Works Cited and Further Readings – Mathematics

Alcantara, Jean-Pascal. 2007. “Le rôle des mathématiques dans la genèse whiteheadienne”, Michel Weber et Pierfrancesco Basile (sous la direction de), Chromatikon III. Annuaire de la philosophie en procès—Yearbook of Philosophy in Process (Louvain-la-Neuve, Presses universitaires de Louvain).

Ariel, Robert Andrew. 1974. “A Mathematical Root of Whitehead’s Cosmological Thought,” Process Studies, 4, 107-13.

Athearn, Daniel. 1997. “Whitehead as Natural Philosopher: Anachronism or Visionary?” Process Studies, 26, 3-4, 293-307.

Barnabei, R., Brini, A. and Rota, G-C. 1985. “On the Exterior Calculus of Invariant Theory,” Journal of Algebra, 96, 120-60.

Beichler, J. 1996. “The Work of W. K. Clifford,” Yggdrasil: The Journal of Paraphysics, 1-13. Online at

Bendall, R. Douglas. 1973. On Mathematical Concepts of the Material World and the Development of Whitehead’s Philosophy of Organism (Berkeley, Master’s thesis for the Graduate Theological Union—forthcoming with Éditions Chromatika, Louvain-la-Neuve).

Berkeley, H. 1910. Mysticism in Modern Mathematics (Oxford, Oxford University Press).

Beth, E. W. 1954. “Review of Grünbaum ‘Whitehead’s method of extensive abstraction’.” In: Math. Reviews.

Birkhoff, G. 1933. “On the combination of subalgebras,” Proceedings of the Cambridge Philosophical Society, 29, 4, 441-64.

Birkhoff, G. 1935. “On the structure of Abstract Algebras,” Proceedings of the Cambridge Philosophical Society, 31, 4, 433-54.

Birkhoff, G. 1944. “Subdirect unions in universal algebra,” Bulletin of the American Mathematical Society, 50, 764-68.

Birkhoff, G. 1969. “Mathematics and Psychology,” SIAM Review, 11, 4, 429-69.

Birkhoff, G. 1973. “Current trends in Algebra,” The American Mathematical Monthly, 80, 7, 760-82.

Blake, S. 2005. A. N. Whitehead’s Geometric Algebra. Ebook available at

Böhme, Gernot. 1984. “Whiteheads Abkehr von der Substanz-Metaphysik,” in Whitehead und der Prozessbegriff, edited by Holz & Wolf-Gazo(Freiburg/München).

Borgo, S., Guarino, N. and Masolo, C. 1996. “A pointless theory of space based on strong connection and congruence, in Principles of Knowledge Representation and Reasoning: Fifth International Conference, edited by L. C. Aiello, J. Doyle, and S. C. Shapiro (KR Inc.), 220-29.

Boyle, Margaret O’Rourke. 1975. “Interpoints: A Model for Divine Spacetime,” Process Studies, 5, 191-94.

Browne, J. 2001. “A note on sources to Grassmann’s work,” online at, p. 5.

Buchheim, A. 1884. “On the Theory of Screws in Elliptic Space,” Proceedings of the London Mathematical Society, XV, January 83-98.

Burris, S. and Sankappanavar, H. P. 1981. A Course in Universal Algebra (New York, Springer Verlag). Online at

Čapek, Milič. 1971. “The fiction of instants,” Stug. Gen. 24, 31-43. Also in The Study of Time, edited by Fraser, J.T., Haber, F.C., Müller, G.H.

Carnap, R. 1929. Abriss der Logistik, mit besondere Berücksichtigung der Relationstheorie und ihre Anwendungen (Vienna, Springer).

Casati, Roberto & Varzi, Achille. 1997. “Spatial Entities,” in Spatial and Temporal Reasoning, edited by Oliviero Stock (Dordrecht, Kluwer), 73-96.

Chappell, V.C. 1961. “Whitehead’s Theory of Becoming,” Journal of Philosophy, 58.

Chisholm, R. 2002. “The Clifford Heritage,” in Such Silver Currents: The Story of William and Lucy Clifford 1845–1929, edited by M. Chisholm (Cambridge, Lutterworth Press), 159-77.

Christian. 1959. An Interpretation of Whitehead’s Metaphysics (New Haven, Yale University Press).

Clarke, B. L. 1981. “A calculus of individuals based on connection,” Notre Dame Journal of. Formal Logic, 22, 204-18.

Clarke, B. L. 1985. “Individuals and points,” Notre Dame Journal of Formal Logic, 26, 61-75.

Clifford, W. K. 1879a. “The Unseen Universe,” in Lectures and Essays Vol. 1, edited by L. Stephen and F. Pollock (London, MacMillan), 228-53.

Clifford, W. K. 1879b. “On the nature of Things-in-Themselves,” in Lectures and Essays Vol. 2, edited by L. Stephen and F. Pollock (London, MacMillan), pp. 71-88.

Clifford, W. K. 1880. “Energy and Force,” Nature, June, 122-24.

Clifford, W. K. 1882. “Applications of Grassmann’s Extensive Algebra,” reprinted from American Journal of Mathematics Pure and Applied, 1, 1878, 350-358, in Mathematical Papers, edited by R. Tucker and introduced by H.J.S. Smith (New York, Chelsea Publishing), 266-76.

Clifford, W. K. 1955 [1885]. The Common Sense of the Exact Sciences, with preface by Bertrand Russell (New York, Dover).

Code, M. 1985. Order and Organism. Steps to a Whiteheadean Philosophy of Mathematics and the Natural Sciences (Albany, SUNY Press).

Cohen, M. 1932. Symposium in Honor of the Seventieth Birthday of Alfred North Whitehead (Cambridge MA, Harvard University Press)

Cohn, P. M. 1981. Universal Algebra (Dordrecht, Reidel).

Couturat, L. 1900. “L’algèbre Universelle de M. Whitehead,” Revue de Métaphysique et de Morale, 8, 323-362.

Couturat, Louis. 1901. La logique de Leibniz d’après des documents inédits (Paris, Félix Alcan). Reprinted 1985, Hildesheim, Georg Olms Verlag.

Cox, H. 1882a. “On the application of Quaternions, and Grassmann’s Ausdehnungslehre to different kinds of uniform space,” Transactions of the Cambridge Philosophical Society, XIII, II, 10-143.

Cox, H. 1882b. “On the application of Quaternions, and Grassmann’s Ausdehnungslehre to different kinds of uniform space,” Proceedings of the Cambridge Philosophical Society, IV, February, 194-96.

Crowe, Michael John. 1967. A History of Vector Analysis. The Evolution of the Idea of a Vectorial System. (Notre Dame, University of Notre Dame Press).

Darrigol, O. 2003. “Number and measure: Herman von Helmholtz at the crossroads of mathematics, physics, and psychology,” Studies in the History and Philosophy of Science, 34, 515-73.

De Laguna, Theodore. 1922. “Point, line and surface as sets of solids,” Journal of Philosophy, 19, 449-61.

De Laguna, Theodore. 1922. “The Nature of Space,” International Journal of Philosophy.

Diek, A. and Kantowski, R. 2005. “Some Clifford Algebra History,” in Clifford Algebras and Spinor Structures (Dordrecht, Kluwer), 3-12. Online at

Dieudonné, J. 1979. “The Tragedy of Grassmann,” Linear and Multilinear Algebra, 8, 1-14.

Einstein, Albert. 1905. “Zur Elektrodynamik bewegter Körper,” Annalen der Physik, 17, 891-921.

Farwell, R. and Knee, C. 1990. “The End of the Absolute: A Nineteenth-Century Contribution to General Relativity,” Studies in the History and Philosophy of Science, 21, 1, 91-121.

Fearnley-Sander, D. 1982. “Hermann Grassmann and the Prehistory of Universal Algebra,” American Mathematical Monthly, 89, 161-66.

Fitzgerald, Janet A. 1979. Alfred North Whitehead’s Early Philosophy of Space and Time (Washington, University Press of America).

Floyd, J. 2001. “Number and Ascriptions of Number in Wittgenstein’s Tractatus,” in Future Pasts: The Analytic Tradition in Twentieth Century Philosophy, edited by J. Floyd and S. Shieh (Oxford, Oxford University Press), 145-91.

Floyd, J. 2005. “Wittgenstein on Philosophy of Logic and Mathematics,” in The Oxford Handbook of Mathematics and Logic, edited by S. Shapiro (Oxford, Oxford University Press), 75-128.

Ford, Lewis S. 1984. The Emergence of Whitehead’s Metaphysics 1925-1929. [The Emergence of Temporal Atomicity, see 51-65. Abstraction, see 66-95.]

Fraser, J.T., Haber, F.C., Müller, G.H. (eds.). 1972. The Study of Time (Berlin, Springer-Verlag).

Gaeta, Luca. 2002. Segni del cosmo. Logica e geometria in Whitehead (Milano, LED).

Gandon, S. 2005. “Algèbre, géométrie et loi d’intensité: l’enjeu de A Treatise on Universal Algebra,” in Chromatikon I, Annuaire de la philosophie en procès—Yearbook of Philosophy in Process, edited by M. Weber et D. d’Eprémesnil (Louvain-la-Neuve, Presses universitaires de Louvain).

Gerla, Giangiacomo & Miranda, Annamaria. 2004. “Graded inclusion and point-free geometry,” International Journal of Pure and Applied Mathematics, 11, 63-81.

Gerla, Giangiacomo & Miranda, Annamaria. 2006. “From the inclusion based to the connection-based point-free geometry,” Preprint n. 5, D.M.I. University of Salerno (Italy).

Gerla, Giangiacomo & Tortora, Roberto. 1992. “La relazione di connessione in A. N. Whitehead: aspetti matematici,” Epistemologia, 15, 341-54.

Gerla, Giangiacomo & Tortora, Roberto. 1996. “Dissezioni, intersezioni di regioni in A. N. Whitehead,” Epistemologia, 19, 289-308.

Gerla, Giangiacomo & Volpe, Roberto. 1985. “Geometry without points,” The American Mathematical Monthly, 92, 707-711.

Gerla, Giangiacomo. 1990. “Pointless metric spaces,” Journal of Symbolic Logic,55, 207-19.

Gerla, Giangiacomo. 1994. “Pointless geometries,” in Handbook of Incidence Geometry, edited by F. Buekenhout (Elsevier Science), 1015-1031.

Grassmann, H. G. 1995. A New Branch of Mathematics: The Ausdehnungslehre of 1844, and Other Works, translated by L. C. Kannenberg (Chicago, Open Court).

Grassmann, H. G. 2000. Extension Theory: The Ausdehnungslehre of 1862, translated by L. C. Kannenberg (American Mathematical Society/London Mathematical Society).

Grattan-Guinness, I. 2000. The Search for Mathematical Roots, 1870-1940. Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel (Princeton, Princeton University Press).

Grattan-Guinness, I. 2002. “Algebras, Projective Geometry, Mathematical Logic, and Constructing the World: Intersections in the Philosophy of Mathematics of A.N. Whitehead,” Historia Mathematica, 29, 427-62.

Grattan-Guinness, I. 2004. “Contexte et contenu de “On mathematical concepts of the material world”, François Beets, Michel Dupuis et Michel Weber (éditeurs), Alfred North Whitehead. De l’algèbre universelle à la théologie naturelle (Frankfurt / Paris / Lancaster, ontos verlag).

Grattan-Guinness, I. 2006. “Mathematics and philosophy, François Beets, Michel Dupuis et Michel Weber (éditeurs), La science et le monde moderne d’Alfred North Whitehead — Alfred North Whitehead’s Science and the Modern World (Frankfurt / Paris / Lancaster, ontos verlag), 77-80.

Gratzer, G. 1979. Universal Algebra, 2nd ed (New York, Springer).

Griffin, N. (ed.). 2003. The Cambridge Companion to Russell (Cambridge, Cambridge University Press).

Grosshans, F. D., Rota, G.-C. and Stein, J. A. 1987. Invariant Theory and Superalgebras, (Providence RI, American Mathematical Society).

Grünbaum, Adolf. 1953. “Whitehead’s method of extensive abstraction,” British Journal of Philosophy, 4, 215-26.

Grünbaum, Adolf. 1957. “The philosophical Retention of absolute space in Einstein’s general theory of relativity,” Phil. Rev., 66, 525-29.

Grünbaum, Adolf. 1962. Review of Whitehead’s Philosophy of Science by Palter, Phil. Rev., 71.

Hájek, Petr. 1998, “Metamathematics of Fuzzy Logic” (Dordrecht, Kluwer).

Hammersmith, William W. 1984. “The Problem of Time,” in Whitehead und der Prozessbegriff, edited by Holz & Wolf-Grazo(Freiburg/München).

Hampe, Michael and Maaßen, Helmut (eds.). 1991a. Prozeß, Gefühl und Raum-Zeit. Materialien zu Whitehead’s “Prozeß und Realität” 1. Suhrkamp. [See in particular M. Hampe, “Einleitung: Whitehead’s Entwicklung einer Theorie der Ausdehnung,” 220-43.]

Hampe, Michael and Maaßen, Helmut (eds.). 1991b. Die Gifford Lectures und ihre Deutung. Materialien zu Whitehead’s “Prozeß und Realität” 2 (Suhrkamp).

Hampe, Michael. 1990. Die Wahrnehmung der Organismen (Vandenhoeck und Ruprecht).

Harman, P. M. 1998. The Natural Philosophy of James Clerk Maxwell (Cambridge, Cambridge University Press).

Harman, Peter Michael. 1998. The Natural Philosophy of James Clerk Maxwell (Cambridge, Cambridge University Press).

Harrell, M. 1988. “Extension to geometry of Principia mathematica and related systems II,” Russell, new ser. 8, 140-60.

Hawking, S.W. and Ellis. 1973. The Large Scale Structure of Space-Time (Cambridge, Cambridge University Press.).

Hecke, Erich. 1948 [1923]. Vorlesungen über die Theorie der algebraischen Zahlen (New York, Chelsea Publishing Company; originally Leipzig, Akademsiche Verlagsgeselschaft).

Hendry, John. 1986. James Clerk Maxwell and the Theory of the Electromagnetic Field (Bristol, Hilger).

Henry, Granville C. 1993. Forms of Concrescence: Alfred North Whitehead’s Philosophy and Computer Programming Structures. (Lewisburg PA, Bucknell University Press.)

Henry, Granville C. and Robert J. Valenza. 1993a. “The dichotomy of idempotency in Whitehead’s mathematics,” Philosophia Mathematica 3, 1, 157-72.

Henry, Granville C. and Valenza, Robert J. 1993b. “Whitehead’s Early Philosophy of Mathematics,” Process Studies, 22, 1, 21-36.

Henry, Granville C. and Robert J. Valenza. 1993c. “Idempotency in Whitehead’s Universal Algebra,” Philosophia Mathematica, 3, 1, 157-72.

Hestenes, D. 1986a. “A unified language for mathematics and physics,” in Clifford Algebras and their Applications in Mathematical Physics, edited by J.S.R. Chisholm and A.K. Commons (Dordrecht, Reidel), 1-23.

Hestenes, D. 1986b. New Foundations for Classical Mechanics (Dordrecht, Reidel).

Hestenes, D. 1988. “Universal Geometric Algebra,” Simon Stevin, A Quarterly Journal of Pure and Applied Mathematics, 62, 3-4. Online at

Heuser, M-L. 1996. “Geometrical Product—Exponentiation—Evolution. Justus Günther Grassmann and Dynamist Naturphilosophie,” in Schubring 1996, 47-58.

Holz, Harald, and Wolf-Gazo, Ernest (eds.). 1984. Whitehead und der Prozessbegriff (Freiburg/München)

Jung, Walter. 1984. “Über Whiteheads Atomistik der Ereignisse,” in Whitehead und der Prozessbegriff, edited by Holz & Wolf-Grazo(Freiburg/München),54.

Keeton, H. 2004. “Whitehead as Mathematical Physicist,” Physics and Whitehead: Quantum Process and Experience, edited by T.E. Eastman and H. Keeton (Albany, SUNY Press).

Keeton, Henry C.S., Jr. 1986. The Topology of Feeling. Extensive Connection in the Thought of Alfred North Whitehead: Its Development and Implications (University Microfilms International).

Kennedy, Hubert C. 1980. Life and Works of Giuseppe Peano (Dordrecht, Reidel).

Klein, F. 1939. Elementary Mathematics from an Advanced Standpoint: Geometry, translated by E.R. Hedrick, and C.A. Noble (New York, Dover).

Kline, M. 1972. Mathematical Thought from Ancient to Modern Times (New York, Oxford University Press).

Kraus, Elizabeth M. 1979. The metaphysics of experience (New York, Fordham University Press).

Langer, Susanne K. 1942. Philosophy in a New Key: A Study in the Symbolism of Reason, Rite, and Art (Cambridge MA, Harvard University Press).

Lasker, E. 1896-97. “An Essay on the Geometrical Calculus,” Proc. London Math. Soc., XXVIII, 217-60 & 500-531.

Lawrence, Nathaniel. 1968. Whitehead’s Philosophical Development (New York, Greenwood Press). [For the Method of Extensive Abstraction, see 35-38].

Lawvere, F. W. 2005. “Review of [Grassmann 1995 & Grassmann 2000],” Historia Mathematica, 32, 1, 99-106.

Leclerc, Ivor. 1961. “Whitehead and the Problem of Extension,” Journal of Philosophy, 58.

Lewis, A. 1977. “H. Grassmann’s 1844 Ausdehnungslehre and Schleiermacher’s Dialektik, Annals of Science, 34, 103-162.

Lewis, A. 2004. “The unity of logic, pedagogy and foundation in Grassmann’s mathematical work,” History and Philosophy of Logic, 25, 15-36.

Lounesto, P. 2001. “A history of Clifford Algebras,” in Clifford Algebras and Spinors, 2nd ed., edited by P. Lounesto (Cambridge, Cambridge University Press), 320-30.

Lowe, Victor. 1951 [1941]. “The Development of Whitehead’s Philosophy,” in The Philosophy of Alfred North Whitehead, edited by P.A. Schilpp (New York, Tudor Publishing Company).

Lowe, Victor. 1962. Understanding Whitehead (Baltimore, The Johns Hopkins Press).

Lowe, V. 1975. “A. N. Whitehead on his Mathematical Goals: a Letter of 1912,” Annals of Science, 32, 85-101.

Lowe, V. 1985. Alfred North Whitehead: The Man and his Work. Vol. 1: 1861-1910 (Baltimore, John Hopkins University Press).

MacColl, H. 1899. “Critical Notices: Alfred N. Whitehead, Universal Algebra with Applications,” Mind, New Series, 8, 29,108-113.

Macfarlane, A. 1899. “A Treatise on Universal Algebra,” Science, New Series, 9, 218, 324-28.

Macfarlane, A. 1916. Lectures on Ten British Mathematicians of the Nineteenth Century (New York, John Wiley & Sons). Available at

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Malonek, H. R. 2004. “Quaternions in Applied Sciences: A historical perspective of a mathematical concept,” paper presented at Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, 16, 2003, Weimar, Bauhaus-Universität. Online at

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Whitehead, A.N. 1906b. The Axioms of Projective Geometry (Cambridge, Cambridge University Press). Reprinted 1971, New York, Hafner.

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Whitehead, A. N. 1951. “Mathematics and the Good” in The Philosophy of Alfred North Whitehead, edited by P.A. Schilpp (La Salle, Illinois, Open Court), 666-81.

Whittaker, E. T. 1948. “Alfred North Whitehead 1861-1947,” Obituary Notices of Fellows of the Royal Society, 6, 281-96.