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)
- –––, 2018, “Explanation by
Constraint”, in A. Reutlinger and J. Saatsi
(eds.), Explanation beyond Causation, Oxford: Oxford
University Press, 15–38. (Scholar)
- 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)
- –––, 2010, Mathematics and Reality, Oxford: Oxford University Press. (Scholar)
- –––, 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)
- Nummela, E., 1987, “No Coincidence”, The
Mathematical Gazette, 71(456): 147. (Scholar)
- Owens, D., 1992, Causes and Coincidences, Cambridge: Cambridge University Press. (Scholar)
- Panza, M., and A. Sereni, 2016, “The Variety of Indispensability Arguments”, Synthese, 193 (2): 469–516. (Scholar)
- Paseau, A., 2010, “Proofs of the Compactness Theorem”, History and Philosophy of Logic, 31: 73–98. (Scholar)
- Pexton, M., 2014, “How Dimensional Analysis Can Explain”, Synthese, 191: 2333–2351. (Scholar)
- Pincock, C., 2007, “A Role for Mathematics in the Physical Sciences”, Noûs, 41: 253–275. (Scholar)
- –––, 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)
- –––, 2016, “Is There a Monist Theory of Causal and Non‐Causal Explanations? The Counterfactual Theory of Scientific Explanation”, Philosophy of Science, 83: 733–745. (Scholar)
- –––, 2017a, “Do Renormalization Group Explanations Conform to the Commonality Strategy?”, Journal for General Philosophy of Science , 48: 143–150. (Scholar)
- –––, 2017b, “Are Causal Facts Really Explanatorily Emergent? Ladyman and Ross on Higher-Level Causal Facts and Renormalization Group Explanation”, Synthese, 194 (7): 2291–2305. (Scholar)
- –––, 2017c, “Explanation Beyond Causation? New Directions in the Philosophy of Scientific Explanation”, Philosophy Compass, first online 08 February 2017. doi: 10.1111/phc3.12395 (Scholar)
- –––, 2018,“Extending the Counterfactual
Theory of Explanation”, in A. Reutlinger and J. Saatsi
(eds.), Explanation beyond Causation, Oxford: Oxford
University Press, 74–95. (Scholar)
- Reutlinger, A., and H. Andersen, 2016, “Abstract versus
Causal Explanations?”, International Studies in the
Philosophy of Science, 30: 129–149. (Scholar)
- Reutlinger, A., and J. Saatsi, eds., 2018, Explanation beyond Causation, Oxford: Oxford University Press. (Scholar)
- Rice, C., 2012, “Optimality Explanations: A Plea for an Alternative Approach”, Biology and Philosophy, 27: 685–703. (Scholar)
- –––, 2015, “Moving beyond Causes: Optimality Models and Scientific Explanation”, Noûs, 49: 589–615. (Scholar)
- Rizza, D., 2011, “Magicicada, Mathematical Explanation and Mathematical Realism”, Erkenntnis, 74: 101–114. (Scholar)
- –––, 2013, “The Applicability of Mathematics: Beyond Mapping Accounts”, Philosophy of Science, 80: 398–412. (Scholar)
- Robinson, J. A., 2000, “Proof = Guarantee +
Explanation”, in S. Hölldobler (ed.), Intellectics and
Computational Logic, Dordrecht: Kluwer, 277–294. (Scholar)
- Roski, S., 2017, Bolzano’s Conception of Grounding,
Frankfurt am Main: Vittorio Klostermann. (Scholar)
- Saatsi, J., 2007, “Living in Harmony: Nominalism and the Explanationist Argument for Realism”, International Studies in the Philosophy of Science, 21 (1): 19–33. (Scholar)
- –––, 2011, “The Enhanced Indispensability Argument”, British Journal for the Philosophy of Science, 63 (1): 143–154. (Scholar)
- –––, 2012, “Mathematics and Program Explanations”, Australasian Journal of Philosophy, 90: 579–584. (Scholar)
- –––, 2016, “On the ‘Indispensable
Explanatory Role’ of Mathematics”, Mind, 125
(500): 1045–1070. (Scholar)
- –––, 2017, “Dynamical Systems Theory and Explanatory Indispensability”, Philosophy of Science, 84 (5): 892–904. (Scholar)
- –––, 2018, “On Explanations from Geometry of Motion”, The British Journal for the Philosophy of Science, 69 (1): 253–273. (Scholar)
- Saatsi, J., and M. Pexton, 2013, “Reassessing Woodward’s
Account of Explanation: Regularities, Counterfactuals, and Non-Causal
Explanations”, Philosophy of Science, 80:
613–624. (Scholar)
- Salmon, W., 1984, Scientific Explanation and the Causal Structure of the World, Princeton: Princeton University Press. (Scholar)
- Salverda, J., 2017, “Characterizing Properties and
Explanation in Mathematics”, Logique et Analyse, 60
(237): 25–46. (Scholar)
- Sandborg, D., 1997, Explanation and Mathematical Practice, Ph. D. Dissertation, University of Pittsburgh. (Scholar)
- –––, 1998, “Mathematical Explanation and the Theory of Why-Questions”, British Journal for the Philosophy of Science, 49: 603–624. (Scholar)
- Sereni, A., 2016, “Equivalent Explanations and Mathematical Realism”, Synthese, 193 (2): 423–434. (Scholar)
- Shapiro, S., 2000, Thinking About Mathematics, Oxford: Oxford University Press. (Scholar)
- Skow, B., 2015, “Are There Genuine Physical Explanations of Mathematical Phenomena?”, British Journal for the Philosophy of Science, 66: 69–93. (Scholar)
- Smart, J. J. C., 1990, “Explanation—Opening Address”, in D. Knowles (ed.), Explanation and Its Limits,, Cambridge: Cambridge University Press, 1–19. (Scholar)
- Steiner, M., 1978a, “Mathematical Explanation”, Philosophical Studies, 34: 135–151. (Scholar)
- –––, 1978b, “Mathematics, Explanation, and Scientific Knowledge”, Noûs, 12: 17–28. (Scholar)
- –––, 1998, The Applicability of Mathematics as a Philosophical Problem, Cambridge, MA: Harvard University Press. (Scholar)
- –––, 2005, “Mathematics—Applications
and Applicability”, in S. Shapiro (ed.), The Oxford Handbook
of Philosophy of Mathematics and Logic, Oxford: Oxford University
Press, 625–650. (Scholar)
- Strevens, M., 2008, Depth: An Account of Scientific Explanation , Cambridge, MA: Harvard University Press. (Scholar)
- –––, 2017, “The Structure of Asymptotic Idealization”, Synthese, first online 20 December 2017, doi: 10.1007/s11229-017-1646-y (Scholar)
- Tallant, J., 2013, “Optimus Prime: Paraphrasing Prime Number Talk”, Synthese, 190: 2065–2083. (Scholar)
- Tappenden, J., 2005, “Proof Style and Understanding in Mathematics I: Visualization, Unification and Axiom Choice”, in P. Mancosu, K. Jørgensen and S. Pedersen (eds.), Visualization, Explanation and Reasoning Styles in Mathematics, Berlin: Springer, 147–214. (Scholar)
- –––, 2008a, “Mathematical Concepts and Definitions”, in P. Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford: Oxford University Press, 256–275. (Scholar)
- –––, 2008b, “Mathematical Concepts: Fruitfulness and Naturalness”, in P. Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford: Oxford University Press, 276–301. (Scholar)
- Thomas, R., 2017, “Beauty is Not All There is to Aesthetics in Mathematics”, Philosophia Mathematica, first online 13 September 2016. doi: 10.1093/philmat/nkw019 (Scholar)
- Wakil, S., and J. Justus, 2017, “Mathematical Explanation and the Biological Optimality Fallacy”, Philosophy of Science, 84: 916–930. (Scholar)
- Wayne, A., 2011, “Expanding the Scope of Explanatory Idealization”, Philosophy of Science, 78: 830–841. (Scholar)
- –––, 2012, “Mathematical Emergence and
Singular Limits”, Synthese, 184: 341–356. (Scholar)
- Weber, E., and J. Frans, 2017, “Is Mathematics a Domain for Philosophers of Explanation? ”, Journal for General Philosophy of Science, 48 (1): 125–142. (Scholar)
- Weber, E., and L. Verhoeven, 2002, “Explanatory Proofs in Mathematics”, Logique et Analyse, 45 (179–180): 299–307. (Scholar)
- Weisberg, M., 2007, “Three Kinds of Idealization”, Journal of Philosophy, 104 (12): 639–659. (Scholar)
- Wigner, E., 1967, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, in Symmetries and Reflections, Bloomington: Indiana University Press, 222–237. (Scholar)
- Woodward, J., 2003, Making Things Happen: A Theory of Causal Explanation, Oxford: Oxford University Press. (Scholar)
- –––, 2013, “Mechanistic Explanation: Its
Scope and Limits”, Proceedings of the Aristotelian Society,
Supplementary Volumes, 87 (1): 39–65. (Scholar)
- –––, 2014, “Mechanisms in
Science”, The Stanford Encyclopedia of Philosophy
(Winter 2014 Edition), Edward N. Zalta (ed.), URL =
<https://plato.stanford.edu/archives/win2014/entries/scientificexplanation/> (Scholar)
- –––, 2018,“Some Varieties of Non-Causal Explanation”, in A. Reutlinger and J. Saatsi (eds.), Explanation beyond Causation, Oxford: Oxford University Press, 117–140. (Scholar)
- Yablo, S., 2012, “Explanation, Extrapolation, and Existence”, Mind, 121: 1007–1030. (Scholar)
- Zelcer, M., 2013, “Against Mathematical Explanation”, Journal for General Philosophy of Science, 44: 173–192. (Scholar)