The Axiomatic Matrix of Whitehead’s Process and Reality by Leemon B. McHenry Leemon B. McHenry teaches in the philosophy department at The Johns Hopkins University, Baltimore, Maryland. The following article appeared in I Commentators on Whitehead’s philosophy often mention his mathematical background as a foundation for his metaphysics. Rarely, however, do they explain just how the rigorous and technical expertise of his early work finds its relevant applications in his later cosmological framework. Nor do they explain his strenuous objections to philosophers following the pattern of mathematical method if indeed he did so himself. Though the particular structure and procedure of A cursory glance at The impact of Some difficulty here arises as regards the manner in which Whitehead’s system may be described as ‘axiomatic’.
The main point for Whitehead then concerns the alleged self-evidence of the axioms. How do we construe the status of the axioms? Are they absolutely certain, or are they subject to revision? How does experience play into the final outcome? A metaphysics, Whitehead wrote in
Whitehead himself, in a memoir published in From the ten year course in which At most the metaphysics tacitly understood in A further insight into the relations of Whitehead’s mathematical procedure and cosmological construction is detailed in his memoir of 1906 "On Mathematical Concepts of the Material World." In this essay, written in the middle of the II Although Whitehead in The scheme is thus set out with four major categories of which three are more special of the one ultimate. For Whitehead, Creativity is the ultimate presupposition or given operation which describes the universe as a harmonizing of data into a novel unity. This is the principle of the highest generality governing the advance of everything that becomes. It is the pulse of existence which conjoins the disjunctive diversity of the antecedent world. Analogously, in The categories of existence in Next are the categories of explanation in the cosmology; here Whitehead explains how the categories of existence interact in the fluid and dynamic nature of process. Generally, the twenty-seven categories of explanation describe the creative activity of actual occasions in terms of the functions of prehension and concrescence. Category xii, for instance, explains the two species of prehension as positive, absorbing antecedent data, and negative, eliminating incompatible data with the present actual occasion. Throughout these categories we find the descriptions of the various types of entity becoming more definite as the categories build to more complex explanations which involve the previous ones. In *1.01. p q.=. ~ (p v q Df. (PM 94), *3.01. p. q.= ~ (~p v ~ q) Df. (PM 109), *4.01. p=q.=.p q q p Df. (PM 115). We now come to comparative analysis of the axioms in the two systems as concise statements governing the relations between the various entities. In *1.2. Hp v p. .p Tautology *1.3. F:q. .p v q Addition, *1.4. Hp v q. .q v p Permutation, *1.5. Hp v (q v r). .q v (p v r) Associative Principle, *1.6. H.q r. :p v q. .p v r Principle of Summation. (PM 96f.) As an . . . this system includes the harmony of logical rationality, and the harmony of aesthetic achievement: to know that, while the harmony of logic lies upon the universe as an iron necessity, the aesthetic harmony stands before it as a living ideal moulding the general flux in its broken progress toward finer, subtler issues. (SMW 24) His solution to this necessity involves a set of entities derived from our experience, which form a field of relations by the complex function of Creativity, operating in accordance with the explanations and obligations of the system.
REFERENCES EWM -- Lewis S. Ford. ILM -- David Harrah. "The Influence of Logic and Mathematics on Whitehead," MCMW -- A. N. Whitehead. "On Mathematical Concepts of the Material World," UW -- Victor Lowe. WPO -- Dorothy Emmet. WRL -- W. V. O. Quine. "Whitehead and the Rise of Modern Logic," NOTES
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