Hi everyone–

In his 7/28 post, Henry makes a great point here re: my last post, and it brought up what might be an important question:  Could PNC taken as an a priori metaphysical first principle (implied by Whitehead’s desideratum of logical coherence), writ large and within the context of the metaphysical system given in Process and Reality, yield a well-ordered series of occasions in a scheme where:

1. The physical-causal efficacy of every actual occasion is restricted to its forward light cone.

and

2. Each and every becoming actual occasion is logically, internally related to each and every being.

I believe that Part III and IV in PR together posit both of these, respectively. With respect to 2 and its relationship to extensiveness, for example, Part IV.II.II Assumption 2 (PR 295) states that any two regions A and B are mediately connected such that both A and B are connected with some region C. (Fig. iii, p.296) The question is, if we bring 1 and 2 together, with added attention to governance of internal relations by PNC, will that yield an interpretation of “The many become one and are increased by one” that is free of the problem Henry raises?

Here is our exchange:

——–

Dear Mike,

Regarding Continua, absolute order, and causal objectification: Part III

I have doubts about your concept:

“the order of occasions ABCDE in I’s actual world”

Because we are interested here in the metaphysical structure, not the spacetime structure of our epoch, we should, I believe, consider your diagram as representing the past, future, and contemporary structure at the *metaphysical* level.

At this metaphysical level we do not want to start with an absolute ordering of occasions, as that would beg the question.

MGE: Yes, it is intended to represent Whitehead’s metaphysical conceptions of objectification (given in Part III) combined with his metaphysical conception of extensiveness (given in Part IV). Indeed, these conceptions contain a number of explicit presuppositions (question begging). The Ontological Principle and the Principle of Relativity are 2 such presupposed principles explored in Part III; and the axioms of his Theory of Extension in Part IV are similarly presupposed. Insofar as Whitehead’s work, and ours, are examples of ’speculative philosophy,’ I have always operated under the impression that starting with presupposed principles or axioms or desiderata is fine for us, as it was for Whitehead, so long as these are empirically applicable, adequate, and logically coherent.

In any case, the purpose of my posts was the same as Jorge’s–simply to demonstrate that the kind of objective ordering we’re talking about “follows from the logic of the theory of causal objectification, which is a wholly metaphysical theory.”

I agree with Jorge’s assessment here, and my posts were intended to substantiate this agreement–not to offer a metaphysical proof that there is an objective ordering among all actual occasions. More specifically, as discussed in my posts, I believe that this ordering follows when the theory of prehension/objectification presented in Part III is combined with the theory of extension in Part IV. Whitehead says that the concepts of extensive connection / ‘extensive abstraction’ are to be read as part of his discussion of the order of nature–i.e., the order of actual occasions. (PR 96-7) And in Part IV he defines this ‘order’ as a mathematical/logical/mereotopological order–as ordered sets with hierarchical relations. That is what I attempted to show, in shorthand, in the graphic.

The question I would like to pursue with the physicists in the group is whether or not Whitehead’s Theory of Prehensions/Objectification together with and in the context of his Theory of Extension, and all the metaphysical presuppositions contained therein, are empirically applicable in the light of modern physics. Both of these theories contain many metaphysical presuppositions / first principles / categoreal obligations, etc–some explicit, and some implicit. I want to explore their scientific applicability and adequacy.

So in my interpretation of your diagram, one is supposed to consider it to be a representation at the metaphysical level of a logically possible set of metaphysically possible causal connections, where the absolute time ordering is not significant —that would beg the question being examined here.

Instead, we are to imagine that the metaphysical past-future-contemporary causal relationships are such that they conformto the usual light-cone conditions.

MGE: Yes, this is the kind of test for empirical adequacy that very much interests me.

Any Lorentz transformation will leave all light-cones unaffected.

But some Lorentz transformations will change the relative time ordering CDE to ECD. So the ordering ABCDE that you cite is, in the context that is pertinent here, is a feature of the diagram that will not be captured in I or J, because it is a purely conventional ordering that is not part of the intrinsic causal structures captured, within this logically conceivable model of the metaphysical connections, by light-cone relationships.

MGE: To say that neither CDE or ECD is ‘captured’ in I or J would be problematic for Whitehead’s model, so I want to make sure I understand what you mean. The causal order of CD is captured. But the relationship of E to CD is not captured, correct? This makes it difficult to correlate ‘capture’ with Whitehead’s term ‘objectify.’ According to the metaphysics, I objectifies E *with* C and D *in relation*–integrating them and recreating them as data for subsequent subject-superjects. H does the same with respect to E, F, and G. And J does the same with I and H. Referring to the PR 65 quotation in my post, J’s potential integrations of I and H are partially reproductive (of the ‘given’ actual world in the back-facing lightcone) and partially creative (the data for creativeness being the ‘real’ potentialities for novel integrations–data that are ‘beyond’ that ‘given’ standpoint bounded by the lightcone)–i.e., Lorentz transformations giving either CDE or ECD. That kind of ‘extensive’ creativeness is, as I understand it, akin to the ‘intensive’ creativeness similarly enjoyed by a becoming occasion. (The former pertains to the coordinate division of satisfaction, the latter pertains to its genetic division.) The only a priori principle governing this creativeness is Whitehead’s desideratum of logical coherence–namely, that no integration/reproduction of data during concrescence will violate PNC. This is the key desideratum in his metaphysics (in my opinion) because it keeps the actual world unified. The only alternative would be a ‘many universes’ model where PNC can be safely violated.

Either way, the physics (and the metaphysics) requires a presupposed first principle: One where PNC is never violated (Whitehead); or one where PNC can be safely violated because of presupposed parallel universes. I believe the former to be the more economical choice.

Perhaps the question at hand is really: To what extent does PNC in Whitehead’s metaphysics yield a single, objectively ordered continuum of settled occasions? Perhaps in my graphic, PNC doesn’t adequately govern the choice between CDE and ECD for J. But might the reason be that there aren’t enough data represented in the graphic? If there were a trillion-trillion occasions added, wouldn’t there then be sufficient logical stricture via global satisfaction of PNC to force I to capture *either* CDE *or* ECD? (Akin to the way coarse-graining gets rid of superpositions in the decoherence approach to QM)? Would that be a viable approach to the problem?

Thus I do not see that the partial ordering implicit in the *metaphysical* concept of Past-Future-Contemporary is converted to a well orderedness by the fact that past occasions, and their connections, are recreated in later occasions. In this counter-example the light-cone representation of the causal relationships are re-presented of later occasions without their defining the relative order of (even) the beginnings and endings of the standpoints of metaphysically contemporaneous occasions.

W’s claim that “The many become one, and are increased by one”

is, it seems to me, hard to reconcile with any idea other than a serial single-file ordering of the complete occasions. The “many” that become X is only the set of occasions in occasion X’s causal past, But the occasions in X’s causal past is not increased by one by the completion of X.

And if the statement refers to some totality of completed (fixed and settled) entities, then by the time that X is completed, many occasions (some of X’s contemporaries) besides the occasions recreated by/in X should have been added to the totality.

MGE: Yes, I believe he meant the latter–that the ‘many’ refers to the totality of occasions. And you have definitely hit on the problem! The question for me is whether or not PNC taken as an a priori metaphysical first principle, writ large, will yield a well-ordered series of occasions in a scheme where:

1. The physical-causal efficacy of every actual occasion is restricted to its forward light cone.

and

2. Each and every becoming actual occasion is logically, internally related to each and every being.

I believe that Part III and IV in PR together posit both of these, respectively. With respect to 2 and its relationship to extensiveness, for example, Part IV.II.II Assumption 2 (PR 295) states that any two regions A and B are mediately connected such that both A and B are connected with some region C. (Fig. iii, p.296) The question is, if we bring 1 and 2 together, with added attention to governance of internal relations by PNC, will that yield an interpretation of “The many become one and are increased by one” that is free of the problem you raise?

So I wonder whether this claim by W, though very neat and beautiful, is rationally compatible with the rest of his claims.

Henry