TY - JOUR
T1 - Whitehead, Alfred North
A1 - Simons, Peter
PY - 2017
N2 - 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.
JF - PCM: Philosophia Contributions – Mereology
JA - PCM: Philosophia Contributions – Mereology
VL - 1
IS - 1
UR -
ER -