The Metaphysics of Whiteheadian Naturalism: reality as an instantiation of the formal categories of process
Michael Heather (Trinity College, United Kingdom) and Nick Rossiter (Northumbria University, United Kingdom)
Whitehead abandoned Principia Mathematica without publishing the fourth volume on geometry and did not involve himself with the second edition of 1925 --1927 because he realized by then that it is a relativistic quantum world we inhabit beyond classical mathematics. Rather paradoxically mainstream science a century later is still trying to understand our world using the models based on the concepts of his early mathematical period (we might call Whitehead I) rather than the informal categorical approach enunciated in the 1929 Process & Reality of his later philosophical period (Whitehead II). A lesser mathematician might have persevered with the tensor mathematics toyed with in his alternative 1922 theory of relativity rather than resorting to words alone but he clearly appreciated that Whitehead I was inadequate to articulate the speculative metaphysics of Whitehead II. However around the time of Whitehead‘s death emerged formal ̳category theory‘ to subsume algebra, geometry and topology as a formal metaphysical language that can integrate his natural philosophy and mathematics to culminate in what we might explore here as a posthumous Whitehead III†.
Whitehead I to Whitehead II is a major upgrade through two levels from models to metaphysics. A model reduces reality that metaphysics generalizes. Just as a mathematical theory is an instantiation of the world so the world is an instantiation of metaphysics. For historical reasons category theory has had to develop from within classical mathematics and current text books deal mainly with the category of sets that resides within Whitehead I and therefore does not satisfy the test for Whitehead II. As metaphysics generalizes the dynamics of nature, metaphysical language relates to natural process without the need for the arbitrary axioms of mathematics. Fortunately therefore metaphysical category theory is simpler than the category theory of classical mathematics and also greatly simplifies the natural language descriptions that flowed from the pen of Whitehead II that are difficult for those of us not endowed with the power of his mind. The formal categories of Whitehead III are therefore simpler but a simplification satisfying his own observation that ― the only simplicity to be trusted is the simplicity to be found on the far side of complexity.‖ Only a few such ̳simple‘ concepts are needed: the World is a topos with monadic objects related by contravariant functors with natural transformations as units of adjunction. These are sufficient to identify formally the Whiteheadian vocabulary of the likes of the onto logical principle, actual entities and occasions, eternal objects, congrescence, creative and emotive advance of becoming, public and private, prehensions, nexus, primordial nature, emergence, etc, together with their other post-modern counterparts.