Symbolic Mathematics and the Intellect Militant: On Modern Philosophy's Revolutionary Spirit

Journal of the History of Ideas

Volumn 57, Issue 2, 1996, Pages 233-252

  Page, Carl ^a  

^a NONE

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EID: 0346342781     PISSN: 00225037     EISSN: None     Source Type: Journal    
DOI: 10.2307/3654097     Document Type: Article

References (57)

1. Some of these questions are taken up in Richard Rorty, J. B. Schneewind, and Quentin Skinner (eds.), Philosophy in History (Cambridge, 1984); and Jorge J. E. Gracia, Philosophy and Its History: Issues in Philosophical Historiography (Albany, 1992). With respect to modernity in general see Reinhart Koselleck, Futures Past: On the Semantics of Historical Time, tr. Keith Tribe (Cambridge, Mass., 1985); Hans Blumenberg, The Legitimacy of the Modern Age, tr. Robert M. Wallace (Cambridge, Mass., 1983), Robert Pippin, "Blumenberg and the Modernity Problem," Review of Metaphysics, 40 (1987), 535-57, and Modernism as a Philosophical Problem: On the Dissatisfactions of European High Culture (Cambridge, Mass., 1991).
2. Some of these questions are taken up in Richard Rorty, J. B. Schneewind, and Quentin Skinner (eds.), Philosophy in History (Cambridge, 1984); and Jorge J. E. Gracia, Philosophy and Its History: Issues in Philosophical Historiography (Albany, 1992). With respect to modernity in general see Reinhart Koselleck, Futures Past: On the Semantics of Historical Time, tr. Keith Tribe (Cambridge, Mass., 1985); Hans Blumenberg, The Legitimacy of the Modern Age, tr. Robert M. Wallace (Cambridge, Mass., 1983), Robert Pippin, "Blumenberg and the Modernity Problem," Review of Metaphysics, 40 (1987), 535-57, and Modernism as a Philosophical Problem: On the Dissatisfactions of European High Culture (Cambridge, Mass., 1991).
3. Some of these questions are taken up in Richard Rorty, J. B. Schneewind, and Quentin Skinner (eds.), Philosophy in History (Cambridge, 1984); and Jorge J. E. Gracia, Philosophy and Its History: Issues in Philosophical Historiography (Albany, 1992). With respect to modernity in general see Reinhart Koselleck, Futures Past: On the Semantics of Historical Time, tr. Keith Tribe (Cambridge, Mass., 1985); Hans Blumenberg, The Legitimacy of the Modern Age, tr. Robert M. Wallace (Cambridge, Mass., 1983), Robert Pippin, "Blumenberg and the Modernity Problem," Review of Metaphysics, 40 (1987), 535-57, and Modernism as a Philosophical Problem: On the Dissatisfactions of European High Culture (Cambridge, Mass., 1991).
4. Some of these questions are taken up in Richard Rorty, J. B. Schneewind, and Quentin Skinner (eds.), Philosophy in History (Cambridge, 1984); and Jorge J. E. Gracia, Philosophy and Its History: Issues in Philosophical Historiography (Albany, 1992). With respect to modernity in general see Reinhart Koselleck, Futures Past: On the Semantics of Historical Time, tr. Keith Tribe (Cambridge, Mass., 1985); Hans Blumenberg, The Legitimacy of the Modern Age, tr. Robert M. Wallace (Cambridge, Mass., 1983), Robert Pippin, "Blumenberg and the Modernity Problem," Review of Metaphysics, 40 (1987), 535-57, and Modernism as a Philosophical Problem: On the Dissatisfactions of European High Culture (Cambridge, Mass., 1991).
5. Some of these questions are taken up in Richard Rorty, J. B. Schneewind, and Quentin Skinner (eds.), Philosophy in History (Cambridge, 1984); and Jorge J. E. Gracia, Philosophy and Its History: Issues in Philosophical Historiography (Albany, 1992). With respect to modernity in general see Reinhart Koselleck, Futures Past: On the Semantics of Historical Time, tr. Keith Tribe (Cambridge, Mass., 1985); Hans Blumenberg, The Legitimacy of the Modern Age, tr. Robert M. Wallace (Cambridge, Mass., 1983), Robert Pippin, "Blumenberg and the Modernity Problem," Review of Metaphysics, 40 (1987), 535-57, and Modernism as a Philosophical Problem: On the Dissatisfactions of European High Culture (Cambridge, Mass., 1991).
6. Some of these questions are taken up in Richard Rorty, J. B. Schneewind, and Quentin Skinner (eds.), Philosophy in History (Cambridge, 1984); and Jorge J. E. Gracia, Philosophy and Its History: Issues in Philosophical Historiography (Albany, 1992). With respect to modernity in general see Reinhart Koselleck, Futures Past: On the Semantics of Historical Time, tr. Keith Tribe (Cambridge, Mass., 1985); Hans Blumenberg, The Legitimacy of the Modern Age, tr. Robert M. Wallace (Cambridge, Mass., 1983), Robert Pippin, "Blumenberg and the Modernity Problem," Review of Metaphysics, 40 (1987), 535-57, and Modernism as a Philosophical Problem: On the Dissatisfactions of European High Culture (Cambridge, Mass., 1991).
7. For the larger context see Carl Page, Philosophical Historicism and the Betrayal of First Philosophy (University Park, Penn., 1995).
8. René Descartes, The Philosophical Writings of Descartes, tr. John Cottingham, Robert Stoothoff, and Dugald Murdoch (2 vols.; Cambridge, 1985), II, 12 (citations will be given in the text by volume and page).
9. Immanuel Kant, Critique of Pure Reason, tr. Norman Kemp Smith (New York, 1965), 25 (Bxx*ii) (citations in the text by standard edition and B-edition pagination).
10. See Carl Page, "From Rationalism to Historicism: the Devolution of Cartesian Subjectivity," St. John's Review, 42 (1994), 95-111.
11. See Alexandre Koyré, Descartes und die Scholastik (Bonn, 1923); Etiènne Gilson, Etudes sur le rôle de la pensée médiévale dans la formation du système Cartésien (Paris, 1951); Hiram Caton, The Origin of Subjectivity: An Essay on Descartes (New Haven, 1973); and Dalia Judovitz, Subjectivity and Representation in Descartes: The Origins of Modernity (Cambridge, 1988).
12. See Alexandre Koyré, Descartes und die Scholastik (Bonn, 1923); Etiènne Gilson, Etudes sur le rôle de la pensée médiévale dans la formation du système Cartésien (Paris, 1951); Hiram Caton, The Origin of Subjectivity: An Essay on Descartes (New Haven, 1973); and Dalia Judovitz, Subjectivity and Representation in Descartes: The Origins of Modernity (Cambridge, 1988).
13. See Alexandre Koyré, Descartes und die Scholastik (Bonn, 1923); Etiènne Gilson, Etudes sur le rôle de la pensée médiévale dans la formation du système Cartésien (Paris, 1951); Hiram Caton, The Origin of Subjectivity: An Essay on Descartes (New Haven, 1973); and Dalia Judovitz, Subjectivity and Representation in Descartes: The Origins of Modernity (Cambridge, 1988).
14. See Alexandre Koyré, Descartes und die Scholastik (Bonn, 1923); Etiènne Gilson, Etudes sur le rôle de la pensée médiévale dans la formation du système Cartésien (Paris, 1951); Hiram Caton, The Origin of Subjectivity: An Essay on Descartes (New Haven, 1973); and Dalia Judovitz, Subjectivity and Representation in Descartes: The Origins of Modernity (Cambridge, 1988).
15. David Lachterman, "Descartes and the Philosophy of History," Independent Journal of Philosophy, 4 (1983), 31-46; Jean-Luc Nancy, "Larvatus Pro Deo," Glyph, 2 (1977), 14-37.
16. David Lachterman, "Descartes and the Philosophy of History," Independent Journal of Philosophy, 4 (1983), 31-46; Jean-Luc Nancy, "Larvatus Pro Deo," Glyph, 2 (1977), 14-37.
17. Translations of the letters are from Descartes: Philosophical Letters, tr. Anthony Kenny (Oxford, 1970).
18. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
19. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
20. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
21. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
22. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
23. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
24. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
25. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
26. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
27. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
28. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
29. Martin Heidegger, What is a Thing? tr. W. B. Barton Jr. and Vera Deutsch (Lanham, 1985), henceforth WT; Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy, tr. David Carr (Evanston, 1970); John Herman Randall, Jr., The Career of Philosophy from the Middle Ages to the Enlightenment (New York, 1962); Ulrich Hommes, "Sicherheit als Maß der Freiheit? Descartes Idee der Mathesis Universalis und die praktische Philosophie der Neuzeit," C. Fabro (ed.) Gegenwart und Tradition: Festschrift für Bernhard Lakebrink (Freiburg, 1969), 105-24; Caton, The Origin of Subjectivity; Jean-Luc Marion, L'ontologie grise de Descartes (Paris, 1975); Leo Strauss and Karl Löwith, "Correspondence concerning Modernity," Independent Journal of Philosophy, 4 (1983), 105-19; Bernard Flynn, "Descartes and the Ontology of Subjectivity," Man and World, 16 (1983), 3-23; Walter Soffer, From Science to Subjectivity: An Interpretation of Descartes' Meditations (New York, 1987); Tom Sorrell, Descartes (Oxford, 1987); Judovitz, Subjectivity and Representation in Descartes; R. Thomas Harris, "Mathematics, Descartes, and the Rise of Modernity," Philosophia Mathematical, 2nd Series, 3 (1988), 1-20.
30. Lewis J. Beck, The Method of Descartes: A Study of the Regulae (Oxford, 1952); Frederick Van De Pitte, "Descartes' Mathesis Universalis," Archiv für Geschichte der Philosophic, 61 (1979), 154-74; Pamela Kraus, "From Universal Mathematics to Universal Method: Descartes' 'Turn' in Rule IV of the Regulae," Journal of the History of Philosophy, 21 (1983), 159-74.
31. Lewis J. Beck, The Method of Descartes: A Study of the Regulae (Oxford, 1952); Frederick Van De Pitte, "Descartes' Mathesis Universalis," Archiv für Geschichte der Philosophic, 61 (1979), 154-74; Pamela Kraus, "From Universal Mathematics to Universal Method: Descartes' 'Turn' in Rule IV of the Regulae," Journal of the History of Philosophy, 21 (1983), 159-74.
32. Lewis J. Beck, The Method of Descartes: A Study of the Regulae (Oxford, 1952); Frederick Van De Pitte, "Descartes' Mathesis Universalis," Archiv für Geschichte der Philosophic, 61 (1979), 154-74; Pamela Kraus, "From Universal Mathematics to Universal Method: Descartes' 'Turn' in Rule IV of the Regulae," Journal of the History of Philosophy, 21 (1983), 159-74.
33. Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, tr. Eva Brann (Cambridge, Mass., 1968), David R. Lachterman, The Ethics of Geometry: A Genealogy of Modernity (New York, 1989). See also A. G. Holland, "Shifting the Foundations: Descartes' Transformation of Ancient Geometry," Historia Mathematica, 3 (1976), 21-49; and Jacob Klein: Lectures and Essays, ed. Robert B. Williamson and Elliot Zuckerman (Annapolis, 1985). The question of how ontological reassessments count as paradigm shifts in mathematical science is addressed in Donald Gillies (ed.), Revolutions in Mathematics (Oxford, 1992). While this volume principally deals with how to assign historical meaning to the history of mathematics (including an excellent bibliography), the essays by Caroline Dunmore, "Metalevel Revolutions in Mathematics" and Jeremy Gray, "The Nineteenth-century Revolution in Mathematical Ontology" are the most congenial to the eidetic orientation of Klein and Lachterman.
34. Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, tr. Eva Brann (Cambridge, Mass., 1968), David R. Lachterman, The Ethics of Geometry: A Genealogy of Modernity (New York, 1989). See also A. G. Holland, "Shifting the Foundations: Descartes' Transformation of Ancient Geometry," Historia Mathematica, 3 (1976), 21-49; and Jacob Klein: Lectures and Essays, ed. Robert B. Williamson and Elliot Zuckerman (Annapolis, 1985). The question of how ontological reassessments count as paradigm shifts in mathematical science is addressed in Donald Gillies (ed.), Revolutions in Mathematics (Oxford, 1992). While this volume principally deals with how to assign historical meaning to the history of mathematics (including an excellent bibliography), the essays by Caroline Dunmore, "Metalevel Revolutions in Mathematics" and Jeremy Gray, "The Nineteenth-century Revolution in Mathematical Ontology" are the most congenial to the eidetic orientation of Klein and Lachterman.
35. Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, tr. Eva Brann (Cambridge, Mass., 1968), David R. Lachterman, The Ethics of Geometry: A Genealogy of Modernity (New York, 1989). See also A. G. Holland, "Shifting the Foundations: Descartes' Transformation of Ancient Geometry," Historia Mathematica, 3 (1976), 21-49; and Jacob Klein: Lectures and Essays, ed. Robert B. Williamson and Elliot Zuckerman (Annapolis, 1985). The question of how ontological reassessments count as paradigm shifts in mathematical science is addressed in Donald Gillies (ed.), Revolutions in Mathematics (Oxford, 1992). While this volume principally deals with how to assign historical meaning to the history of mathematics (including an excellent bibliography), the essays by Caroline Dunmore, "Metalevel Revolutions in Mathematics" and Jeremy Gray, "The Nineteenth-century Revolution in Mathematical Ontology" are the most congenial to the eidetic orientation of Klein and Lachterman.
36. Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, tr. Eva Brann (Cambridge, Mass., 1968), David R. Lachterman, The Ethics of Geometry: A Genealogy of Modernity (New York, 1989). See also A. G. Holland, "Shifting the Foundations: Descartes' Transformation of Ancient Geometry," Historia Mathematica, 3 (1976), 21-49; and Jacob Klein: Lectures and Essays, ed. Robert B. Williamson and Elliot Zuckerman (Annapolis, 1985). The question of how ontological reassessments count as paradigm shifts in mathematical science is addressed in Donald Gillies (ed.), Revolutions in Mathematics (Oxford, 1992). While this volume principally deals with how to assign historical meaning to the history of mathematics (including an excellent bibliography), the essays by Caroline Dunmore, "Metalevel Revolutions in Mathematics" and Jeremy Gray, "The Nineteenth-century Revolution in Mathematical Ontology" are the most congenial to the eidetic orientation of Klein and Lachterman.
37. Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, tr. Eva Brann (Cambridge, Mass., 1968), David R. Lachterman, The Ethics of Geometry: A Genealogy of Modernity (New York, 1989). See also A. G. Holland, "Shifting the Foundations: Descartes' Transformation of Ancient Geometry," Historia Mathematica, 3 (1976), 21-49; and Jacob Klein: Lectures and Essays, ed. Robert B. Williamson and Elliot Zuckerman (Annapolis, 1985). The question of how ontological reassessments count as paradigm shifts in mathematical science is addressed in Donald Gillies (ed.), Revolutions in Mathematics (Oxford, 1992). While this volume principally deals with how to assign historical meaning to the history of mathematics (including an excellent bibliography), the essays by Caroline Dunmore, "Metalevel Revolutions in Mathematics" and Jeremy Gray, "The Nineteenth-century Revolution in Mathematical Ontology" are the most congenial to the eidetic orientation of Klein and Lachterman.
38. Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, tr. Eva Brann (Cambridge, Mass., 1968), David R. Lachterman, The Ethics of Geometry: A Genealogy of Modernity (New York, 1989). See also A. G. Holland, "Shifting the Foundations: Descartes' Transformation of Ancient Geometry," Historia Mathematica, 3 (1976), 21-49; and Jacob Klein: Lectures and Essays, ed. Robert B. Williamson and Elliot Zuckerman (Annapolis, 1985). The question of how ontological reassessments count as paradigm shifts in mathematical science is addressed in Donald Gillies (ed.), Revolutions in Mathematics (Oxford, 1992). While this volume principally deals with how to assign historical meaning to the history of mathematics (including an excellent bibliography), the essays by Caroline Dunmore, "Metalevel Revolutions in Mathematics" and Jeremy Gray, "The Nineteenth-century Revolution in Mathematical Ontology" are the most congenial to the eidetic orientation of Klein and Lachterman.
39. Jacob Klein, Greek Mathematical Thought and the Origin of Algebra, tr. Eva Brann (Cambridge, Mass., 1968), David R. Lachterman, The Ethics of Geometry: A Genealogy of Modernity (New York, 1989). See also A. G. Holland, "Shifting the Foundations: Descartes' Transformation of Ancient Geometry," Historia Mathematica, 3 (1976), 21-49; and Jacob Klein: Lectures and Essays, ed. Robert B. Williamson and Elliot Zuckerman (Annapolis, 1985). The question of how ontological reassessments count as paradigm shifts in mathematical science is addressed in Donald Gillies (ed.), Revolutions in Mathematics (Oxford, 1992). While this volume principally deals with how to assign historical meaning to the history of mathematics (including an excellent bibliography), the essays by Caroline Dunmore, "Metalevel Revolutions in Mathematics" and Jeremy Gray, "The Nineteenth-century Revolution in Mathematical Ontology" are the most congenial to the eidetic orientation of Klein and Lachterman.
40. Greek Mathematical Thought and the Origin of Algebra, 122.
41. Ibid., 125.
42. See John J. Cleary, "On the Terminology of 'Abstraction' in Aristotle," Phronesis, 30 (1985), 13-45.
43. Gottlob Frege, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, 2nd Revised Edition, tr. J. L. Austin (Evanston, 1980), 79-80: "The Number which belongs to the concept F is the extension of the concept 'equal to the concept F'..."
44. Ibid., 7.
45. Ethics of Geometry, 29 ff.
46. Ibid., 32.
47. Ibid., 115.
48. Emily Grosholz, Cartesian Method and the Problem of Reduction (Oxford, 1991), argues for an important qualification here regarding Descartes, that he is so seduced by symbolic generalization he fails to appreciate ontological heterogeneity in both the purely mathematical and the physical domains, mistakenly reducing to relations of discursive order what nonetheless absolutely requires an intuitive component for its accurate comprehension. This point does not, however, effect the distinction between eikonic and symbolic abstraction.
49. Herbert Mehrtens, Moderne-Sprache-Mathematik: Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme (Frankfurt am Main, 1990); Jean Van Heijenoort, From Frege to Gödel: A Source Book in Mathematical Logic (Cambridge, Mass., 1967), and Stephan Körner, The Philosophy of Mathematics: An Introductory Essay (London, 1960). See also Janet Folina, Poincaré and the Philosophy of Mathematics (London, 1992); and Mary Tiles, Mathematics and the Image of Reason (New York, 1991).
50. Herbert Mehrtens, Moderne-Sprache-Mathematik: Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme (Frankfurt am Main, 1990); Jean Van Heijenoort, From Frege to Gödel: A Source Book in Mathematical Logic (Cambridge, Mass., 1967), and Stephan Körner, The Philosophy of Mathematics: An Introductory Essay (London, 1960). See also Janet Folina, Poincaré and the Philosophy of Mathematics (London, 1992); and Mary Tiles, Mathematics and the Image of Reason (New York, 1991).
51. Herbert Mehrtens, Moderne-Sprache-Mathematik: Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme (Frankfurt am Main, 1990); Jean Van Heijenoort, From Frege to Gödel: A Source Book in Mathematical Logic (Cambridge, Mass., 1967), and Stephan Körner, The Philosophy of Mathematics: An Introductory Essay (London, 1960). See also Janet Folina, Poincaré and the Philosophy of Mathematics (London, 1992); and Mary Tiles, Mathematics and the Image of Reason (New York, 1991).
52. Herbert Mehrtens, Moderne-Sprache-Mathematik: Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme (Frankfurt am Main, 1990); Jean Van Heijenoort, From Frege to Gödel: A Source Book in Mathematical Logic (Cambridge, Mass., 1967), and Stephan Körner, The Philosophy of Mathematics: An Introductory Essay (London, 1960). See also Janet Folina, Poincaré and the Philosophy of Mathematics (London, 1992); and Mary Tiles, Mathematics and the Image of Reason (New York, 1991).
53. Herbert Mehrtens, Moderne-Sprache-Mathematik: Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme (Frankfurt am Main, 1990); Jean Van Heijenoort, From Frege to Gödel: A Source Book in Mathematical Logic (Cambridge, Mass., 1967), and Stephan Körner, The Philosophy of Mathematics: An Introductory Essay (London, 1960). See also Janet Folina, Poincaré and the Philosophy of Mathematics (London, 1992); and Mary Tiles, Mathematics and the Image of Reason (New York, 1991).
54. Klein, op. cit., 353.
55. Ludwig Wittgenstein, Tractatus Logico-Philosophicus, tr. D. F. Pears and Brian F. McGuinness (London, 1961), 4.
56. Klein, op. cit., 169.
57. Eugene Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," Communications on Pure and Applied Mathematics, 13 (1960), 1-14.