An Approximative Logical Structure for Whitehead’s Categoreal Scheme

It should not be forgotten that Whitehead was a professional mathematician for most of his academic life and that he spent ten years or so collaborating with Bertrand Russell on Principia Mathematica. Logico-mathematical methods and procedures must have become thoroughly ingrained in his habits of thought by the time the later metaphysical works were written. The suggestion that Whitehead may have forgotten these methods or no longer trusted them must surely be in error. For him, it would seem, to think at all was to think mathematically. Even in Process and Reality 1 it is interesting to discern mathematical or quasi-mathematical notions, definitions, and statements creeping in almost unawares on every page. The great categoreal scheme of this book, in fact, it will be contended, may be viewed as a kind of logico-mathematical system in disguise. It is the purpose of this present paper, in any case, to take a few first, tentative steps towards substantiating such a claim.