Russell heard Peano deliver a paper on the construction of arithmetic using "a successor relation." After the conference, Russell said "Peano had the best logic." After that, Russell wrote Principles of Mathematics, using the successor relation to build up everything, and this became Principia Mathematica when Whitehead got involved.
The focus on a successor relation gave us the formalization of mathematics. For Russell and Whitehead, the next step was "eventism," which is their Theory of Everything. For them, space-time, like anything that is presumed to have order or structure, is subject to analysis by a successor relation. Whitehead characterized the physical world, so analyzed, as "temporal succession." Russell favors the term "causal succession," but both men agree that the two terminologies have but a single successor relation as the primitive referent.
The mode of thought that works exclusively with a successor relation is what helped me to find what eventism looks like when only finite structural possibilities are considered. This led me to draw arrow diagrams of time order possiblities, where I find relative frequencies formed that serve eventism as relative energies in accord with Planck's E=hf. That means that eventism, in its simplest finite form, has the structural definition of energy inherent in it, without need of any imposed metric or quantity.
I elaborated on the successor relation to produce a paper that fulfills the goals of Wittgenstein's Tractatus. He spoke of "primitive facts" without specifying what they are. That is remedied in my paper. I delivered the paper to a Whitehead Conference held in Salzburg in 2006. It is posted on their website. I will give a link to it, and a copy of its abstract, below. -- Carey
http://www2.sbg.ac.at/whiteheadconfe...20Language.pdf
The Adequacy of Language for Finite Domains of Reference
A formal system is constructed which generates a finite set of statements that correlate 1-to-1 with the facts of a finite domain. Each formal statement transcribes directly to English, so the adequacy of language in general is entailed by the adequacy of the formal system. The crux of the argument involves giving precision to the phrase "finite domain of reference." It is assumed that any such domain consists of a finite number of individuals connected to one another by a finite number of relations. A domain of three individuals is examined in detail, which serves to show that any relation is constructible from a pair-wise relation. This in turn implies that the realm of finite mathematical structure can be systematically generated by an algorithm. An important domain of reference for the formalism is obtained by interpreting the primitive relation as "time order." We then see what Russell and Whitehead's "eventism" looks like when restricted to a finite domain.