Serial Order and Part IV of Process and Reality
by H Stapp ● July 30th, 2008 ●
Stapp’s Comments of 7/30/08 on the first part of Epperson’s:
Whitehead’s Theory of Extension as it Pertains to Henry’s Question: Part 2
Dear Mike,
Many thanks for sending your more concise attachment, which focuses on the particular passages in PR that you believe lead to the logical conclusion that W’s scheme, as described in PR, entails a single universal time in which the coming into being of the ALL occasions can be plotted.
MGE: Well, nothing in my attached document said anything about time ordering. The ordering he talks about in his Theory of Extension is purely mereological. Again, the thesis in W’s Theory of Extension, which I attempted to summarize in the attached document, is that Spatiotemporal ordering is a ‘more specialized’ form of ordering embedded in a more fundamental, purely mereological, serially ordered, inclusively related regions—regions that are NOT spatiotemporal! These regions are, for Whitehead, purely first-order regions describing the internal relatedness of actualities. They are, in other words, metaphysical regions, not physical regions. They are denumerable. They are serially ordered.
“It is to be noticed that each abstractive set is to be conceived with its members in serial order, determined by the relation of inclusion.
[i.e., 'The many become one and are increased by one.']
The series starts with a region of any size, and converges indefinitely towards smaller and smaller regions, without any limiting region…”
An abstractive set is one where “(i) any two members of the set are such that one of them includes the other non-tangentially and (ii) there is no region included in every member of the set.”
Perhaps we can look at it another way. A more fundamental ordering such as the mereological scheme of extensive abstraction proposed by Whitehead in Part IV may not be wholly revealed in some more specialized ordering, such as spatiotemporal ordering.
HPS: My understanding of Part IV is that it was W’s attempt to deduce Geometric properties from logical properties. In our epoch physics is imbedded in a 4-dimensional space time filled with straight lines. W makes it clear at the outset of Part IV that he finds the usual approaches to the introduction of straight lines Into the spacetime of physics unsatisfactory. Part IV is his attempt to get this undergirding of physics from what he regards as more satisfactory assumptions. These assumptions are weaker than just a blatant assumption of a metric spacetime continuum. He uses weaker topological assumptions, plus an assumption of the existence of a class of ovate regions. From these weaker assumptions he is able to get the straight lines that in our Epoch undergird physics. Thus his work in Part IV when applied to our own special case gives a geometric structure to the 4-d spacetime continuum that underlies our lives, and in which each occasion has its standpoint. The construction of these straight line depends upon the nesting property that you emphasize above. It is part of the construction of the geometry, which in our own special case is exactly the 4-d spacetime continuum of present day physics. There is not, in our own world, also some other pertinent geometry, or at least there need not be any other. The most direct interpretation of W is that the geometry that he erects in Part IV is, for our lives, exactly to spacetime upon which our physics is based.
“The many become one and are increased by one” in context (PR 21) refers to the process of the coming into being of a single actual occasion. There is no presumption that it entails in any way an absolute serial ordering of contemporary occasions. Indeed, he endorses “relativity” which essentially denies such an absolute serial ordering for contemporaries. The central thrust of his whole work is to provide an ontological foundation that explains “creative advance” and reconciles it with the existence of contemporaries in conformity with the relativistic notion that contemporaries do not come into being in a serially ordered manner..
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MGE: The most fundamental extensive order for Whitehead, as he lays out in his theory of extensive abstraction, is DENUMERABLE. Any more specialized super-denumerable extensiveness, such as relativistic space-time extensiveness, must be shown to derive from that more fundamental denumerable mereological order. I’m not saying his argument is flawless; in fact, it’s a bit counterintuitive. Normally, one considers the set Q of rational numbers (denumerable) to be a dense subset of the set R of all real numbers, which is super-denumerable.
HPS:This nestedness pertains, I believe, in our universe, to regions of spacetime: it pertains to nested open sets in spacetime. It pertains to geometry, not to some serial order of coming into beingness. I believe, at present, that your construal of Part IV is a misapplication of the content and intent of that part. In short, I see Part IV as W’s attempt to deduce an aspect of the geometric structure of the spacetime in which we live from essentially logical premises, including his essential-for-this-purpose assumption of the existence of a preferred nested set of ovate regions.
PR 35: “In these lectures the term ‘creative advance’ is not to be regarded in the sense of a uniquely serial advance.”
PR 65 “Curiously enough, even at this early stage of metaphysical discussion the influence of the ‘relativity theory’ of modern physics is important. According to the ‘uniquely serial” view of time two contemporary actual entities define the same actual world. According to the modern view, no two actual entities define the same actual world. Actual entities are called ‘contemporary’ when neither belongs to the actual world of the other.”
As regards the meaning of ” The many become one, and are increased by one.” the context (PR 21) makes clear, I think, that this refers to the coming into being of a single occasion: the many in its actual world become integrated into itself, which actual world now includes also itself. Its contemporaries are not incorporated. Indeed, the description of the incorporation of a created IMAGE of a present world now (PR 121-127) makes it clear, I think, that the creation of this image is rather analogous to the creation in our own consciousness, on the basis of delayed data arriving from our receptors, and of past experiences, of an ‘imagined best guess’ for a ‘contemporary now’ that we cannot yet know or access. I do not see in this account by W any suggestion of any serial order of coming into being of contemporary occasions. Any such suggestion must, I think, be regarded as going what W’s words entail or suggest.
All the best,
Henry
Hi Henry:
Please see my post of August 3 (http://c-p-n-s.org/discussion/?p=32 )for a comprehensive reply to this post.
Here, however, are just a couple of specific replies which I will offer here as excerpts from my August 3 post:
“HPS: My understanding of Part IV is that it was W’s attempt to deduce Geometric properties from logical properties. In our epoch physics is imbedded in a 4-dimensional space time”
I agree. For Whitehead, it is the logical/mereological order that is fundamental to the spatiotemporal geometric order. This is specified in his Theory of Extension. And the ‘embedding of physics in 4d spacetime,’ to which you refer, is second-order for Whitehead, according to his Theory of Extension in Part IV. For Whitehead, physics is, indeed, embedded in 4d spatiotemporal extensiveness. But this 4d spatiotemporal extensiveness is likewise embedded in this first-order logical-mereological extensiveness. That is the fundamental order of the extensive continuum. He specifically states this in Part IV. Per Part IV, 4d spacetime is not the fundamental extensive order in Whiteheadian cosmology and metaphysics.
“HPS:This nestedness pertains, I believe, in our universe, to regions of spacetime: it pertains to nested open sets in spacetime. It pertains to geometry, not to some serial order of coming into beingness.”
I disagree. The nestedness described is strictly mereological as developed in IV.II-IV.III. Later in Part IV, this mereological extensiveness is *applied* to spatiotemporal extensiveness–but not in a way that the later somehow becomes promoted to the fundamental, overriding order of the extensive continuum–totally displacing the mereological order. I do not find this reversal of relationship anywhere in any of Whitehead’s writings.
“HPS: I believe, at present, that your construal of Part IV is a misapplication of the content and intent of that part. In short, I see Part IV as W’s attempt to deduce an aspect of the geometric structure of the spacetime in which we live from essentially logical premises…”
Exactly. And since the geometric structure is deduced from the mereological structure, the latter is obviously fundamental; indeed, it reflects and is founded on first principles of extensiveness that Whitehead explicitly says are to be correlated with the first principles of prehension–i.e., the categoreal obligations are reflected in both.
I am confused because you seem to be saying two contradictory things: First, you say that “I see Part IV as W’s attempt to deduce an aspect of the geometric structure of the spacetime in which we live from essentially logical premises…” This, I think, accurately reflects what Whitehead is saying in Part IV.
But then you characterize the mereological order in Part IV as an abstraction from a *more fundamental* 4d spatiotemporal order–’more fundamental’ because the relativistic strictures of the latter override the fundamental mereological order. How can this be if it is the logical-mereological that is fundamental? How can this be if it is the order from which, as you rightly say, the 4d spatiotemporal extension is deduced?
On my reading of Part IV, I see no evidence that the ‘more special’ second-order relativistic spatiotemporal order in any way overrides the mereological order which Whitehead clearly states is the fundamental order of the extensive continuum.
Finally, I would like to contextualize the two quotes from PR you offer:
PR 35: “In these lectures the term ‘creative advance’ is not to be regarded in the sense of a uniquely serial advance.”
PR 65 “Curiously enough, even at this early stage of metaphysical discussion the influence of the ‘relativity theory’ of modern physics is important. According to the ‘uniquely serial” view of time two contemporary actual entities define the same actual world. According to the modern view, no two actual entities define the same actual world. Actual entities are called ‘contemporary’ when neither belongs to the actual world of the other.”
In the preface to PR, Whitehead says that the proper understanding of his philosophy is given in Parts III and IV when taken together. One ought not, in other words, base ones understanding of ‘extensive continuum’ by reference primarily to Part II.II (the source of your 2nd quote)–even though it is entitled ‘Extensive Continuum.’ For example, your second quote says nothing about how contemporary regions are ordered by subsequent occasions whose regions include them both. This is the sort of problem that is addressed in Part IV; this is why in the preface to PR, Whitehead recommends that any particular treatment of any particular topic in PR (he specifically mentions spatiotemporal extension in this admonition) must be properly contexualized within the whole presentation–which he says is given in Part III and IV taken together:
“In the third and fourth parts, the cosmological scheme is developed *in terms of its own categoreal notions, and without much regard to other systems of thought.* For example, in Part II there is a chapter on the ‘Extensive Continuum,’ which is largely concerned with the notions of Descartes and Newton, compared with the way in which the organic philosophy must interpret this feature of the world. ***But in Part IV, this question is treated from the point of view of developing the detailed method in which the philosophy of organism establishes the theory of this problem.*** (PR xii).
This, I think, is why it is so easy to find seemingly contradictory quotations in PR. It is because of the non-linear presentation of the scheme in PR. I think such quotations cease to be contradictory when properly contextualized as Whitehead recommends. To me, the non-linear treatment is more of an ‘inward spiral’ treatment, where each quadrant is revisited again and again, but with increasing precision each time.
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