Skip to main content
SpringerLink
Log in

Geometry and generality in Frege's philosophy of arithmetic

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege'sGrundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes ofGrundlagen are developed: the relationship Frege envisions between arithmetic and geometry and the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

Works of Frege: (Date of publication (composition for unpublished writings) follows the references)

  • ‘On the Aim of the “Conceptual Notation”’ in Bynum (1972) (1882).

  • Begriffschrift, a Formula Language, Modeled on that of Arithmetic, For Pure Thought, Stephan Bauer-Mengelberg, trans. inFrom Frege to Godel, van Heijenoort, J. (ed.), Harvard University Press, Cambridge, 1967 (1879).

    Google Scholar 

  • The Basic Laws of Arithmetic: Exposition of the System, Furth, M. trans., University of California Press, Berkeley, 1964 (1893).

  • ‘Boole's Logical Calculus and the Concept-Script’ inPosthumous Writings (1880/81).

  • ‘Critical Elucidation of some Points’, E. Schröder,Vorlesungen über die Algebra der Logik” (1895).

  • ‘On Concept and Object’, inCollected Papers (1893).

  • Philosophical and Mathematical Correspondence, Gabriel, G., Hermes, H., Kambartel, F., Thiel, C. and Verhaart, A. Abridged from the German edition by McGuinness, B. Translated by Kaal, H., University of Chicago Press, Chicago, 1980.

    Google Scholar 

  • ‘Comments on Sense and Meaning’, inPosthumous Writings (1892–1895).

  • The Foundations of Arithmetic, J. L. Austin, trans. 2nd rev. ed. Northwestern University Press, Evanston, 1980 (1884).

  • ‘Function and Concept’ inCollected Papers (1891).

  • ‘On the Foundations of Geometry: First Series’, inCollected Papers (1903).

  • ‘On the Foundations of Geometry: Second Series’, inCollected Papers (1906).

  • ‘On Formal Theories of Arithmetic’, inCollected Papers (1885).

  • ‘On a Geometrical Representation of Imaginary Forms in the Plane’, inCollected Papers (1873).

  • ‘Logic’ (second of two essays with that title) inPosthumo us Writings (1897).

  • ‘Logic in Mathematics’ inPosthumous Writings (1914).

  • ‘Lecture on the Geometry of Pairs of Points in the Plane’,Collected Papers (1883).

  • ‘On the Law of Inertia’, inCollected Papers (1891).

  • ‘Lecture on a Way of Conceiving the Shape of a Triangle as a Complex Quantity’, inCollected Papers (1878).

  • ‘Methods of Calculation Based on an Extension of the Concept of Magnitude’, inCollected Papers (1874).

  • ‘Notes for Ludwig Darmsteader’, inPosthumous Writings (1919).

  • ‘On Mr. Peano's Conceptual Notation and My Own’, inCollected Papers (1897).

  • Review of H. Cohen,Das Princip der Infinitesimal-Methode und Seine Geschichte, in Collected Papers (1885).

  • Review of Gall and Winter:Die Analytische Geometrie des Punktes und der Geraden und ihre Anwendung auf Aufgaben inCollected Papers (1877).

  • ‘On the Scientific Justification of a Conceptual Notation’ (Bynum, T. trans.) Reprinted in Bynum [1972] (1882).

  • ‘On Sense and Meaning’ inCollected Papers (1892).

  • ‘Thoughts’ inCollected Papers (1918).

  • ‘What is a Function?’ inCollected Papers (1904).

Collections referred to above:

  • Collected Papers on Mathematics, Logic and Philosophy (1984) McGuinness, B. (ed.) Basil Blackwell, Oxford.

    Google Scholar 

  • Posthumous Writings (1979) Hermes, H. Kambartel, F. and Kaulbach, F. (eds.) Basil Blackwell, Oxford.

    Google Scholar 

Other References:

  • Artin, E.: 1957,Geometric Algebra, Interscience, New York.

    Google Scholar 

  • Baker, G. and Hacker, P.: 1984,Frege: Logical Excavations, Oxford University Press, New York.

    Google Scholar 

  • Ball, R.: 1889, ‘On the Theory of Content’,Transactions of the Royal Irish Academy, vol. 29, pp. 123–82.

    Google Scholar 

  • Benacerraf, P.: 1981, ‘Frege: The Last Logicist’, in P. French, T. Uehling and H. Wettstein (eds.),Midwest Studies in Philosophy, vol. 6, University of Minnesota Press, Minneapolis.

    Google Scholar 

  • Biermann, K: 1988,Die Mathematik Und Ihre Dozenten an Der Berliner Universität 1810–1933, Academie-Verlag, Berlin.

    Google Scholar 

  • Birkhoff, G.: 1973,A Source Book in Classical Analysis, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Birkhoff, G. and M. Bennett: 1988, ‘Felix Klein and his “Erlanger Programm”’, in W. Aspray and P. Kitcher,History and Philosophy of Modern Mathematics, University of Minnesota Press, Minneapolis, pp. 145–76.

    Google Scholar 

  • Bottozini, U.: 1986,The Higher Calculus: A History of Real and Complex Numbers from Euler to Weierstrass, Springer, New York.

    Google Scholar 

  • Boyer, C.: 1956,A History of Analytic Geometry, Scholar's Bookshelf, Princeton Junction, NJ.

    Google Scholar 

  • Brandom, B.: 1986, ‘Frege's Technical Concepts’, in L. Haaparanta and J. Hintikka (eds.),Frege Synthesised, D. Reidel, Dordrecht.

    Google Scholar 

  • Brill, A. and M. Nöther: 1874, ‘Über die Algebraischen Functionen und ihre Anwendung in der Geometrie’,Mathematische Annalen 7, 269–312.

    Google Scholar 

  • Brill, A. and M. Nöther: 1894, ‘Die Entwicklung der Theorie der Algebraischen Functionen’,Jahresbericht der Deutschen Mathematiker Vereinigung 3, 107–566.

    Google Scholar 

  • Burgess, J.: 1984, ‘Review of Wright (1983)’,Philosophical Review 93, 638–40.

    Google Scholar 

  • Burgess, J.: 1993, ‘Hintikka et Sandu in re Arbitrary Functions’,Philosophica Mathematica, pp. 50–65.

  • Bynum, T.: 1972, ‘On the Life and Work of Gottlob Frege’, in T. Bynum (ed.), trans., Clarendon, Oxford, pp. 1–54.

    Google Scholar 

  • Cajori, F.: 1985,A History of Mathematics, 4th rev. ed. (Reissue of a volume first published 1893), Chelsea Publishing Co., New York.

    Google Scholar 

  • Cayley, A.: 1872, ‘On the Non-Euclidean Geometry’,Mathematischen Annalen,V, 630–4.

    Google Scholar 

  • Cayley, A.: 1889, ‘Notes to “Sixth Memoir of Quantics”’,Collected Papers, vol. II, pp. 603–6.

    Google Scholar 

  • Clebsch, A.: 1872, ‘Notice Sur les Travaux de Jules Plücker’, P. Mansion (trans.),Bullettino di Bibliografia e di Storia delle Scienze Matematische e Fisiche, 5, pp. 183–212.

    Google Scholar 

  • Clebsch, A. and F. Lindemann: 1876,Vorlesungen Über Geometrie (lectures by Clebsch transcribed and edited by Lindemann) (vol. 1) Leipzig.

  • Chevalley, C.: 1951,Introduction to the Theory of Algebraic Functions of One Variable, American Mathematical Society, New York.

    Google Scholar 

  • Coolidge, J.: 1924,The Geometry of the Complex Domain, Clarendon Press, Oxford.

    Google Scholar 

  • Coolidge, J.: 1940,A History of Geometrical Methods, Clarendon Press, Oxford.

    Google Scholar 

  • Coolidge, J.: 1945,A History of the Conic Sections and Quartic Surfaces, Clarendon Press, Oxford.

    Google Scholar 

  • Coxeter, H.: 1965, ‘Geometry’, in T. Saaty (ed.),Lectures in Modern Mathematics, Wiley, New York, pp. 58–94.

    Google Scholar 

  • Coxeter, H.: 1992,The Real Projective Plane (3rd ed.), Springer, New York.

    Google Scholar 

  • Crowe, M.: 1967,A History of Vector Analysis: The Evolution of the Idea of A Vectorial System, Notre Dame University Press, Notre Dame.

    Google Scholar 

  • Currie, G.: 1982,Frege: An Introduction to his Philosophy, Barnes and Noble, Totowa, NJ.

    Google Scholar 

  • Daston, L.: 1986, ‘The Physicalist Tradition in Early Nineteenth Century French Geometry’,Studies in the History and Philosophy of Science 17, 269–95.

    Google Scholar 

  • Dedekind, R.: 1963,Essays on the Theory of Numbers, W. Beman, Trans. Dover, New York.

    Google Scholar 

  • Dedekind, R. and H. Weber: 1882, ‘Theorie der Algebraischen Funktionen einer Veränderlichen’,Journal für Mathematik 92 (in Dedekind'sGessamelte Werke I, 238–350).

  • Demopoulos, W.: 1994, ‘Frege and the Rigorization of Analysis’,Journal of Philosophical Logic 23, 225–45.

    Google Scholar 

  • Dieudonné, J.: 1985,History of Algebraic Geometry, J. Sally (trans.), Wadsworth Books, Monterey.

    Google Scholar 

  • Dummett, M.: 1981,The Interpretation of Frege's Philosophy, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Dummett, M.: 1991a,Frege: Philosophy of Mathematics, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Dummett, M.: 1991b, ‘Frege and the Paradox of Analysis’, inFrege and other Philosophers, Oxford University Press, Oxford.

    Google Scholar 

  • Dummett, M.: 1992, ‘Review of Weiner (1990)’,Journal of Symbolic Logic.

  • Etcheverria, J.: 1979, ‘L'Analyse Geometrique de Grassmann et ses Rapports avec la characteristique geometrique de Leibnitz’,Studia Leibnitiana 11, 223–73.

    Google Scholar 

  • Field, H.: 1984, ‘Is Mathematical Knowledge just Logical Knowledge?’, reprinted in Field (1989), pp. 79–124.

  • Field, H.: 1989,Realism, Mathematics and Modality, Basil Blackwell, Oxford.

    Google Scholar 

  • Friedman, M.: 1992,Kant and the Exact Sciences, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Freudenthal, H.: 1981, ‘The Impact of von Staudt's Foundations of Geometry’, in P. Plaumann and K. Strambach (eds.),Geometry — von Staudt's Point of View, D. Reidel, Dordrecht.

    Google Scholar 

  • Fulton, W.: 1969,Algebraic Curves, Benjamin and Cummings Publ. Co., Reading, MA.

    Google Scholar 

  • Grattan-Guinness, I.: 1970,The Development of the Foundations of Analysis from Euler to Riemann, MIT Press, Cambridge, MA.

    Google Scholar 

  • Grattan-Guinness, I.: 1975, ‘Preliminary Notes on the Historical Significance of Quantification and of the Axioms of Choice in the Development of Mathematical Analysis’,Historia Mathematica 2, 475–88.

    Google Scholar 

  • Gray, J.: 1984, ‘The Riemann-Roch Theorem: Acceptance and Rejection of Geometric Ideas’,Asterisque N.

  • Gray, J.: 1989, ‘Algebraic Geometry in the late Nineteenth Century’, in D. Rowe and J. McCleary (eds.),The History of Modern Mathematics, vol. I, Academic Press, Boston, pp. 361–85.

    Google Scholar 

  • Gray, J.: 1992, ‘The Nineteenth Century Revolution in Mathematical Ontology’, inRevolutions in Mathematics. D. Gillies (ed.), Clarendon, Oxford.

    Google Scholar 

  • Grossmann, R.: 1969,Reflections on Frege's Philosophy, Northwestern University Press, Evanston.

    Google Scholar 

  • Hankel, H.: 1867,Vorlesungen Über die Complexen Zahlen und Ihren Functionen, vol. 1,Theorie der Complexen Zahlensysteme, Leipzig.

    Google Scholar 

  • Hankel, H.: 1870,Unendlich oft Oscillirende und Unstetige Functionen, Tübingen.

  • Hawkins, T.: 1989, ‘Jacobi and the Birth of Lie's Theory of Groups’, inArchive for the History of the Exact Sciences, pp. 187–276.

  • Hawkins, T.: 1989b, ‘Line Geometry, Differential Equations, and the Birth of Lie's Theory of Groups’, in D. Rowe and J. McCleary (eds.),The History of Modern Mathematics, vol. I, Academic Press, Boston, pp. 275–327.

    Google Scholar 

  • Heck, R.: 1993, Critical Notice of Dummett (1991a),Philosophical Quarterly, pp. 223–33.

  • Heck, R. and Stanley, J.: 1993, ‘Reply to Hintikka and Sandu: Frege and Second Order Logic’,Journal of Philosophy, pp. 416–24.

  • Hellman, G.: 1989,Mathematics Without Numbers, Oxford University Press, Oxford.

    Google Scholar 

  • Herstein, I.: 1975,Topics in Algebra, 2nd ed., Wiley and Sons, New York.

    Google Scholar 

  • Hintikka, J. and G. Sandu: 1992, ‘The Skeleton in Frege's Cupboard: The Standard vs. Nonstandard Distinction’,Journal of Philosophy, 290–315.

  • Hodes, H.: 1985, ‘Logicism and the Ontological Committments of Arithmetic’,Journal of Philosophy 81, 123–49.

    Google Scholar 

  • Horty, J.: 1986, ‘Some Aspects of Meaning in Non-contingent Language’, Ph.D. thesis, University of Pittsburgh.

  • Horty, J.: 199?, ‘Frege on the Psychological Significance of Definitions’, forthcoming.

  • Kant, I.: 1965,Critique of Pure Reason (Smith, N. Trans.), St. Martin's Press, New York.

    Google Scholar 

  • Katz, J.: 1992, ‘The New Intensionalism’,Mind 101, 689–719.

    Google Scholar 

  • Kirwan, F.: 1992,Complex Algebraic Curves, Cambridge University Press, Cambridge.

    Google Scholar 

  • Kitcher, P.: 1979, ‘Frege's Epistemology’,Philosophical Review 88, 235–62.

    Google Scholar 

  • Kitcher, P.: 1984,The Nature of Mathematical Knowledge, Oxford University Press, Oxford.

    Google Scholar 

  • Kitcher, P.: 1986, ‘Frege, Dedekind, and the Philosophy of Mathematics’, in L. Haaparanta and J. Hintikka (eds.),Frege Synthesised, D. Reidel, Dordrecht.

    Google Scholar 

  • Klein, F.: 1871, ‘Ueber die Sogenannte Nicht-Euklidische Geometrie’,Mathematische Annalen,IV, 573–625.

    Google Scholar 

  • Klein, F.: 1873, ‘Ueber die Sogennannte Nicht-Euklidische Geometrie’,Mathematische Annalen VI, 112–45.

    Google Scholar 

  • Klein, F.: 1893, ‘A Comparative Review of Recent Researches in Geometry (Programme on Entering the Philosophical Faculty and the Senate of the University of Erlangen in 1872)’, (also called ‘The Erlanger Programm’), M. Haskell (trans.),Bulletin of the New York Mathematical Society, June–July, pp. 215–49.

  • Klein, F.: 1894,The Evanston Colloquium, Macmillan and Co., New York.

    Google Scholar 

  • Klein, F.: 1925,The Development of Mathematics in the Nineteenth Century, M. Ackermann (trans.), Math. Sci. Press, Brookline. (No date, originally published 1925).

    Google Scholar 

  • Kline, M.: 1972,Mathematical Thought From Ancient to Modern Times, Oxford University Press, Oxford.

    Google Scholar 

  • Kratzsch, I.: 1979, ‘Materialien zu Leben und Wirken Freges aus dem Besitz der Universitats-bibliotek Jena’, inBegriffsschrift — Janaer Frege Konferenz, Fr. Schiller Universitat, Jena, pp. 534–5.

    Google Scholar 

  • Kreisel, G.: 1971, ‘Survey of Proof Theory II’, in J. Fensted (ed.),Second Scandinavian Logic Symposium, North-Holland, Amsterdam.

    Google Scholar 

  • Lambek, J. and P. Scott: 1988,Introduction to Higher Order Categorical Logic, Cambridge University Press, Cambridge.

    Google Scholar 

  • Lang, S.: 1982,Introduction to Algebraic and Abelian Functions, 2nd ed., Springer, New York.

    Google Scholar 

  • Lewis, A. C.: 1977, ‘H. Grasmann's 1844Ausdehnungslehre and Schleiermacher'sDialectik’,Annals of Science 34, 103–62.

    Google Scholar 

  • Lie, S.: 1922,Gesammelte Abhandlungen, Teubner, Leipzig.

    Google Scholar 

  • Manders, K.: 1987, ‘Logic and Conceptual Relationships in Mathematics’, inLogic Colloquium '85, Elsevier, Amsterdam.

    Google Scholar 

  • Nagel, E.: 1979, ‘The Foundation of Modern Conceptions of Formal Logic in the Development of Geometry’, inTeleology Revisited and Other Essays in the Philosophy and History of Science, Columbia University Press, New York, (originally published in 1939).

    Google Scholar 

  • Nowak, G.: 1989, ‘Riemann'sHabilitationsvortrag and the Synthetica Priori Status of Geometry’, in D. Rowe and J. McCleary (eds.),The History of Modern Mathematics, vol. I, Academic Press, Boston, pp. 17–47.

    Google Scholar 

  • Otte, M.: 1989, ‘The Ideas of Hermann Grassmann in the Context of the Mathematical and Philosophical Tradition since Leibniz’,Historia Mathematica 16, 1–35.

    Google Scholar 

  • Parshall, K.: 1989, ‘Toward a History of Nineteenth Century Invariant Theory’, in D. Rowe and J. McCleary (eds.),The History of Modern Mathematics, vol. I, Academic Press, Boston, pp. 157–206.

    Google Scholar 

  • Picardi, E.: 1988, ‘Frege on Definition and Logical Proof’, in C. Cellucci and G. Sambin (eds.),Temi e Prospettive della Logica e della Filosofia della Scienza Contemporanee, vol. I, Bologna, pp. 227–30.

  • Plücker, J.: 1865, ‘On a New Geometry of Space’,Philosophical Transactions of the Royal Society of London, pp. 725–91 (1868).

  • Plücker, J.: 1868,Neue Geometrie des Raumes gegrundet auf die Betrachtung der geraden Linie als Raumelement, vol. 1, A. Clebsch (ed.), vol. 2, F. Klein (ed.), Leipzig.

  • Portnoy, E.: 1982, ‘Riemann's Contribution to Differential Geometry’,Historia Mathematica 9, 1–18.

    Google Scholar 

  • Proust, J.: 1989,Questions of Form: Logic and the Analytic Proposition from Kant to Carnap, A. Brenner (trans.), University of Minnesota Press, Minneapolis.

    Google Scholar 

  • Prawitz, D.: 1971, ‘Ideas and Results in Proof Theory’, in J. Fensted (ed.),Second Scandinavian Logic Symposium, North-Holland, Amsterdam.

    Google Scholar 

  • Ricketts, T.: 1986, ‘Generality, Meaning and Sense in Frege’,Pacific Philosophical Quarterly, p. 172–95.

  • Ricketts, T.: 1986, ‘Objectivity and Objecthood: Frege's Metaphysics of Judgement’, in L. Haaparanta and J. Hintikka (eds.),Frege Synthesised, D. Reidel, Dordrecht.

    Google Scholar 

  • Rowe, D.: 1989a, ‘Klein, Hilbert, and the Göttingen Mathematical Tradition’,Osiris 2nd Ser., pp. 186–213.

  • Rowe, D.: 1989b, ‘The Early Geometrical Works of Sophus Lie and Felix Klein’, in D. Rowe and J. McCleary (eds.),The History of Modern Mathematics, vol. I, Academic Press, Boston, pp. 209–73.

    Google Scholar 

  • Russell, B.: 1956,An Essay on the Foundations of Geometry (first published 1897), Dover, New York.

    Google Scholar 

  • Scott, C.: 1900, ‘On von Staudt'sGeometrie der Lage’, Mathematical Gazette.

  • Sluga, H.: 1980,Gottlob Frege, Routledge and Kegan Paul, London.

    Google Scholar 

  • Sluga, H.: 1984, ‘Frege: the Early Years’, in R. Rorty (ed.),Philosophy in History, Cambridge University Press, Cambridge.

    Google Scholar 

  • Sluga, H.: 1987, ‘Frege Against the Booleans’,Notre Dame Journal of Formal Logic 28.

  • Smith, D.: 1959,A Source Book in Mathematics, Dover, Mineola, NY.

    Google Scholar 

  • Stein, H.: 1988, ‘Logos, Logic and Logistike’, in W. Aspray and P. Kitcher (eds.),History and Philosophy of Modern Mathematics, University of Minnesota Press, Minneapolis, pp. 145–76.

    Google Scholar 

  • Stolz, O.: 1871, ‘Die Geometrische Bedeutung der Komplexen Elemente’,Mathematische Annalen, vol. iv.

  • Tappenden, J.: 1995?, ‘Extending Knowledge and “Fruitful Concepts”: Fregean Themes in the Foundations of Mathematics’, forthcoming inNoûs.

  • Tobies, R. and D. Rowe (eds.): 1989,Korrespondenz Felix Klein — Adolph Mayer, Teubner, Leipzig.

    Google Scholar 

  • Torretti, R.: 1984,The Philosophy of Geometry from Riemann to Poincaré, D. Reidel, Dordrecht.

    Google Scholar 

  • Van der Waerden, B.: 1985,A History of Algebra from al-Khwarizmi to Emmy Noether, Springer, Berlin.

    Google Scholar 

  • Van der Waerden, B.: 1991,Algebra (vol. II), J. Schulenberger (trans.), Springer, New York.

    Google Scholar 

  • van Heijenoort, J.: 1967, ‘Logic as Calculus and Logic as Language’,Synthese 17.

  • von Staudt, G.: 1847,Die Geometrie der Lage, Erlangen.

  • von Staudt, G.: 1856,Beiträge zur Geometrie der Lage, Nürnberg.

  • Wagner, S.: 1992, ‘Logicism’, in M. Detlefsen (ed.),Proofs and Knowledge in Mathematics, Routledge, London, pp. 65–110.

    Google Scholar 

  • Wang, H.: 1957, ‘The Axiomatisation of Arithmetic’,Journal of Symbolic Logic 22, 145–59.

    Google Scholar 

  • Weiner, J.: 1984, ‘The Philosopher Behind the Last Logicist,’ inFrege: Tradition and Influence, Blackwell, Oxford.

    Google Scholar 

  • Weiner, J.: 1990,Frege in Perspective, Cornell University Press, Ithaca.

    Google Scholar 

  • Wilson, M.: 1992, ‘Frege: The Royal Road from Geometry’,Noûs 26(2), 149–80.

    Google Scholar 

  • Wright, C.: 1983,Frege's Conception of Numbers as Objects, Aberdeen University Press, Aberdeen.

    Google Scholar 

  • Wussing, H.: 1984,The Genesis of the Abstract Group Concept, A. Schenitzer (trans.), MIT Press, Cambridge, MA.

    Google Scholar 

  • Youschkevich, A. P.: 1976, ‘The Concept of a Function up to the Middle of the 19th Century’,Archive for the History of the Exact Sciences 7, 37–85.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, University of Pittsburgh, 15260, Pittsburgh, PA

    Jamie Tappenden

Authors
  1. Jamie Tappenden
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

I am indebted to many people for helpful conversations and comments on this paper, notably Stephen Glaister, Phil Kremer, Madeline Larson, John McDowell, Jim Conant, Charles Chihara, William Craig, Jan Alnes, Joan Weiner, Leon Henkin, Paul Benacerraf, Juliet Floyd, Bill Demopoulos, Jose Ferreiros, Tom Hawkins, Gideon Rosen. Two superb papers on Frege — Bill Demopoulos' (1994) and Mark Wilson (1992) played a significant role in the early stages of composition. Special thanks are due to Hans Sluga, Mark Wilson, Bob Brandom, and Ken Manders for comments, encouragement, information and advice.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tappenden, J. Geometry and generality in Frege's philosophy of arithmetic. Synthese 102, 319–361 (1995). https://doi.org/10.1007/BF01064120

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01064120

Keywords

Search

Navigation