The Nature of Mathematical Knowledge, Oxford: Oxford University Press. (Scholar)
–––, 1989, “Explanatory Unification and the Causal Structure of the World”, in P. Kitcher and W. Salmon (eds.), Scientific Explanation, (Minnesota Studies in the Philosophy of Science, Volume XIII), Minneapolis: University of Minnesota Press, 410–505. (Scholar)
Kistler, M., 2013, “The Interventionist Account of Causation and Non-Causal Association Laws”, Erkenntnis, 78 (1): 1–20. (Scholar)
Kostic, D., 2016, “Mechanistic and Topological Explanations: An Introduction”, Synthese, 195 (1): 1–10. (Scholar)
Lange, M., 2007, “Laws and Meta-laws of Nature: Conservation Laws and Symmetries”, Studies in History and Philosophy of Modern Physics, 38: 457–481. (Scholar)
–––, 2009, “Dimensional Explanations”, Noûs, 43: 742–775. (Scholar)
–––, 2010a, “Why Proofs by Mathematical Induction are Generally not Explanatory”, Analysis, 69: 203–211. (Scholar)
–––, 2010b, “What are Mathematical Coincidences (and Why does it Matter)?”, Mind, 119: 307–340. (Scholar)
–––, 2013a, “How to Explain the Lorentz Transformations”, in S. Mumford and M. Tugby (eds.), Metaphysics and Science, Oxford: Oxford University Press, 73–98. (Scholar)
–––, 2013b, “Really Statistical Explanations and Genetic Drift”, Philosophy of Science, 80: 169–188. (Scholar)
–––, 2013c, “What Makes a Scientific Explanation Distinctively Mathematical”, British Journal for the Philosophy of Science, 64: 485–511. (Scholar)
–––, 2014, “Aspects of Mathematical Explanation: Symmetry, Unity and Salience”, Philosophical Review, 123 (4): 485–531. (Scholar)
–––, 2015a, “On ‘Minimal Model Explanations’: A Reply to Batterman and Rice”, Philosophy of Science, 82: 292–305. (Scholar)
–––, 2015b, “Explanation, Existence, and Natural Properties in Mathematics. A Case Study: Desargues’ Theorem”, Dialectica, 69: 435–472. (Scholar)
–––, 2015c, “Depth and Explanation in Mathematics”, Philosophia Mathematica, 23 (2): 196–214. (Scholar)
–––, 2016, “Explanatory Proofs and Beautiful Proofs”, Journal of Humanistic Mathematics, 6 (1): 8–51. (Scholar)
–––, 2017, Because Without Cause: Non-causal Explanations in Science and Mathematics, Oxford: Oxford University Press. (Scholar)
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Leibowitz, U., and N. Sinclair, eds., 2016, Explanation in Ethics and Mathematics. Debunking and Dispensability, Oxford: Oxford University Press. (Scholar)
Leng, M., 2005, “Mathematical Explanation”, in C. Cellucci and D. Gillies (eds.), Mathematical Reasoning and Heuristics, London: King’s College Publications, 167–189. (Scholar)
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–––, 2012, “Taking it Easy: A Response to Colyvan”, Mind, 121 (484): 983–995. (Scholar)
Liggins, D., 2016, “Grounding and the Indispensability Argument”, Synthese, 193: 531–548. (Scholar)
Lipton, P., 2004, “What Good is an Explanation”, in J. Cornwell (ed.), Explanations. Styles of Explanation in Science, Oxford: Oxford University Press, 1–21. (Scholar)
Lyon, A., 2012, “Mathematical Explanations of Empirical Facts, and Mathematical Realism”, Australasian Journal of Philosophy, 90 (3): 559–578. (Scholar)
Lyon, A., and M. Colyvan, 2008, “The Explanatory Power of Phase Spaces”, Philosophia Mathematica, 16: 1–17. (Scholar)
Malament, D., 1982, “Review of Field’s Science without Numbers”, Journal of Philosophy, 79: 523–534. (Scholar)
Mancosu, P., 1996, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford: Oxford University Press. (Scholar)
–––, 1999, “Bolzano and Cournot on Mathematical Explanation”, Revue d’Histoire des Sciences, 52: 429–455. (Scholar)
–––, 2000, “On Mathematical Explanation”, in E. Grosholz and H. Breger (eds.), The Growth of Mathematical Knowledge, Dordrecht: Kluwer, 103–119. (Scholar)
–––, 2001, “Mathematical Explanation: Problems and Prospects”, Topoi, 20: 97–117. (Scholar)
–––, 2008a, ed., The Philosophy of Mathematical Practice, Oxford: Oxford University Press.
–––, 2008b, “Mathematical Explanation: Why it matters”, in P. Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford: Oxford University Press, 134–150. (Scholar)
–––, 2017, “Mathematical Style”, The Stanford Encyclopedia of Philosophy (Winter 2017 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2017/entries/mathematical-style/>. (Scholar)
Mancosu, P., K. Jørgensen and S. Pedersen, eds., 2005, Visualization, Explanation and Reasoning Styles in Mathematics, Berlin: Springer. (Scholar)
Marcus, R., 2013, “Intrinsic Explanation and Field’s Dispensabilist Strategy”, International Journal of Philosophical Studies, 21: 163–183. (Scholar)
Melia, J., 2000, “Weaseling Away the Indispensability Argument”, Mind, 109: 455–479. (Scholar)
–––, 2002, “Response to Colyvan”, Mind, 111: 75–79. (Scholar)
Minio, R., 1984, “An Interview with Michael Atiyah”, The Mathematical Intelligencer, 6: 9–19. (Scholar)
Molinini, D., 2011, “Towards a Pluralist Approach to Mathematical Explanation of Physical Phenomena”, Lille: Atelier National de Reproduction des Thèses. (Scholar)
–––, 2012, “Learning from Euler. From Mathematical Practice to Mathematical Explanation”, Philosophia Scientiae, 109: 105–127. (Scholar)
–––, 2014, “Deductive Nomological Model and Mathematics: Making Dissatisfaction more Satisfactory”, Theoria. An International Journal for Theory, History and Foundations of Science, 80: 223–242. (Scholar)
–––, 2016, “Evidence, Explanation and Enhanced Indispensability ”, Synthese, 193 (2): 403–422. (Scholar)
Molinini, D., F. Pataut and A. Sereni, 2016, “Indispensability and Explanation: An Overview and Introduction”, Synthese, 193 (2): 317–332. (Scholar)
Morrison, M., 2000, Unifying Scientific Theories. Physical Concepts and Mathematical Structures, Cambridge: Cambridge University Press. (Scholar)
–––, 2015, Reconstructing Reality. Models, Mathematics and Simulations, Oxford: Oxford University Press. (Scholar)
–––, 2018, “The Non-Causal Character of Renormalization Group Explanations”, in A. Reutlinger and J. Saatsi (eds.), Explanation beyond Causation, Oxford: Oxford University Press, 206–230. (Scholar)
Norton, J., 2012, “Approximation and Idealization: Why the Difference Matters”, Philosophy of Science, 79: 207–232. (Scholar)
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Panza, M., and A. Sereni, 2016, “The Variety of Indispensability Arguments”, Synthese, 193 (2): 469–516. (Scholar)
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Pexton, M., 2014, “How Dimensional Analysis Can Explain”, Synthese, 191: 2333–2351. (Scholar)
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–––, 2011a, “On Batterman’s ‘On the Explanatory Role of Mathematics in Empirical Science’”, British Journal for the Philosophy of Science, 62: 211–217. (Scholar)
–––, 2011b, “Mathematical Explanations of the Rainbow”, Studies in History and Philosophy of Modern Physics, 42 (1): 13–22. (Scholar)
–––, 2011c, “Modeling Reality”, Synthese, 180: 19–32. (Scholar)
–––, 2012, Mathematics and Scientific Repesentation, Oxford: Oxford University Press. (Scholar)
–––, 2015a, “Abstract Explanations in Science”, British Journal for the Philosophy of Science, 66: 857–882. (Scholar)
–––, 2015b, “The Unsolvability of the Quintic: A Case Study in Abstract Mathematical Explanation”, Philosophers’ Imprint, 15 (3). (Scholar)
–––, 2018, “Accommodating Explanatory Pluralism”, in A. Reutlinger and J. Saatsi (eds.), Explanation beyond Causation, Oxford: Oxford University Press, 39–56. (Scholar)
Plebani, M., 2016, “Nominalistic Content, Grounding, and Covering Generalization: A Reply to ‘Grounding and the Indispensability Argument’”, Synthese, 193 (2): 549–558. (Scholar)
Potochnik, A., 2007, “Optimality Modeling and Explanatory Generality”, Philosophy of Science, 74: 680–691. (Scholar)
Povich, M., 2018, “Minimal Models and the Generalized Ontic Conception of Scientific Explanation”, British Journal for the Philosophy of Science, 69 (1): 117–137. (Scholar)
Proclus, A Commentary on the First Book of Euclid’s Elements, translated by G. R. Morrow, Princeton: Princeton University Press, 1970. (Scholar)
Railton, P., 1980, Explaining Explanation: A Realist Account of Scientific Explanation and Understanding, Ph.D. Dissertation, Princeton University. (Scholar)
Raman-Sundström, M., L.-D. Öhman, and N. Sinclair, 2016, “The Nature and Experience of Mathematical Beauty”, Journal of Humanistic Mathematics, 6 (1): 3–7. (Scholar)
Rantala, V., 1992, “Reduction and Explanation: Science vs. Mathematics”, in J. Echeverria, A. Ibarra, and T. Mormann (eds.), The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations, New York: Walter de Gruyter, 47–59. (Scholar)
Raven, M., 2015, “Ground”, Philosophy Compass, 10 (5): 322–333. (Scholar)
Räz, T., 2013, “On an Application of the Honeycomb Conjecture to the Bee’s Honeycomb”, Philosophia Mathematica , 10 (5): 322–333. (Scholar)
–––, 2017, “The Silent Hexagon: Explaining Comb Structures”, Synthese, 194: 1703–1724. (Scholar)
Redhead, M., 2004, “Asymptotic Reasoning”, Studies in History and Philosophy of Modern Physics B, 35 (3): 527–530. (Scholar)
Resnik, M., and D. Kushner, 1987, “Explanation, Independence, and Realism in Mathematics”, British Journal for the Philosophy of Science, 38: 141–158. (Scholar)
Reutlinger, A., 2014, “Why is There Universal Macro-Behavior? Renormalization Group Explanation as Non-Causal Explanation”, Philosophy of Science, 81: 1157–1170. (Scholar)
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