Notes on Whitehead’s Analysis of Abstraction in Science and the Modern World

Science and the Modern World (1925) is not only a historical treatment of the rise and fall of “scientific materialism” in the modern period. It also records Whitehead’s turn to metaphysics in search of an alternative cosmological scheme that replaces matter in motion with organic process as that which is most fundamental in Nature. 

Perhaps the most difficult chapter in Science and the Modern World is “Chapter X: Abstraction.” Whitehead puts aside the peculiar problems of the special sciences that he has treated in earlier chapters (e.g., the quandaries of quantum and relativity theories), and directs attention instead to a dispassionate consideration of the nature of things as such (158). He aims to justify his metaphysics in three ways: 

  1. experientially by way of a descriptive account of the actual occasions composing our immediate awareness of ourselves and the natural world; 
  2. systematically by bringing many types of such occasions into categorical harmony; and 
  3. onto-epistemically such that the account of what there is to be known reveals also how we can know it (i.e., knowledge in Whitehead’s scheme comes to be understood “as an adjunct within things known,” rather than as a view from nowhere).

“In any occasion of cognition, that which is known is an actual occasion of experience, as diversified by reference to a realm of entities which transcend that immediate occasion” (158). In his chapter on “Abstraction,” Whitehead is seeking to unveil the metaphysical conditions of finite knowledge. What must the metaphysical situation be such that limited minds like ours can reflect upon particular truths? His so-called “organic realism” is radically empirical, but unlike prior empiricists, Whitehead argues that the proper understanding of actuality requires that reference also be made to ideality, that is, to a realm of “alternative suggestions” or unrealized potentials. Thus, actuality cannot be made sense of without some reference being made to alternative possibilities; and, at the same time, infinite possibility cannot be made sense of without some reference being made to definite matters of fact.

Any given occasion of experience may include within its aesthetic synthesis various untrue propositions about the actual world. It frequently occurs that we entertain delusive perceptions, say, mistaking a balloon at the edge of our field of view for a stop sign, or an airplane in the night sky for a star. These untruths represent alternative possibilities that are not but may be. They ingress into occasions of experience not only to paint them with definite characteristics (e.g., “red” or “brightness,” etc.), but to aid occasions in their interpretation of the given facts by availing alternative possibilities. Whitehead calls these possibilities “eternal objects” in order to distinguish them from the classical philosophical conception of “universals.” Like universals, eternal objects are abstract, meaning they can be understood independently of their ingression into particular concrete occasions of experience. “Red” or “sphere,” as eternal objects, may be realized together in an actual entity, say, a balloon; but they could also ingress separately into other actualities, like a stop sign or the Sun. But Whitehead wants to avoid further association with the philosophical baggage of “universals,” especially Aristotle’s system of logical classification in terms of genera and species, which while useful for the analysis of actual fact distorts the analysis of abstract possibility that he seeks to undertake. Rather than a classificatory logic, Whitehead analyzes the realm of eternal objects in a more mathematical way. 

Whitehead thus begins his analysis of the metaphysics of possibility. He admits that many may find the procedure “irksome,” and advises those without the patience for such an inquiry to skip the chapter entirely. He tells us that eternal objects have both an individual and a relational essence. The relational essence is the object’s determinate internal relation to every other object in the infinite realm of possibility. This means that each eternal object is systematically and necessarily constituted by its relations to every other eternal object. “Red,” for example, has a perfectly definite relationship not only to other colors but to all other eternal objects (the internal relations among colors considered abstractly is an interesting issue that I hope to go into in a subsequent post*). These relationships come in the form of “abstractive hierarchies,” with simpler objects (like colors or geometric points, which cannot be further decomposed) at their bases, more complex objects at their vertexes, and objects of proximate complexity in-between. There are many such hierarchies in the realm of possibility. The Platonic solids offer one example of an abstractive hierarchy. The tetrahedron is the simplest regular solid, and so if the abstractive hierarchy we are analyzing is defined as that of regular solids, it forms the “base,” with the octahedron, hexahedron/cube, and icosahedron as proximates, and the dodecahedron as the “vertex.” But we could also define a hierarchy more broadly as that of regular shapes: then the tetrahedron can be analyzed into flat triangles, which are themselves composed of lines, themselves composed of points. The point is then the simple “base” of a new abstractive hierarchy. (For purposes of illustration, I am ignoring the fact that the Platonic solids are depicted as colored below, as including this feature would complicate the example too much; just note that, at least for human perception and imagination, without color there can be no such thing as a definite shape or solid).

As internally related among themselves, eternal objects remain “isolated” within their abstractive hierarchies from the definite values achieved by particular actual occasions. It is this isolation that allows incompatible possibilities to coexist. Eternal objects considered in abstraction have contraries in their relational essences which cannot be simultaneously actualized. Thus, in the realm of possibility, the law of non-contradiction cannot be applied. 

The individual essence of an object, then, is its unique contribution or mode of ingression into a particular occasion. Once ingressed, eternal objects are liberated from their isolation by way of the “realized togetherness” achieved in the aesthetic synthesis of an actual occasion. In contrast to the determinate internal relations among eternal objects in abstraction from particular actualities, relations between these objects and actual occasions are indeterminate and so external. In Whitehead’s terms, objects have “patience” for many possible relations or modes of ingression into occasions. While an eternal object in its isolation remains internally determined by its place in one or more abstractive hierarchies, when and where it ends up ingressing into particular spatiotemporal situations remains open-ended, a problem awaiting its solution, as it were. 

Each actual occasion is a prehensive synthesis of the entire infinite realm of eternal objects, with an aesthetic gradation determining the relevant value of each eternal object for its experience. Every occasion is thus a self-creative synthesis of positively prehended “being” (i.e., those eternal objects that are valued and thus individually effective in its aesthetic synthesis) and negatively prehended “non-being” (i.e., the systematic substratum of unfulfilled because unvalued alternatives). The synthetic prehension, or concrescence, achieved by a particular actual occasion is thus the solution of the indeterminateness of its relation to the realm of possibility into the determinateness of spatiotemporal actualization. “Every actual occasion is the solution of all modalities into actual categorical ingressions: truth and falsehood take the place of possibility” (161). In other words, upon ingressing into the “realized togetherness” of a particular actual occasion, eternal objects must conform to the law of non-contradiction. An actual entity cannot be both a square and a sphere. 

It becomes apparent at this point that a further general fact about our universe must be acknowledged: that is, the systematic mutual relatedness inherent to the character of the possibilities with patience for actualization. This general fact is the spatiotemporal continuum, which for Whitehead “is nothing else than a selective limitation within the general systematic relationships among eternal objects” (161). Space-time limits how possibilities can ingress into actualities. Space-time is thus “the locus of relational possibility” (162). Whitehead reserves further discussion of this selective limitation for the subsequent chapter on “God.”

Whitehead next clarifies that he has so far been focusing on actual occasions as natural events (i.e., their physical poles), which is only half the picture. In their full concreteness, occasions also include a mental pole (i.e., “that which in cognitive experience takes the form of memory, anticipation, imagination, and thought”). While in the physical pole, eternal objects and their infinite associated hierarchies have full concrete ingression, in the mental pole there is only partial ingression of a finite associated hierarchy, which terminates in a definite complex concept. Whitehead further characterizes this partiality in terms of its “abruptness.” These partially ingressed eternal objects, in that they lack the infinite individuation that comes from complete ingression, can be grasped in conceptual terms: “There is a limitation which breaks off the finite concept from the higher grades of illimitable complexity” (172). This is in contrast to the ingression of eternal objects in the physical pole, which due to their individual essences and infinite associated hierarchies remain indefinable in terms of anything other than themselves, and so also cannot be described completely by means of concepts.

The finitude and abruptness of conceptual prehensions is significant because it provides a basis for the correspondence theory of truth and thus the possibility of finite knowledge (173). An eternal object, no matter its mode of ingression, is just itself. Any change to its individual essence would produce a new eternal object. Thus, we can justify the notion that our cognitive experience of knowing something corresponds to that which is known: the conceptually prehended eternal object is (at least in true propositions) the realization of the same object in the knower as in the entity known. Whitehead calls this the “principle of the translucency of realization” (172).

It is necessary to say a few words about the next chapter on “God” to round out Whitehead’s metaphysical account of abstraction. He begins by discussing Aristotle’s theology. Whitehead has criticisms of Aristotle, but he does not hesitate to declare him the greatest metaphysician. He adds that Aristotle was the last European philosopher to dispassionately consider the topic of theology. “It may be doubted whether any properly general metaphysics can ever, without the illicit introduction of other considerations, get much further than Aristotle” (174). That said, Aristotle’s “Prime Mover” was based on an erroneous physical cosmology. So his exact argument fails. But despite all the progress in physics and in logic, Whitehead still believes an analogous metaphysical problem remains to be solved. The problem to be solved in Whitehead’s world of becoming is not the source of motion, but the source of limitation: “Every actual occasion is a limitation imposed on possibility” (174). Whitehead therefore replaces God as “Prime Mover” with God as “Principle of Concretion” or of “Limitation.” 

“Actuality is through and through togetherness—togetherness of otherwise isolated eternal objects, and togetherness of all actual occasions” (174-5). Whitehead conceives of God as as the source of the concrete togetherness of the universe, which would otherwise remain in indeterminate disjunction. God is that by reason of which there is concrescence. God is the instigator of aesthetic synthesis. To the extent that there is unity in the universe (whether the unity of the whole of that of any of its parts), God is its efficient and final cause. God is the generic fact ingredient in all experiences by virtue of which metaphysical description is possible for finite minds like ours. 

We are capable of metaphysical description in terms of categorical determinations of otherwise unbounded possibility because in addition to our physical prehensions of the temporal past and spatial present, we also conceptually prehend the full sweep of eternal relatedness through our participation in God’s “graded envisagement.” “This graded envisagement is how the actual includes what (in one sense) is not-being as a positive factor in its own achievement. It is the source of error, of truth, of art, of ethics, and of religion. By it, fact is confronted with alternatives” (177). In Process and Reality, Whitehead will refer to this envisagement as “the Primordial Nature of God.” 

Whitehead compares his scheme to Spinoza’s, identifying his “substantial activity” (what he later calls “Creativity”) with Spinoza’s “one infinite substance.” But he makes significant alterations to Spinoza’s scheme: “[Creativity’s] attributes are its character of individualization into a multiplicity of modes, and the realm of eternal objects which are variously synthesized in these modes. Thus eternal possibility and modal differentiation into individual multiplicity are the attributes of the one substance” (177). Whitehead is clearer on his differences from Spinoza in Process and Reality (81): “Spinoza bases his philosophy upon the monistic substance, of which the actual occasions are inferior modes. The philosophy of organism inverts this point of view.”


*Typically when philosophers have tried to think through the abstract relations among colors, they think of them in terms of the Newtonian spectrum, as though the relation was simply a continuous gradient, with all the colors on the same “base” level of an abstractive hierarchy. But if we consider the Goethean color theory, dark/black and light/white have to be considered primal or basic, with blue and yellow the proximate result of their mixing, followed by green which arises when blue and yellow mix, etc. So the Goethean understanding of color as an archetypal process of metamorphosis implies a totally different understanding of the relation of the colors to one another. It’s a qualitative/emergent rather than a quantitative/continuous relation. For more see this presentation on Goethean science (timestamped).

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