Linked bibliography for the SEP article "Structuralism in the Philosophy of Mathematics" by Erich Reck and Georg Schiemer

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Assadian, Bahram, 2018, “The Semantic Plights of the Ante-Rem Structuralist”, Philosophical Studies, 175(12): 3195–3215. doi:10.1007/s11098-017-1001-7 (Scholar)
Awodey, Steve, 1996, “Structure in Mathematics and Logic: A Categorical Perspective”, Philosophia Mathematica, 4(3): 209–237. doi:10.1093/philmat/4.3.209 (Scholar)
–––, 2004, “An Answer to Hellman’s Question: ‘Does Category Theory Provide a Framework for Mathematical Structuralism?’”, Philosophia Mathematica, 12(1): 54–64. doi:10.1093/philmat/12.1.54 (Scholar)
–––, 2010, Category Theory, second edition, Oxford: Oxford University Press. (Scholar)
–––, 2014, “Structuralism, Invariance, and Univalence”, Philosophia Mathematica, 22(1): 1–11. doi:10.1093/philmat/nkt030 (Scholar)
Benacerraf, Paul, 1965 [1983], “What Numbers Could Not Be”, The Philosophical Review, 74(1): 47–73. Reprinted in Benacerraf and Putnam 1983: 272–294. doi:10.2307/2183530 doi:10.1017/cbo9781139171519.015 (Scholar)
–––, 1996, “Recantation or Any Old ω-Sequence Would Do after All”, Philosophia Mathematica, 4(2): 184–189. doi:10.1093/philmat/4.2.184 (Scholar)
Benacerraf, Paul and Hilary Putnam (eds.), 1983, Philosophy of Mathematics: Selected Readings, second edition, Cambridge: Cambridge University Press. doi:10.1017/CBO9781139171519 (Scholar)
Burgess, John P., 1999, “Book Review: Stewart Shapiro. Philosophy of Mathematics: Structure and Ontology (1997)”, Notre Dame Journal of Formal Logic, 40(2): 283–291. doi:10.1305/ndjfl/1038949543 (Scholar)
–––, 2015, Rigor and Structure, Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780198722229.001.0001 (Scholar)
Button, Tim, 2006, “Realistic Structuralism’s Identity Crisis: A Hybrid Solution”, Analysis, 66(3): 216–222. doi:10.1093/analys/66.3.216 (Scholar)
Button, Tim and Sean Walsh, 2016, “Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics”, Philosophia Mathematica, 24(3): 283–307. doi:10.1093/philmat/nkw007 (Scholar)
Carter, Jessica, 2008, “Structuralism as a Philosophy of Mathematical Practice”, Synthese, 163(2): 119–31. doi:10.1007/s11229-007-9169-6 (Scholar)
Caws, Peter, 1988, Structuralism. A Philosophy for the Human Sciences, Atlantic Highlands, NJ: Humanities Press. (Scholar)
Chihara, Charles S., 2004, A Structural Account of Mathematics, Oxford: Oxford University Press (Scholar)
Cole, Julian C., 2010, “Mathematical Structuralism Today”, Philosophy Compass, 5(8): 689–699. doi:10.1111/j.1747-9991.2010.00308.x (Scholar)
Corry, Leo, 2004, Modern Algebra and the Rise of Mathematical Structures, second edition, Basel: Birkhäuser Basel. doi:10.1007/978-3-0348-7917-0 (Scholar)
Dedekind, Richard, 1888, Was sind und was sollen die Zahlen?, Braunschweig: Vieweg. Translated as “The Nature and Meaning of Numbers”, in his Essays on the Theory of Numbers, Wooster Woodruff Beman (trans.), Chicago: Open Court, 1901, pp. 29–115. (Scholar)
Dosse, François, 1991–92 [1997], Histoire du structuralisme, 2 volumes, Paris: Éditions La Découverte. Translated as History of Structuralism, 2 volumes, Deborah Glassman (trans.), Minneapolis, MN: University of Minnesota Press, 1997. (Scholar)
Eilenberg, Samuel and Saunders MacLane, 1945, “General Theory of Natural Equivalences”, Transactions of the American Mathematical Society, 58(2): 231–294. doi:10.2307/1990284 (Scholar)
Feferman, Solomon, 1977, “Categorical Foundations and Foundations of Category Theory”, in Logic, Foundations of Mathematics, and Computability Theory, Robert E. Butts and Jaakko Hintikka (eds.), Dordrecht: Springer Netherlands, 149–169. doi:10.1007/978-94-010-1138-9_9 (Scholar)
–––, 2014, “Logic, Mathematics, and Conceptual Structuralism”, in The Metaphysics of Logic, Penelope Rush (ed.), Cambridge: Cambridge University Press, 72–92. doi:10.1017/cbo9781139626279.006 (Scholar)
Franklin, James, 2014, An Aristotelian Realist Philosophy of Mathematics, London: Palgrave Macmillan UK. doi:10.1057/9781137400734 (Scholar)
French, Steven, 2014, The Structure of the World: Metaphysics and Representation, Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780199684847.001.0001 (Scholar)
Hale, Bob, 1996, “Structuralism’s Unpaid Epistemological Debts”, Philosophia Mathematica, 4(2): 124–147. doi:10.1093/philmat/4.2.124 (Scholar)
Halimi, Brice, 2019, “Settings and Misunderstandings in Mathematics”, Synthese, 196(11): 4623–4656. doi:10.1007/s11229-017-1671-x (Scholar)
Hellman, Geoffrey, 1989, Mathematics without Numbers: Towards a Modal-Structural Interpretation, Oxford: Oxford University Press. doi:10.1093/0198240341.001.0001 (Scholar)
–––, 1996, “Structuralism Without Structures”, Philosophia Mathematica, 4(2): 100–123. doi:10.1093/philmat/4.2.100 (Scholar)
–––, 2001, “Three Varieties of Mathematical Structuralism†”, Philosophia Mathematica, 9(2): 184–211. doi:10.1093/philmat/9.2.184 (Scholar)
–––, 2003, “Does Category Theory Provide a Framework for Mathematical Structuralism?”, Philosophia Mathematica, 11(2): 129–157. doi:10.1093/philmat/11.2.129 (Scholar)
–––, 2005, “Structuralism”, in Shapiro 2005: 536–562. (Scholar)
Hellman, Geoffrey and Stewart Shapiro, 2019, Mathematical Structuralism (Elements in The Philosophy of Mathematics), Cambridge: Cambridge University Press. doi:10.1017/9781108582933 (Scholar)
Horsten, Leon, forthcoming, “Generic Structure”, Philosophia Mathematica, first online: 16 July 2018. doi:10.1093/philmat/nky015 (Scholar)
Isaacson, Daniel, 2011, “The Reality of Mathematics and the Case of Set Theory”, in Truth, Reference, and Realism, Zsolt Novák and András Simonyi (eds), Budapest: CEU Press, pp. 1–75. (Scholar)
Keränen, Jukka, 2001, “The Identity Problem for Realist Structuralism”, Philosophia Mathematica, 9(3): 308–330. doi:10.1093/philmat/9.3.308 (Scholar)
Ketland, Jeffrey, 2006, “Structuralism and the Identity of Indiscernibles”, Analysis, 66(4): 303–315. doi:10.1093/analys/66.4.303 (Scholar)
–––, 2011, “Identity and Indiscernibility”, The Review of Symbolic Logic, 4(2): 171–185. doi:10.1017/s1755020310000328 (Scholar)
Korbmacher, Johannes and Georg Schiemer, 2018, “What Are Structural Properties?”, Philosophia Mathematica, 26(3): 295–323. doi:10.1093/philmat/nkx011 (Scholar)
Ladyman, James, 2005, “Mathematical Structuralism and the Identity of Indiscernibles”, Analysis, 65(3): 218–221. doi:10.1093/analys/65.3.218 (Scholar)
–––, 2007 [2019], “Structural Realism”, Stanford Encyclopedia of Philosophy (Fall 2019 edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2019/entries/structural-realism/> (Scholar)
Landry, Elaine, 1999, “Category Theory as a Framework for Mathematical Structuralism”, The 1998 Annual Proceedings of the Canadian Society for the History and Philosophy of Mathematics, pp. 133–142 (Scholar)
–––, 2006, “Category Theory as a Framework for an in re Interpretation of Mathematical Structuralism”, in The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today, Johan van Benthem, Gerhard Heinzmann, Manuel Rebuschi, and Henk Visser (eds.), Dordrecht: Springer Netherlands, 163–179. doi:10.1007/978-1-4020-5012-7_12 (Scholar)
–––, 2011, “How to Be a Structuralist All the Way Down”, Synthese, 179(3): 435–454. doi:10.1007/s11229-009-9691-9 (Scholar)
––– (ed.), 2017, Categories for the Working Philosopher, Oxford: Oxford University Press. doi:10.1093/oso/9780198748991.001.0001 (Scholar)
Landry, Elaine and Jean-Pierre Marquis, 2005, “Categories in Context: Historical, Foundational, and Philosophical”, Philosophia Mathematica, 13(1): 1–43. doi:10.1093/philmat/nki005 (Scholar)
Lawvere, F. William, 1964, “An Elementary Theory of the Category of Sets”, Proceedings of the National Academy of Sciences of the United States of America, 52(6): 1506–1511. (Scholar)
–––, 1966, “The Category of Categories as a Foundation for Mathematics”, in Proceedings of the Conference on Categorical Algebra, La Jolla 1965, S. Eilenberg, D. K. Harrison, S. MacLane, and H. Röhrl (eds.), Berlin, Heidelberg: Springer Berlin Heidelberg, 1–20. doi:10.1007/978-3-642-99902-4_1 (Scholar)
Leitgeb, Hannes, forthcoming, “On Non-Eliminative Structuralism: Unlabelled Graphs as a Case Study (Part A and B)”, Philosophia Mathematica (III). (Scholar)
Leitgeb, Hannes and James Ladyman, 2008, “Criteria of Identity and Structuralist Ontology”, Philosophia Mathematica, 16(3): 388–396. doi:10.1093/philmat/nkm039 (Scholar)
Lévi-Strauss, Claude, 1958 [1963], Anthropologie structurale, Paris, Plon. Translated as Structural Anthropology, Claire Jacobson and Brooke Grundfest Schoepf (trans.), Basic Books, 1963. (Scholar)
Linnebo, Øystein, 2008, “Structuralism and the Notion of Dependence”, The Philosophical Quarterly, 58(230): 59–79. doi:10.1111/j.1467-9213.2007.529.x (Scholar)
Linnebo, Øystein and Richard Pettigrew, 2011, “Category Theory as an Autonomous Foundation”, Philosophia Mathematica, 19(3): 227–254. doi:10.1093/philmat/nkr024 (Scholar)
–––, 2014, “Two Types of Abstraction for Structuralism”, The Philosophical Quarterly, 64(255): 267–283. doi:10.1093/pq/pqt044 (Scholar)
Makkai, Michael, 1998, “Towards a Categorical Foundation of Mathematics”, in Logic Colloquium ‘95: Proceedings of the Annual European Summer Meeting of the Association of Symbolic Logic, held in Haifa, Israel, August 9–18, 1995, Johann A. Makowsky and Elena V. Ravve (eds), (Lecture Notes in Logic, 11), Berlin: Springer-Verlag Berlin Heidelberg, pp. 153–190. [Makkai 1998 available online] (Scholar)
Mac Lane, Saunders, 1986, Mathematics Form and Function, New York, NY: Springer New York. doi:10.1007/978-1-4612-4872-9 (Scholar)
–––, 1996, “Structure in Mathematics”, Philosophia Mathematica, 4(2): 174–183. doi:10.1093/philmat/4.2.174 (Scholar)
MacBride, Frazer, 2005, “Structuralism Reconsidered”, in Shapiro 2005: 563–589. (Scholar)
Marquis, Jean-Pierre, 1995, “Category Theory and the Foundations of Mathematics: Philosophical Excavations”, Synthese, 103(3): 421–447. doi:10.1007/bf01089735 (Scholar)
–––, 1997 [2019], “Category Theory”, The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), Edward N. Zalta (ed.), URL: <https://plato.stanford.edu/archives/fall2019/entries/category-theory/> (Scholar)
–––, 2009, From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory, (Logic, Epistemology, and the Unity of Science 14), Dordrecht: Springer Netherlands. doi:10.1007/978-1-4020-9384-5 (Scholar)
–––, 2013, “Categorical Foundations of Mathematics: Or How to Provide Foundations for Abstract Mathematics”, The Review of Symbolic Logic, 6(1): 51–75. doi:10.1017/s1755020312000147 (Scholar)
McLarty, Colin, 1993, “Numbers Can Be Just What They Have To”, Noûs, 27(4): 487–498. doi:10.2307/2215789 (Scholar)
–––, 2004, “Exploring Categorical Structuralism”, Philosophia Mathematica, 12(1): 37–53. doi:10.1093/philmat/12.1.37 (Scholar)
–––, 2008, “What Structuralism Achieves”, in The Philosophy of Mathematical Practice, Paolo Mancosu (ed.), Oxford: Oxford University Press, 354–369. doi:10.1093/acprof:oso/9780199296453.003.0014 (Scholar)
–––, 2011, “Recent Debate over Categorical Foundations”, in Foundational Theories of Classical and Constructive Mathematics, Giovanni Sommaruga (ed.), (Western Ontario Series in Philosophy of Science 76), Dordrecht: Springer Netherlands, 145–154. doi:10.1007/978-94-007-0431-2_7 (Scholar)
–––, 2012, “Categorical Foundations and Mathematical Practice”, Philosophia Mathematica, 20(1): 111–113. doi:10.1093/philmat/nkr041 (Scholar)
Menzel, Christopher, 2018, “Haecceities and Mathematical Structuralism”, Philosophia Mathematica, 26(1): 84–111. doi:10.1093/philmat/nkw030 (Scholar)
Nodelman, Uri and Edward N. Zalta, 2014, “Foundations for Mathematical Structuralism”, Mind, 123(489): 39–78. doi:10.1093/mind/fzu003 (Scholar)
Parsons, Charles, 1990, “The Structuralist View of Mathematical Objects”, Synthese, 84(3): 303–346. doi:10.1007/bf00485186 (Scholar)
–––, 2004, “Structuralism and Metaphysics”, The Philosophical Quarterly, 54(214): 56–77. doi:10.1111/j.0031-8094.2004.00342.x (Scholar)
–––, 2008, Mathematical Thought and Its Objects, Cambridge: Cambridge University Press. doi:10.1017/cbo9780511498534 (Scholar)
–––, 2018, “Concepts versus Objects”, in Reck 2018b: 91–112. (Scholar)
Pettigrew, Richard, 2008, “Platonism and Aristotelianism in Mathematics”, Philosophia Mathematica, 16(3): 310–332. doi:10.1093/philmat/nkm035 (Scholar)
Piaget, Jean, 1968 [1970], Le structuralisme, Paris: Presses Universitaires de France. Translated as Structuralism, Chaninah Maschler (trans.), New York: Basic Books, 1970. (Scholar)
Putnam, Hilary, 1967, “Mathematics without Foundations”, The Journal of Philosophy, 64(1): 5–22. Reprinted in Benacerraf and Hilary Putnam 1983: 295–312. doi:10.2307/2024603 doi:10.1017/CBO9781139171519.016 (Scholar)
Reck, Erich H., 2003, “Dedekind’s Structuralism: An Interpretation and Partial Defense”, Synthese, 137(3): 369–419. doi:10.1023/b:synt.0000004903.11236.91 (Scholar)
–––, 2018a, “On Reconstructing Dedekind Abstraction Logically”, in Reck 2018b: 113–138. (Scholar)
––– (ed.), 2018b, Logic, Philosophy of Mathematics, and their History: Essays in Honor of W.W. Tait, London: College Publications. (Scholar)
Reck, Erich H. and Michael P. Price, 2000, “Structures And Structuralism In Contemporary Philosophy Of Mathematics”, Synthese, 125(3): 341–383. doi:10.1023/a:1005203923553 (Scholar)
Reck, Erich H. and Georg Schiemer (eds.), forthcoming, Prehistory of Mathematical Structuralism, Oxford: Oxford University Press. (Scholar)
Resnik, Michael D., 1981, “Mathematics as a Science of Patterns: Ontology and Reference”, Noûs, 15(4): 529–550. doi:10.2307/2214851 (Scholar)
–––, 1982, “Mathematics as a Science of Patterns: Epistemology”, Noûs, 16(1): 95–105. doi:10.2307/2215419 (Scholar)
–––, 1988, “Mathematics from the Structural Point of View”, Revue Internationale de Philosophie, 42(167): 400–424. (Scholar)
–––, 1996, “Structural Relativity”, Philosophia Mathematica, 4(2): 83–99. doi:10.1093/philmat/4.2.83 (Scholar)
–––, 1997, Mathematics as a Science of Patterns, Oxford: Oxford University Press. doi:10.1093/0198250142.001.0001 (Scholar)
Russell, Bertrand, 1903, The Principles of Mathematics, Cambridge: Cambridge University Press. Republished by Norton & Company, New York, 1996. [Russell 1903 available online]. (Scholar)
Schiemer, Georg and John Wigglesworth, forthcoming, “The Structuralist Thesis Reconsidered”, The British Journal for the Philosophy of Science, first online: 30 January 2018. doi:10.1093/bjps/axy004 (Scholar)
Richart, Charles E., 1995, Structuralism and Structures: A Mathematical Perspective, London: World Scientific. (Scholar)
Shapiro, Stewart, 1983, “Mathematics and Reality”, Philosophy of Science, 50(4): 523–548. doi:10.1086/289138 (Scholar)
–––, 1989, “Structure and Ontology”, Philosophical Topics, 17(2): 145–171. (Scholar)
–––, 1996, “Space, Number and Structure: A Tale of Two Debates”, Philosophia Mathematica, 4(2): 148–173. doi:10.1093/philmat/4.2.148 (Scholar)
–––, 1997, Philosophy of Mathematics: Structure and Ontology, Oxford: Oxford University Press. doi:10.1093/0195139305.001.0001 (Scholar)
––– (ed.), 2005, The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford: Oxford University Press. doi:10.1093/oxfordhb/9780195325928.001.0001 (Scholar)
–––, 2008, “Identity, Indiscernibility, and ante rem Structuralism: The Tale of i and −i”, Philosophia Mathematica, 16(3): 285–309. doi:10.1093/philmat/nkm042 (Scholar)
Tsementzis, Dimitris, 2017, “Univalent Foundations as Structuralist Foundations”, Synthese, 194(9): 3583–3617. doi:10.1007/s11229-016-1109-x (Scholar)
Univalent Foundations Program, 2013, Homotopy Type Theory: Univalent Foundations of Mathematics, The Univalent Foundations Program. [Homotopy Type Theory available online] (Scholar)
van Fraassen, Bas C., 2008, Scientific Representation: Paradoxes of Perspective, Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780199278220.001.0001 (Scholar)
Wigglesworth, John, 2018, “Grounding in Mathematical Structuralism”, in Reality and Its Structure: Essays in Fundamentality, Ricki Bliss and Graham Priest (eds.), Oxford: Oxford University Press, 217–236. doi:10.1093/oso/9780198755630.003.0012 (Scholar)
Worrall, John, 1989, “Structural Realism: The Best of Both Worlds?”, Dialectica, 43(1–2): 99–124. doi:10.1111/j.1746-8361.1989.tb00933.x (Scholar)

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