“The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.”
–Alfred North Whitehead

Standing Firm in the Flux: On Whitehead’s Eternal Objects (draft article)

The article to follow is a draft posted here for your review. As usual, I invite your comments and criticisms (Note that I have been continually updating the draft below in light of helpful feedback and my own ongoing reflection: the doctrine of eternal objects is a deep ocean, but hopefully this study at least shines some light a bit below the surface of the water). I’ll be presenting some morsels from this study of Whitehead’s eternal objects in mid-September at the Whitehead Research Project’s free online conference focused on his Harvard lecture student notes.



16 responses to “Standing Firm in the Flux: On Whitehead’s Eternal Objects (draft article)”

  1. Herman Greene Avatar
    Herman Greene

    Will review and comment.

  2. dltooley Avatar

    I am not clear on the distinction and/or relation between ingression and prehension.

    At my stage of Whitehead this piece of as helpful, but I am also critical of the term eternal objects. At least as I understand it!

    I’m interpreting eternal objects as qualia, and as such I don’t see them as eternal, though they may well be so within a species of organism.

  3. perkwunos Avatar

    Your interpretation of what Whitehead means by an “abstractive hierarchy” seems very different from my own, and I’m not sure who’s more accurate to what Whitehead meant or which makes more sense. These platonic solids are all in themselves patterns, relations: they are the forms of how simple sensa can then hang together—but for them to be part of one abstractive hierarchy you’d have to clarify how these five are then relating to one another in one complex form to truly find the vertex (otherwise, you’re just thinking of five distinct eternal objects that could all be their own vertex in distinct abstractive hierarchies)—and you’d have to further clarify the simplest eternal objects to truly find the base, because none of the platonic solids in themselves can qualify as simple. Imagine we had a colorful diagram in front of us illustrating the five platonic solids together. I think abstracting the form of this diagram constitutes a better example of one complex eternal object that then forms the vertex of an abstractive hierarchy. At the vertex you have the form of the diagram: all the component eternal objects together in just that form of relatedness with just those colors in their right places to help illustrate the lines and sides of each solid. But from there we could start analytically discriminating the component forms. For one thing you have the pattern of how all five solids are situated among each other: maybe the tetrahedron is the first on the left, dodecahedron last on the right, with them all in a linear sequence. Then also each solid itself constitutes a patterned, complex eternal object: it is the relation of the colored lines and spaces constituting faces. Then there are patterns within the solids: patterns of the straight lines we can discriminate as components of each solid. And as far as color goes, maybe we can say the lines are all black and the faces are alternating shades of blue, red, and yellow. Then that means that we discriminate the eternal objects for these colors as well. At the base of the abstractive hierarchy you would then have all these patterns discriminated from one another and from the colors—as simply patterns that could take on any sense and could combine with any other patterns—and then you’d have all these colors (which at the simplest may just be four sensa for four exact shades of black, blue, red, and yellow). That is what I had believed the meaning of an “abstractive hierarchy” is for Whitehead in Science and the Modern World, with some help clarifying the fundamental types of simple eternal objects as he more rigorously defines them in Process and Reality (namely, there are sensa and there are patterns for how sensa relate: those are thus the two types of eternal objects you’d find at the base).

    1. Matthew David Segall Avatar

      Thanks for this, Ben. You sent me back to SMW to reread. When Whitehead says we can conceive of a route of progress in some “assigned mode of abstraction” (SMW 167), I took him to mean that it is up to the one doing the analysis to define which set of eternal objects they are analyzing. In this case, I took Whitehead’s example of a tetrahedron, but assigned it a different mode of abstraction by referring to the hierarchy of regular solids. (Incidentally, in his reading of a tetrahedron as a complex of colored surfaces, he refers to only three faces, instead of four… I guess he is thinking of the solid only from a spatiotemporal perspective, wherein the fourth face is hidden, but this seems odd as I had thought he was analyzing the realm of possibilities as they stand in relation among themselves, rather than in relation to some actual occasion…). In the set of objects so defined, it is the simplest conceivable and so at the base of the abstractive hierarchy. Now, a lot hinges on Whitehead’s meaning with regard to assigning modes of abstraction, because this implies the participation of my conceptual prehension (i.e., it is a view on pure possibility from the perspective of actuality). Can we examine the internal relations among possibilities themselves? We can do so to the extent that an ingressed eternal object carries its associated hierarchy with it into actuality, but the “abruptness” of our conceptual prehensions means we can only trace these relations so far. Whitehead says the relations among eternal objects themselves are entirely “unselective” (SMW 164), which I guess means that the sort of assignment of mode made by defining a hierarchy as that of “regular solids” is in some sense arbitrarily imposed by my interests. As far as the more complex Platonic solids, my understanding is that the simpler are derivable from the more complex (e.g., the icosahedron to be analyzed into the dodecahedron by finding the center of each triangle and connecting these points to one another, and so on using analogous operations progressing to the tetrahedron at the base), though in re-reading my original sense of this progression I had the dodecahedron at the vertex when it should really be the icosahedron. But given your reflections I really must admit that much of what Whitehead has to say about progress along routes of abstraction and abstractive hierarchies remains somewhat obscure to me.
      Another question I have here concerns how we are to determine what objects are truly simple. Color is not as straightforward as it first appears, as I try to spell out. Nor are geometrical forms (points, for instance).

      1. Matthew David Segall Avatar

        Well, I need to follow upon this, as Euclid has the dodecahedron at the vertex. The two solids can nest inside one another in either direction, so this example is seemingly breaking down. Back to the drawing board…

      2. Matthew David Segall Avatar

        Having thought this through, I can see that you are right, the Platonic solids don’t work as an example. I’m grateful to you for zeroing in on this! I’ve edited the paper and added footnote 7

      3. perkwunos Avatar

        This response ended up being longer than I thought it would, and I am not sure if I am touching upon quite exactly the interpretation you seem to have in mind.

        You are referring to the abstractive hierarchy as if it only concerns a set of eternal objects, of which one is found to be most complex whereas another one is found to be the simplest. However, I would say an abstractive hierarchy does not concern merely a set—which for the later Whitehead of PR would be to say merely a multiplicity—but rather it concerns a definite relationship among any such identified set: if a finite hierarchy, then it concerns a vertex, one complex eternal object expressing a definite relationship among any set of component eternal objects (or, if it is an infinite hierarchy, then we do not have a vertex, i.e. a maximum grade of complexity, so much as an indefinite progression into increasing complexity that therefore progresses into more unified relationships among the components). This is the difference, to use Whitehead’s example, between “the set of three eternal objects A, B, C” and “R(A, B, C)” which is “some definite possible relatedness of A, B, C” (166). From the vertex R(A, B, C) you then find as its base the set A, B, C, which are its components. So as in your example, we start with the set of platonic solids—but for that very reason, we have no single vertex forming one hierarchy, no relationship among the five solids. (As an aside, I’m made to think again of how Auxier and Herstein argue eternal objects are determinate but not definite, despite the fact Whitehead talks about definite eternal objects, i.e. as he just said there a “definite possible relatedness”. I still don’t get that.)

        I believe this is also expressed by Whitehead’s “condition of connexity”, where an abstractive hierarchy “springs from its base; it includes every successive grade from its base either indefinitely onwards [if it is infinite], or to its maximum grade [if it is finite]; and it is ‘connected’ by the reappearance (in a higher grade) of any set of its members belonging to lower grades, in the function of a set of components or derivative components of at least one member of the hierarchy” (168). That is to say, the members of the base are in the vertex in one form of relatedness to each other.

        Problems with what really constitutes a simple eternal object per se aside, I think it is still important to note that Whitehead requires an abstractive hierarchy to be “based upon some definite group of simple eternal objects” (167). Not relatively simpler compared to other eternal objects, but simple per se, so that “the base … is a set of objects of zero complexity” (167). I believe this and the condition of connexity referenced above also means that the base must have more than one simple eternal object–or else the higher grades have no components to form their complexity–i.e., if your base is just A then all you can have is just A; you need at least A and B to then have R(A, B).

        Your point about abstraction feels like a difficult one for me to unpack. In SMW Whitehead distinguishes between “abstraction from actuality” and “abstraction from possibility” (167). The former is easy enough to understand—simply the abstraction of eternal objects from any actualization, to consider them as they may possibly exist in any actuality. But abstraction from possibility means you’re considering some of the possible relationships of an eternal object to the exclusion of others. Hence, R(A, B, C) is more abstract in this sense than just A. That therefore means the vertex of any abstractive hierarchy will also be the most abstract, in the sense of abstraction from possibility: it excludes the most possibilities compared to the lower grade components within it; in turn, simple eternal objects are the least abstract. So when he says an abstractive hierarchy is a “definite progress towards some assigned mode of abstraction from the realm of possibility” what he means is that whatever progression we do choose to look at, and thus whatever eternal objects we conceive of in exclusion of other eternal objects, we must increasingly exclude possible relationships as we move away from the base. This is the same as what I had said earlier, that the hierarchy progresses into more unified relationships among the components.

        This is why each actual occasion’s physical pole then ultimately has one infinite abstractive hierarchy defining its essence: it realizes that essence, in space and time, to the exclusion of other possibilities. Thus as he says we are more concretely descriptive when we are also more abstract in possibility. So every actual occasion has as its definite relational essence an infinite abstractive hierarchy, which would be _the_ accurate descriptive predicate of it if we were to judge of that actual occasion. But then, as you write about, the multiplicity of eternal objects find their primordial unity of possible relationships in their entertainment by God—and this entertainment thus cannot exclude any relationships but considers all possibilities, which must, then, mean God’s mental pole is not one abstractive hierarchy. Thus I do not think you are right in describing God as “the vertex of vertexes”, nor can God be entertaining merely one complex eternal object (“one idea” as you put it). Physical realization creates an infinite abstractive hierarchy (which means there’s no vertex)—excluding possibilities of relationship; our mental entertainment creates a finite abstractive hierarchy (with a vertex), for we do not have infinite conceptual power. But for God’s primordial nature I think we must get rid of this claim to abruptness and instead identify the conceptual entertainment as infinite and not consisting of any one abstractive hierarchy (rather we may say it consists of infinitely many infinite abstractive hierarchies).

        Returning to this part of SMW, I’m made to feel again like I need to better understand the logic Whitehead has in mind. As you note in this paper, Whitehead is doing all this in conscious distinction to earlier Aristotelian taxonomic logic. He is, instead, appealing in some ways to classical predicate logic and its theory of relations (i.e., Principia logic) and then also set theory—but also, from what I just said, the abstractive hierarchy is his analysis of eternal objects as more than just sets, as being internally defined by possibilities of relationship among each other.

        Also, of everything I have written, this is truly up there as something that would come across to most as the unintelligible ravings of a madman if they have no familiarity with Whitehead. I’d be curious if anyone brings up things such as this in the peer review.

      4. Matthew David Segall Avatar

        Very helpful. I am going to have to think more re: God as vertex of vertexes. I grant that God’s primordial envisagement includes every possible relationship, but all such relationships are nonetheless graded, with the most beautiful winning priority. If *Beauty* is not what God ultimately has in mind, how are we to conceive of the gradation of the primordial nature’s envisagement? Doesn’t an infinite abstractive hierarchy have a vertex of infinite complexity?

      5. Matthew David Segall Avatar

        In reviewing the secondary literature going back to the 50s, it is clear enough that little agreement exists among interpreters of Ch. 10 of SMW! So I suppose we are in good company

  4. perkwunos Avatar

    On the relationships among eternal objects in God’s primordial nature being “graded, with the most beautiful winning priority”:

    I think the valuing of eternal objects in God’s primordial envisagement—and any resultant hierarchy of the value or beauty of eternal objects—must be sharply distinguished from the grading of complexity of eternal object’s individual essences, which then constitutes an abstractive hierarchy. Perhaps these two things—the hierarchy of eternal objects’ value to God and an abstractive hierarchy encompassing all eternal objects—converge in some ways, but I think that is left to be seen only after clarifying their two distinct meanings.

    For one thing, there is the argument I had mentioned before on twitter, that this is conflating a hierarchy of valuing that belongs to the determinacy of an actuality—God’s subjective form—and a hierarchy of complexity that belongs to the determinacy of eternal objects. Abstractive hierarchies concern the eternal objects in themselves; gradations of value concern God’s activity.

    Now this is where it’d be appropriate to respond to your tweet that asked, “Are we as finite occasions capable of analyzing eternal objects independent of God’s infinite conceptual prehension of the realm?” I would say yes, if by that we mean we can analyze the intrinsic determinations of eternal objects—their “individual essence” and “definite status”—in abstraction from God’s own feeling of such. Now, obviously we could never actually do such if God didn’t primordially supply the relevance of these eternal objects for our experience; all eternal objects we are capable of conceptually prehending, are abstracted either from the actual world or God’s primordial nature (Whitehead’s accepted form of “Hume’s principle”). But the ability to abstract eternal objects is nonetheless real.

    As Whitehead says in SMW, an eternal object is abstract because it “is comprehensible without reference to some one particular occasion of actual happening” (SMW 159). You might object here that this doesn’t necessarily exclude the requirement of reference to God—in the sense that the entity “God” will take on in Whitehead’s mature scheme of thought—for God is not an actual occasion, a “particular occasion of actual happening”, but rather a non-occasional actual entity. But Whitehead had not really developed his theory of God in SMW, and in PR he makes his point about eternal objects far more clearly: “an eternal object refers only to the purely general any among undetermined actual entities” (256), which is to say a proposition about eternal objects’ own intrinsic determinations is one where the logical subject is quantified and ranges over all possible actual entities, but requires no reference to a particular actuality, even God, for its truth-value to be secured (this is distinct, say, from the claim, “For all people in that room over there, they are not drinking coffee”—which also has a quantified logical subject—where you’d actually have to check to make sure there’s not a single person drinking coffee). So we can entertain an eternal object in itself—its own definite status and intrinsic determinations—and this will require no reference to any actual entities, only reference to the eternal object’s definite status as possibly ingressing into any or some actual entities.

    Now, granted, as Whitehead puts it in AI, “the qualitative content of the object prehended enters into the qualities exemplified in the subjective form of that prehension” such that “the subjective form of a prehension is partly dictated by the qualitative element in the objective content of that prehension” (251). Thus the hierarchical grading of eternal objects in terms of how they may contribute to beautiful experience could be entirely determined by their individual essences without any necessary reference to God’s own entertainment of this. Still, in this case we would be dealing with two distinct aspects of an eternal object’s intrinsic determinacy: abstractive hierarchies concern grades of complexity, while the primordial envisagement would in this sense concern how beautiful each object is. Complexity in feeling is not synonymous with beauty or intensity of feeling, even if it contributes to it, and so these two cannot be conflated. To state that the most beautiful complex eternal object is the vertex of an abstractive hierarchy would require that the most beautiful will also be the most complex. This is possible but must be argued for.

    But I do think we also need to be careful and point out here that the primary meaning of beauty is the beauty of experience, i.e. an aspect of the subjective form of a prehension. God’s primordial nature is in fact deficient in its realization of this (whereas God’s consequent nature is the maximum realization of beauty possible by any actual entity).

    God’s primordial envisagement does not so much concern beauty, but rather concerns the beautiful, i.e. it concerns an object’s capacity to contribute to the beauty of an actual entity’s subjective form. The leap from objective datum to subjective form is all-important for Whitehead, constituting the very process of reality itself, and for actual occasions mere conformity of the subjective form to the objective datum is of course just death. To quote Whitehead: “The objective content is ‘beautiful’ by reason of the Beauty that would be realized in that occasion by a fortunate exercise of its spontaneity” (AI 255). The beauty any eternal objects may contribute to is only realized if the actual entity is also exercising its spontaneity: intensity of feeling requires a level of autonomy and novelty in subjective form. Whitehead did not favor that view of the supreme Good that saw it as some pre-existing static ideal, and cast our contingent adventures into a secondary role, a mere shadow of the eternal. The potential of God’s primordial nature is valuable when used creatively and constructively, not when merely dealt with as a contemplative spectator, and for that reason it also has no final culminating end but contributes to a plurality of ends. So, does it make sense to talk about _the_ vertex of beauty that would be the final end of actuality, if only it could realize it? This seems to me something Rorty missed in Whitehead when he starts talking about the ”Being” of the “final eternal object”, and it perhaps leads him to miss how Whitehead is very much cosmologizing in the spirit of the American pragmatists.

    Now as for the question of if infinite abstractive hierarchies “have a vertex of infinite complexity”:
    An abstractive hierarchy is finite “if it stops at a finite grade of complexity” and, given this, it will therefore “possess a grade of maximum complexity” (SMW 169). I thus infer that an infinite abstractive hierarchy is defined by not possessing a grade of maximum complexity—for its progression into higher grades of complexity must by definition never stop. This grade of maximum complexity will by definition have one member in which all components are connected, a complex eternal object: this is the vertex. So saying an abstractive hierarchy has no maximum grade of complexity is the same as saying it has no vertex. This is the only definition of the term Whitehead gives in this book, and the only context for its use is him discussing finite abstractive hierarchies (it only comes up again after this initial defining of it when he discusses how abruptness results in finite abstractive hierarchies—which thus each have a vertex). This is why I have concluded only a finite abstractive hierarchy has a vertex.

    But something does further complicate this. Whitehead also clarifies that “the infinity of the number of the members of the base has nothing to do with the question as to whether the hierarchy be finite or infinite” (SMW 169). This means that you could have an infinitely complex eternal object as the vertex of a finite abstractive hierarchy—so long as that one eternal object expresses a definite relationship among the infinity of its components (said components at their simplest then making up the base)—but wouldn’t this one definite relationship among the infinite set still be to the exclusion of other possible relationships? It would be a relation relating an infinity of other relations to itself to the exclusion of no others (and we must keep in mind in all this, that any two infinite sets are not necessarily equivalent). Here I’m not so sure of what to conclude; having already written way too much, I feel like I’ve swum out beyond what I can reasonably discern the premises and principles of, and am like Odysseus when he is shipwrecked, left to hope some gods might push him to the island of Phaeacia.

    As Abner Shimony said in an AIP oral history interview, in SMW Whitehead’s “exposition of his own philosophy is almost incomprehensible.” I have to agree, though with emphasis on “almost.” I think it is very hard to make full use of the book without looking at in retrospect with an understanding of a coherently intelligible system you can develop by reading PR.

    1. Matthew David Segall Avatar

      This is a really helpful set of reflections. My first question in response is “Why aren’t you participating in this conference?!” I hope you are attending, at least.

      These are deep waters. I admit to feeling somewhat embarrassed by the task we have set ourselves here, namely, peering into the soul of the world, into God’s mind or primordial appetition, to see what in the way of metaphysical principles may be apprehensible to us there. Your sympathy for Odysseus got me thinking of the whole history of European metaphysics by analogy to the successive discovery of wider waters by westward sailing explorers. At one time, the Mediterranean seemed endless. Then the Atlantic and Pacific were mapped, then the moon, the sky, other planets and galaxies… Whitehead took the new ideas from evolutionary, quantum, and relativistic theories, generalized them, and I’d say swam out as far into the encompassing oceanic mystery as any in his lineage prior. But at the extreme edges of abstraction knitting his scheme together, such as those explored in this essay and our exchange, I admit I cannot but perceive confusedly. Whitehead (like Leibniz) admits as much himself, blaming the abruptness of our finite (nondivine) conceptual prehensions of otherwise infinite physicality. Whitehead’s is a strange sort of physics, of course, since for him every drop of physis is impregnated with God’s initial Eros. I cannot bring myself to understand how I would ever have the inclination to pursue metaphysics, or to conceive of its possibility, much less actually succeed at the task of discerning necessary ideas, without God’s initial Eros. What becomes interesting at this point is the role we play, as metaphysicians contemplating the original urge to emerge, in the realization of God’s consequent nature. I don’t mean to say that only philosophers participate in the completion of God’s nature, but rather that every creature is in some measure a metaphysician, a lover of wisdom. So, hearkening back to the spirit of cosmologizing effective in the American pragmatists (sans Rorty!), perhaps the important issue of this exchange is simply the question (one which, to his credit, Rorty insisted on): What good does any of this do us?

      1. perkwunos Avatar

        I am indeed registered to attend the conference; I may not make it on the first session, on Friday, if I’m working, but ought to be able to make it for your part on Saturday. It actually does look promising. Lots of new names I’m not familiar with, to be honest, so very interested to see what they’ve got.

        I remember being struck by a passage in John Hermann Randall, Jr.’s book on Aristotle, where he points out that when Aristotle says in the Metaphysics that all human beings by their nature desire to know, he’s saying that as part of a systematic view that all things by their nature have urges towards some ends: on a general level we are lured towards knowledge just as heavy bodies incline towards the earth, etc. I think Whitehead himself makes clear that even if the truth per se is not an intrinsic good–only beauty has that status–the search after truth so heavily enhances the intensity of beauty we can appreciate in the world around us, that knowledge virtually becomes an intrinsic good. So I agree in general with your point that any metaphysical pursuit is itself carrying out the Eros that initiates all natural events. If I may speculate, I don’t think God blushes at the attempts to conjecture the rational outlines of this very activity, but is rather pleased by it.

        At any rate, I’m interested to see any changes you make and what this paper looks like in its final form.

      2. Matthew David Segall Avatar

        Ben, I’ve substantially revised the version now posted above (including footnote 11 acknowledging your helpful feedback). Thanks for your engagement!!

  5. First Cause Avatar
    First Cause

    “What good does any of this do us?”

    Well said, for Rorty was a genius in his own right. The short answer to Rorty’s question is this: as long as we as a species insist upon perceiving reality through the prism of subject/object metaphysics, it does us absolutely no good whatsoever. All original assumptions are grounded by the metaphysics upon which they are constructed, and as long as the metaphysical foundation is flawed, any subsequent intellectual construction built upon that foundation will be flawed also.

    Robert Pirsig was an obscure genius who recognized that fact, preceded by other historic geniuses the likes of Kant, Nagarjuna and Parmenides.

  6. Herman Greene Avatar
    Herman Greene

    I agree with your analysis entirely Matt.


  7. Herman Greene Avatar
    Herman Greene

    I just read our article and agree with it entirely. 

    One idea to keep in mind when speaking to people who disagree with your analysis (and with Whitehead’s) is this thought on page 1 of Modes of Thought. Whitehead says philosophy should consist in a free examination of some ultimate notions. He then proceeds to say: “There are no definitions of such notions. They are incapable of analysis in terms of factors more far-reaching than themselves.”
    These ultimate notions are necessary to various groups of meanings. 

    So Whitehead can only posit eternal objects he cannot explain why there are eternal objects or what they are other than his description of them.

    The test is whether they have explanatory value. 

    What I object to when I hear from some Whiteheadians is their interpretation of “God knows all the possibilities.” They interpret this as God is envisioning all the outcomes of actual occasions and in an extreme view that God envisions the sequential possibilities for future actual occasions depending on the outcome of a prior one.

    God knows all the possibilities only in the sense of the primordial envisagement of eternal objects.

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