Dedekind Website

This website is part of a research project on Richard Dedekind (1831-1916), his philosophy of mathematics, and its contemporary significance. It serves both to make results from the project available and to allow for direct feedback to the principal investigator. Both the research project and the website are in their initial phases. If you have information relevant for either (e.g., additional secondary literature on Dedekind that should, or at least could, be included in the list below), please contact me here.

(I) Completed Work on the Project:

(a) Main publications:

Reck, Erich (2003a): “Dedekind's Structuralism: An Interpretation and Partial Defense”, Synthese 137, 369–419.

____ (2008): “Dedekind's Contributions to the Foundations of Mathematics”, Stanford Encyclopedia of Philosophy, E. Zalta, ed., 32 pp.

(b) Related pieces:

Awodey, S. & Reck, E. (2002a): “Categoricity and Completeness, Part I: 19-Century Axiomatics to 20th-Century Metalogic”, History and Philosophy of Logic 23 (1), 1–30.

____ (2002b): “Categoricity and Completeness, Part II: 20th-Century Metalogic to 21st-Century Semantics”, History and Philosophy of Logic 23 (2), 77-94.

Reck, Erich (2003b): “Frege, Natural Numbers, and Arithmetic's Umbilical Cord”, Manuscrito 26:2, 427–470.

____ (2009): “Dedekind, Structural Reasoning, and Mathematical Understanding”, in New Perspectives on Mathematical Practices, B. van Kerkhove, eds., Singapore: WSP Press, pp. 15-173

Reck, E. & Price, M. (2000): “Structures and Structuralism in Contemporary Philosophy of Mathematics”, Synthese 125, 341–383.

(II) Related Internet Resources:

Dedekind's Essays on the Theory of Numbers (originally published in 1901).

Dedekind's Gesammelte Mathematische Werke, Vols. 1-3 (1930-32).

MacTutor site, entry on Richard Dedekind

(III) Literature on Dedekind:

Alten, H.-W., et al., eds. (2003): 4000 Jahre Algebra: Geschichte, Kulturen, Menschen, Springer: Berlin; especially Chapter 9, “Algebra an der Wende zum 20. Jahrhundert”, by K.-H. Schlote et al., pp. 475–550.

Avigad, Jeremy (2006): “Methodology and Metaphysics in the Development of Dedekind's Theory of Ideals”, in The Architecture of Modern Mathematics, J. Ferreirós & J. Grey, eds., Oxford University Press, pp. 159–186.

Bell, E.T. (1937): Men of Mathematics; reprinted by Simon & Schuster: New York, 1965; especially Chapter 27, “Arithmetic the Second: Kummer (1810–1893), Dedekind (1831–1916)”, pp. 510–525.

Belna, Jean-Pierre (1996): La Notion de nombre chez Dedekind, Cantor, Frege: Théories, conceptions, et philosophie, Vrin: Paris.

Biermann, Kurt R. (1971): “Dedekind”, in Dictionary of Scientific Biography, Vol. 4, C.C. Gillespie, ed., pp. 1–5.

Boolos, George (1990): “The Standard of Equality of Numbers”, in Meaning and Method: Essays in Honor of Hilary Putnam, G. Boolos, ed., pp. 261–277; reprinted in Logic, Logic, and Logic, Harvard University Press, 1998, pp. 202–219.

Boyer, C. & Merzbach, U. (1991): A History of Mathematics, second edition (revised), Wiley & Sons: New York; especially Chapter 25, “Analysis”, pp. 553–574, and Chapter 26, “Algebra”, pp. 575–598.

Burris, Stanley (1983): "Boolean Constructions", in Universal Algebra and Lattice Theory, Proceedings, Puebla 1982, Springer Lecture Notes Vol. 1004, pp. 67-90.

Cooke, Roger (2005): “Richard Dedekind, Stetigkeit und irrationale Zahlen (1872)”, Chapter 43 of Landmark Writings in Western Mathematics, 1640–1940, I. Grattan-Guinness, ed., Elsevier, pp. 553–563.

Corfield, David (2003): Towards a Philosophy of Real Mathematics, Cambridge University Press; especially Chapter 8, “Beyond the Methodology of Mathematical Research Programmes”, pp. 175–203.

Corry, Leo (2004): Modern Algebra and the Rise of Mathematical Structures, second edition (revised), Birkhäuser: Boston; especially Chapter 2: “Richard Dedekind: Numbers and Ideals”, pp. 66–136.

Demopoulos, W. & Clark, P. (2005): “The Logicism of Frege, Dedekind, and Russell”, in The Oxford Handbook of Philosophy of Mathematics and Logic, S. Shapiro, ed., Oxford University Press, pp. 166–202.

Dieudonné, Jean, ed. (1985): Geschichte der Mathematik 1700–1900, Deutscher Verlag der Wissenschaften: Berlin, 1985; especially Chapter 5, “Zahlentheorie”, by W. & F. Ellison, pp. 171–358, and Chapter 6, “Grundlagen der Analysis”, by P. Dugac, pp. 359–421; originally published in French, 1978.

Dugac, Pierre (1976): Richard Dedekind et les fondements des mathématiques, Vrin: Paris; with selections from Dedekind's Nachlass.

Edwards, Harold M. (1977): Fermat's Last Theorem. A Genetic Introduction to Algebraic Number Theory, Springer: New York.

____ (1980): “The Genesis of Ideal Theory”, Archive for History of Exact Sciences 23, 321–378.

____ (1983): “Dedekind's Invention of Ideals”, Bulletin of the London Mathematical Society 15, 8–17.

____ (1990): Divisor Theory, Birkhäuser: Boston.

Ewald, William B., ed. (1996a): From Kant to Hilbert. A Source Book in the Foundations of Mathematics, Vols. 1–2, Oxford University Press.

____ (1996b): Editor's introduction to Dedekind (1996a), pp. 753–754.

Ferreirós, José (1993): “On the Relation between Georg Cantor and Richard Dedekind”, Historia Mathematica 20, 343–363.

____ (1999): Labyrinth of Thought: A History of Set Theory and its Role in Modern Mathematics, Birkhäuser: Boston; especially: Chapter 3, “Dedekind and the Set-theoretic Approach to Algebra”, pp. 81–116; Chapter 4, “The Real Number System”, pp. 117–144; and Chapter 7, “Sets and Maps as a Foundation for Mathematics”, pp. 215–255; second edition (with added postscript), 2007.

____ (2005): “Richard Dedekind (1888) and Giuseppe Peano (1889), Booklets on the Foundations of Arithmetic”, Chapter 47 of Landmark Writings in Western Mathematics, 1640–1940, I. Grattan-Guinness, ed., Elsevier, pp. 613–626.

____ (2007): “The Early Development of Set Theory”, Stanford Encyclopedia of Philosophy (Summer 2007 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2007/entries/settheory-early/>.

____ (2009): “Hilbert, Logicism, and Mathematical Existence”, Synthese 170, 33-70.

Gardies, Jean-Louis (1984): “Eudoxe et Dedekind”, Revue d'histoire des sciences 37, 111–125.

Geyer, Wulf-Dieter (1981): “Die Theorie der algebraischen Funktionen einer Veränderlichen nach Dedekind und Weber”, in Scharlau (1981a), pp. 109–133.

Gillies, D.A. (1982): Frege, Dedekind, and Peano on the Foundations of Arithmetic, Van Gorcum: Assen.

Grattan-Guinness, Ivo, ed. (1980): From the Calculus to Set Theory 1630–1910. An Introductory History, Princeton University Press; especially Chapter 6, “Developments in the foundations of mathematics, 1870–1920”, by R. Bunn, pp. 220–255.

Gray, Jeremy (1986): “The Nineteenth-Century Revolution in Mathematical Ontology”, in Revolutions in Mathematics, D. Gillies, ed., Oxford University Press; second edition, 1992, pp. 226–248.

____ (2000): Linear Differential Equations and Group Theory, from Riemann to Poincaré, second edition, Birkhäuser: Boston; especially Chapter IV, “Modular Equations”, pp. 101–140.

____ (2008): Plato's Ghost: The Modernist Transformation of Mathematics, Princeton University Press; especially Chapter 3, “Mathematical Modernism Arrives”, pp. 113-175.

Hallett, Michael (1994): “Hilbert's Axiomatic Method and the Laws of Thought”, in Mathematics and Mind, A. George, ed., Oxford University Press, pp. 158-198.

____ (1995): “Hilbert and Logic”, in Québec Studies in the Philosophy of Science 1, 135-187.

____ (2003): “Foundations of Mathematics”, in The Cambridge History of Philosophy, 1870-1945, T. Baldwin, ed., Cambridge University Press, pp. 128-154.

Harborth, H., Heuer, M., Löwe, H., Löwen, R. & Sonar, T., eds. (2007): Gedenkschrift für Richard Dedekind, Appelhans Verlag: Braunschweig

Haubrich, Ralf (1992): Zur Entstehung der algebraischen Zahlentheorie Richard Dedekinds, Ph.D. dissertation, University of Göttingen.

Hawking, Stephen, ed. (2005a): God Created the Integers. The Mathematical Breakthroughs that Changed History, Running Press: London.

____ (2005b): Editor's introduction to “Richard Julius Wilhelm Dedekind (1831–1916). His Life and Work”, in Hawking (2005a), pp. 901–905.

Jahnke, Hans Niels, ed. (2003): A History of Analysis, American Mathematical Society; especially: Chapter 1, “Antiquity”, by R. Thiele, pp. 1–40, and Chapter 10, “The End of the Science of Quantity: Foundations of Analysis, 1860–1910”, by J. Lützen, pp. 291–324; originally published in German, 1999.

Jourdain, P.E.B. (1916): “Richard Dedekind (1833–1916)”, The Monist 26, 415–427; reprinted in Modern Logic 3, 1993, 207–214.

Kitcher, Philip (1986): “Frege, Dedekind, and the Philosophy of Mathematics”, in Frege Synthesized, L. Haaparanta & J. Hintikka, eds., Reidel: Dordrecht, pp. 299–343.

Kolmogorov, A.N. & Yushkevich, A.P. (2001): Mathematics of the 19th Century. Vol. I: Mathematical Logic, Algebra, Number Theory, Probability Theory, second edition (revised), Birkhäuser: Boston; especially Chapter 2, Section 3, “The Theory of Algebraic Numbers and the Beginnings of Commutative Algebra”, by I.G. Bashmakova & A.N. Rudakov, pp. 86–135; originally published in Russian, 1978.

Landau, Edmund (1917): “Richard Dedekind”, Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Geschäftliche Mitteilungen, 50–70.

Laugwitz, Detlef (1999): Bernhard Riemann 1826–1866. Turning Points in the Conception of Mathematics, Birkhäuser: Boston; originally published in German, 1996.

McCarty, David (1995): “The Mysteries of Richard Dedekind”, in From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics, J. Hintikka, ed., Springer: New York, pp. 53–96.

McLarty, Colin (2006): “Emmy Noether's ‘Set Theoretic’ Topology: From Dedekind to the Rise of Functors”, in The Architecture of Modern Mathematics, J. Ferreirós & J. Grey, eds., Oxford University Press, pp. 187–208.

Mehrtens, Herbert (1979a): Entstehung der Verbandstheorie, Gerstenberg: Hildesheim; especially Chapter 2, “Die ‘Dualgruppe’ von Richard Dedekind”, pp. 66–126.

____ (1979b): “Das Skelett der modernen Algebra. Zur Bildung mathematischer Begriffe bei Richard Dedekind”, in Disciplinae Novae, C.J. Sciba, ed., Vanderhoeck & Ruprecht: Göttingen, pp. 25–43.

____ (1982): “Richard Dedekind – Der Mensch und die Zahlen”, Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft 33, 19–33.

Potter, Michael (2000): Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap, Oxford University Press; especially Chapter 3, “Dedekind”, pp. 81–104.

Reed, David (1995): Figures of Thought, Routledge: London; especially Chapter 4, “Number Theory in the Nineteenth Century”, pp. 76–116.

Scharlau, Winfried, ed. (1981a): Richard Dedekind, 1831/1981: Eine Würdigung zu seinen 150. Geburtstag, Vieweg: Braunschweig.

____ (1981b): “Erläuterungen zu Dedekinds Manuskript über Algebra”, in Scharlau (1981a), pp. 101–108.

Schlimm, Dirk (2000): Richard Dedekind: Axiomatic Foundations of Mathematics, M.A. thesis, Carnegie Mellon University, Pittsburgh; with selections from Dedekind's Nachlass.

____ (2009): "On the Creative Role of Axiomatics: The Discovery of Lattices by Schröder, Dedekind, Birkhoff, and Others", Synthese (online first)

Sieg, W. & Schlimm, D. (2005): “Dedekind's Analysis of Number: System and Axioms”, Synthese 147, 121–170.

Sinaceur, H.B. (2008): Richard Dedekind: La création des nombres, Vrin: Paris

Sinaceur, M.A. (1974): “L'infini et les nombres – Commentaires de R. Dedekind à ‘Zahlen’ – La correspondance avec Keferstein”, Revue d'histoire des sciences 27, 251–278.

____ (1979): “La méthode mathématique de Dedekind”, Revue d'histoire des sciences 32, 107–142.

____ (1990): “Dedekind et le programme de Riemann”, Revue d'histoire des sciences 43, 107–142.

Stein, Howard (1988): “Logos, Logic, and Logistiké: Some Philosophical Remarks on Nineteenth-Century Transformations of Mathematics”, in History and Philosophy of Modern Mathematics, W. Aspray & P. Kitcher, eds., University of Minnesota Press, pp. 238–259.

____ (1990): “Eudoxos and Dedekind: On the Ancient Greek Theory of Ratios and its Relation to Modern Mathematics”, Synthese 84, 163–211.

____ (1998): “Dedekind, Julius Wilhelm Richard”, in Routledge Encyclopedia of Philosophy, Vol. 2, Routledge: London/New York, pp. 840–842.

Stillwell, John (1996): Editor's introduction to Dedekind (1996a), pp. 1–50.

____ (2000): Mathematics and its History, Springer: New York, second edition (revised); especially Chapter 21, “Algebraic Number Theory”, pp. 404–430.

Tait, W.W. (1996): “Frege versus Cantor and Dedekind: On the Concept of Number”, in Frege: Importance and Legacy, M. Schirn, ed., de Gruyter: Berlin, pp. 70–113.

Tappenden, Jamie (1995): “Geometry and Generality in Frege's Philosophy of Arithmetic”, Synthese 102, 319–361.

____ (2005a): “The Caesar Problem in its Historical Context: Mathematical Background”, Dialectica 59, 1–28.

____ (2005b): “Proof Style and Understanding in Mathematics I: Visualization, Unification, and Axiom Choice”, in Visualization, Explanation and Reasoning Styles in Mathematics, P. Mancosu et al., eds., Springer: New York, pp. 147–214.

____ (2006): “The Riemannian Background of Frege's Philosophy”, in The Architecture of Modern Mathematics, J. Ferreirós & J. Grey, eds., Oxford University Press, pp. 97–132.

Van Heijenoort, Jean, ed. (1967): From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press.

Wilson, Mark (1992): “Frege: The Royal Road from Geometry”, Noûs 26, 149–180.

Wussing, Hans (1984): The Genesis of the Abstract Group Concept, MIT Press; especially Part III, Chapter 4, “The shaping and axiomatization of the abstract group concept”, pp. 230–254; reprinted by Dover: New York, 2007; originally published in German, 1969.

Yap, Audrey (2009a): “Logical Structuralism and Benacerraf's Problem”, Synthese 171, 157-173.

____ (2009b): "Predicativity and Structuralism in Dedekind's Construction of the Reals", Erkenntnis 71, 151-173.