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Whitehead, Alfred North

Peter Simons

Pages 593 - 598

Whitehead was one of the first logicians to engage in mereology. He did so in the course of his lifelong project to provide an adequate metaphysical account of the physical universe. A principal aspect of this was his endeavour to provide a properly, physically grounded geometry. This was understood by him as a theory of space in which the occupants of this space were not merely passively present at locations in a three-dimensional Euclidean continuum, but rather formed an interrelated system, whose governing principles were such that the axioms of geometry would be derivable from them. Standard modern geometry has treated geometric figures such as lines, triangles, cubes and so on as sets of points, and mathematically this is nothing to object to, but Whitehead was always against taking points as the basis of geometry as they are necessarily imperceptible. Even in his early memoir “On Mathematical Concepts of the Material World” (1906) he prefers systems where the basic elements are lines rather than points. Later, prompted by ideas of Grassmann and using the logical tools he and Russell developed in Principia Mathematica, he reconceptualised points and other geometric elements of zero thickness, such as lines and surfaces, as logical constructions out of threedimensional items, and for this he needed the relation of (proper) part to whole. He developed his mereology to the extent required for his geometrical purpose. The unfinished fourth volume of PM, assigned to Whitehead alone, was to be on geometry, and this would surely have contained an axiomatised mereology. As it was, the project was shelved and the ideas and techniques plundered piecemeal for Whitehead’s logically less systematic writings in natural philosophy and process philosophy. The ordained destruction of Whitehead’s Nachlass after his death deprives us of a fully developed formal mereology from his pen, but we can gain a fair idea of the general outlines from the published work.

1Department of Philosophy, Trinity College Dublin

1 Clarke, B. L., (1981), “A Calculus of Individuals Based on Connection”, Notre Dame Journal of Formal Logic 22: 204-218.

2 Russell, B., (1914), Our Knowledge of the External World As a Field for Scientific Method in Philosophy, La Salle: Open Court. 2nd ed. London: Allen & Unwin, 1926.

3 Simons, P. M., (1991), “Whitehead und die Mereologie”, in: Hampe, M.; Maaßen, H. (eds.), Die Gifford Lectures und ihre Deutung. Materialien zu Whiteheads Prozess and Realität, Band 2. Frankfurt/Main: Suhrkamp, 1991: 369-388. Revised translation: Whitehead and Mereology, in: Durand G.; Weber, M. (eds.), Les Principes de la connaissance naturelle d’Alfred North Whitehead/Alfred North Whitehead’s Principles of Natural Knowledge. Frankfurt/Main: Ontos, 2007: 215-233.

4 Whitehead, A. N., (1906), “On Mathematical Concepts of the Material World”, Philosophical Transactions of the Royal Society Series A, 205, 465-525; reprinted in Northrop, F. C. and Gross, M. W., (eds.) Alfred North Whitehead. An Anthology. Cambridge: Cambridge University Press, 1953: 11-82.

5 Whitehead, A. N., (1916), “La théorie relationniste de l’espace”, Revue de Metaphysique et de Morale 23: 423-454 (TRE).

6 Whitehead, A. N., (1919), An Enquiry Concerning the Principles of Natural Knowledge, Cambridge: Cambridge University Press. 2nd ed. 1925 (PNK).

7 Whitehead, A. N., (1978), Process and Reality: An Essay in Cosmology. Corrected edition, Griffin, D. R.; Sherburne, D. W. (eds.), New York: The Free Press, 1978. 1st eds. 1929: New York: Macmillan; Cambridge: Cambridge University Press. (= PR)


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