1. A Core Method
Whitehead’s Method of Extensive Abstraction (MEA) has been often treated in secondary literature as a purely technical device that can be introduced without reference either to its place in Whitehead’s intellectual development or to its general philosophical context. This paper claims that the method needs to be understood both developmentally and philosophically. On the one hand, the method originated in the Memoir of 1906 (MCMW) and the Parisian paper of 1916 (“La théorie relationniste de l’espace”) and was elaborated between 1917–1922 in seminal works such as “The Anatomy of Some Scientific Ideas,” PNK, CN and R. On the other hand, even in the forceful critical commentaries of Theodore de Laguna and Jules Vuillemin, the authors are concerned only with the logical and epistemological problem of the link between scientific concepts and sense-experience. They never consider the philosophically puzzling theory of objects in itself. Such an approach, however, seems inadequate to the ideas involved.
The central tension in the three major works of Whitehead’s philosophy of nature is the relation between events and objects—how to connect flux, durability and recurrence within a philosophy of events. Or, more precisely: if everything is to be thought in terms of events, how can we distinguish different types of elements of recurrence and durability in the most immediate sense-experience—as for instance this particular shade of color (which is called “sense-object”), this tree (“perceptual object”), this cat that I recognize as remaining the same through time (“physical object”), and this molecule or this electron (“scientific object”) as in physics. The fundamental problem in the philosophy of nature, therefore, is not events, which are once and for all defined as ultimate elements of experience, but rather objects—their status and place within nature. But scholars have usually conflated objects and events, overlooking the fact that Whitehead defines objects as abstract entities vis-à-vis ultimate concrete sense-experience which is defined by events:
The concrete facts are the events themselves—I have already explained to you that to be an abstraction does not mean that an entity is nothing. It merely means that its existence is only one factor of a more concrete element of nature (CN 171).
From this standpoint, the main part of the method of extensive abstraction is acquiring a new rightfulness. It is the central point of the theory of abstraction that Whitehead develops in PNK and CN. The method in its most abstract primitive forms (MCMW, TRE and ASI) consists in defining a geometric point by a class of convergent volumes. Later, it allows us to express different types of abstract objects—such as colors—in more concrete terms of abstractive classes and series of events. The aim is an empirical foundation of the most abstract objects, as well as a new semantic of events and relations. The method of extensive abstraction is thus the basis of the construction of a new concept of nature, one that is based on events and their relations (cf. Durand 2005, 2006).
2. Method and Process
The method of extensive abstraction involves four essential steps, from the most concrete elements—events—to the most abstract entities—sense-figures and sense-objects:
From PNK to R, Whitehead starts from the immediate fact of sense-experience, defined as an event, a duration, or a “complete whole of nature” (PNK 68). It is the whole of nature that is passing in a certain duration. A duration is defined as a special type of event, and as such, it is spatio-temporal. It is spatially infinite, but temporally finite. The separation of space and time—a volume, a duration—comes second and is abstracted by means of the method. In discussing this abstractive process, we will consider the example of some color enduring through a span of time.
As an event, a duration is defined in the first place by its non-recurrence (e.g. PNK 61-62). In the second place, it is defined by its essential nature of relata in the homogeneous and internal relation of extension:
Every event extends over other events which are parts of itself, and every event is extended over by other events of which it is part (PNK 61).
This concrete slab of nature is not a mere undifferentiated passage: it includes on the contrary a complex infinity of relata and relations—at this stage, only confusedly perceived, like events connected by the general and fundamental relation of extension. Events form a sort of ether, or rather a sort of continuum, defined by the MEA’s axiomatic of the relation K as a relation of extension:
(i) aKb implies that a is distinct from b, namely, “part” here means “proper part;”
(ii) Every event extends over other events and is itself part of other events: the set of events which an event e extends over is called the set of parts of e;
(iii) If the parts of b are also parts of a and a and b are distinct, then aKb;
(iv) The relation K is transitive, i.e. aKb and bKc, then aKc;
(v) If aKc, there are events such as b where aKb and bKc;
(vi) If a and b are any two events, there are events such as e where eKa and eKb (PNK 101).
Accordingly, the relation of extension is non-reflexive (i), transitive (iv), and consequently asymmetric, since if a extends over b, then b cannot extend over a. The second axiom demands that there is neither a “minimum” nor “maximum” event. To guarantee the continuity of the continuum, Whitehead adds to this essential relation of extension the relations of intersection, of junction, adjunction and injunction between events. For the sake of our argument, we will add two axioms to the general axiomatic:
(vii) Every event has junctions (and adjunctions) with other events;
(viii) Every event has injunctions with other events.
But now, if the relation of extension is asymmetric, transitive and compact, it is still neither connex, nor, therefore, serial.
The second step of the process corresponds (i) to the birth of a real connexity and setting in series of events, or, in more general terms, to the birth of an order; and (ii) to the birth of distinctive forms, different abstractive classes or type or relations, that we must bring closer to entities that approximate rhythms in PNK rhythms. Events form spatio-temporal patterns (cf. PNK 195-200), particular geometrical figures, defined within the method as abstractive classes, and classes of classes called abstractive elements. An abstractive class is defined with these two conditions:
(i) Given any two of its members, one extends over the other;
(ii) There is no event which is extended over by every event of the set.
Given that it is asymmetric, transitive and connex, the first condition consists in turning the relation of extension into a serial relation. The second implies that an abstractive class has no last term: it builds up an infinite series. Every member of the series extends over other smaller members. By the means of these different abstractive classes (infinite as a matter of principle), and the classes of abstractive classes, the method makes it possible to express—in the concrete terms of events and relation of extension—different figures abstracted from a Euclidean three-dimensional and quadri-dimensional geometry: rects, levels, routes, stations and matrices.
PNK, III, IX
PNK, III, X
PNK, III, X
Now it is from the immediate comparison of these different figures that the first type of objects will be abstracted: in PNK, sense-figures, then sense-objects. It is to this topic that we now turn.
3. The First Objects: Figures and Colors
3.1. From Series to Figures
Sense-figures are the first types of objects immediately recognized by experience. First of all, recognizing a sense-figure presupposes the perception of congruent volumes within a single duration: a sense-figure is not a singular volume of a particular shape, but it presupposes several volumes perceived as congruent through a duration. We are referring now to the appearance of a kind a periodicity: now these geometrical figures, defined in the first steps of the method in terms of abstractive classes and elements, appear in sense-experience to be congruent. Whitehead specifies that such a congruence is only an ideal condition, one that can only be approached through perception but that is sufficient to recognize a sense-figure (PNK, 190). Finally, if there were changing and perpetual motion, it would be difficult, or even impossible to recognize such figures.
Secondly, the recognition of a sense-figure does not imply the recognition of equality between several volumes, but rather the recognition that there is one and only one volume during the duration. What does this abstraction of figures consist of? This is indeed the first real step in the “climb” towards abstraction from events to objects: the reduction of several congruent volumes to one and only sense-figure; in other words, the reduction of the relation of equality or congruence between sets of events to the relation of identity. In the MEA this comes down to considering the limit-element of an abstractive series in itself and for itself, apart from the most concrete series, that just approaches it:
Let there be two types of convergence and abstractive series: the first is the type of classes and abstractive elements that allows us to define any volume. Convergence is mainly spatial and temporal. The second type of convergence requires more: the convergence does not reduce to an element of smaller dimensions, but to a common identity that different elements of the series seem to share. Abstraction is no longer the mere cutting or reduction of the given fact; it is an almost immediate induction or generalization. First, the various members of the series are taken as equal. Then, we pass from the Many to the One. The sense-figure is posited and recognized as independent from the convergent series. It is this transformation from the series to the object, from the series to the limit-element, that brings about the origin of our most primary thoughts. Now, the MEA requires and allows the expression of an object (i.e. a sense-figure) in terms of the convergent series of events. Therefore, our understanding of the method does not lead to the exclusion of objects from nature: it only suggests a concrete and relational expression of these objects. What does the abstraction of a sense-object consist of? How can we express a color in terms of events?
3.2. Colors and Harmonics
Each particular sense-object, such as a certain color, smell, or sound, is always linked to a particular sense-figure in sense-experience: I do not experience blue, but only a blue patch or a blue volume. Now, as we have seen before, a sense-figure is already an abstraction, an object. Consequently, the recognition of a sense-object—that particular shade of red—requires at least two more steps:
The abstraction of a sense-figure is the first element of identity, only approached through concrete experience; The abstraction of the sense-object itself—this particular shade of red—from its figure. In this way, any color, when grasped in itself, is always more abstract than a corresponding colored figure.
With regard to the first step: should we admit two simultaneous applications of the method? One would concern the mere geometrical properties of events—events as congruent volumes—from which the figure is abstracted; the other would consider the particular sense-qualities from which the quality with the sense-figure would be abstracted. Given a particular sense-quality q, let’s state an infinite series of qualities, converging to the sense-object O:
q1, q2, q3, …, qn, qn+1,… → O.
This is one of Russell’s interpretations of MEA, in Our Knowledge of the External World (1914). Whitehead himself suggests such an idea in R (Chapter 3, 42-43), although in fact the MEA is never applied to sense-qualities in Whitehead’s works. Such an analysis would suppose the abstraction and separation between figure and quality, which are only second in experience. In the most concrete experience, a sense-quality is always linked to a particular figure.
So let’s distinguish here between
1. Geometrical forms of events, and their sense-qualities that are by themselves events: in R, events are “a part of the becomingness of nature, colored with all the hues of its contents” (R 21.)
2. Kinds of objects that are both sense-figures and sense-objects, from the most concrete to the most abstract.
Now, how must we think the abstraction of a particular color? Let’s take for example a series of events, illustrated by a series of colored squares:
Let’s suppose that the congruence of these figures were only approximate. Each figure is singular, just as the color which is linked to it: it is also defined as an event. What can we deduce from this?
First of all, according to Whitehead, these are first analogies between geometrical forms and events that lead to the recognition of one and only colored figure and so one and only color, by abstracting the identity of a color from events. It does not imply that we do not have a direct experience of analogies between colors. But the abstractive process, the convergence of the abstractive series, relies on mathematical and quantitative analogies between extensive properties of events. Figures and colors belong to concrete experience as well, but the first are more important in ordinary experience:
Perceptive insistency is not ranged in the order of simplicity as determined by a reflective analysis of the element of our awareness of nature. Sense-figures possess a higher perceptive insistency than the corresponding sense-object. We first notice a dark-blue figure and pass to the dark-blueness […]. This perceptive power of figures carries us to the direct recognition of sorts of objects which otherwise would remain in the region of abstract logical concept. For example, our perception of sight-figures leads to the recognition of colour as being what is common to all particular colour (PNK 192).
In sense-experience, figures and analogies between figures are first and fundamental to the recognition of sense-objects as “generalised sense-objects.”
Second, if a color is always essentially linked to a particular figure, we can deduce that quantitative analogies between figures, which are the basis of convergence, are at the same time qualitative analogies between colors. The separation of quantity and quality is also an abstraction. This is one of the examples of the Pythagoreanism which underlies Whitehead’s Platonism in PR, as reflected in the recurrent references to the Timaeus:
The practical counsel to be derived from Pythagoras, is to measure, and as to express quality in terms of numerically determined quantity (SMW 41).
Third, the abstractive process is composed of an infinity of infinite series, containing an infinity of events, or analogue forms and colors, in the recognition of a particular color within a present duration. I propose the following schema: infinite vertical series are the first kinds of abstractive series, showing the abstractive classes and elements that determine ordinary volumes or figures. The infinite horizontal series is the second kind of series, converging into a superior type of identity—the particular sense-figure or colored figure, recognized as one and identical within a duration. Sense object and figure are there abstracted from a harmonic or scale of colored figures, which is the concrete expression of the only ideal figure and color, that is, the figure and color considered by the mind to be simple and independent entities.
Such harmonics are not only applicable to sense-objects of the other senses (such as sounds or smells), but also to physical and scientific objects. The MEA thus forms the basis for a periodic or rhythmic theory of different types of objects.
A first conclusion that we can draw is that the different applications of the method allow us to express the most abstract objects in concrete relational terms. For the different types of simple and substantial identities of traditional philosophies of nature—conceived on the basis of the classical dyadic relation between substance and attribute—Whitehead’s philosophy of events substitutes new forms of identities and relations which are more complex: rhythms, configurations of events, which go beyond the second and more abstract dualism of mere events and objects. The notion of rhythm appears briefly at the end of PNK, but it is bound to the axiomatic of the method and to the ultimate issue of the articulation between events and objects; it acquires here the fundamental place suggested by the author himself. A rhythm is defined as the primitive unity of events and objects within an ultimate flux: it is a form that is produced in and by the flux. It is not a mere structure or configuration, but an ongoing “structuration”—a mode of flowing, a particular configuration that the motion takes. The Whiteheadian rhythm is thus closer to the Heraclitean “panta rei” than to the Platonic rhythm: it is the flux which is primary, or rather, it is a condition of identity, which is itself immanent in the flux. Thus, this primary unity remains essentially an event: a rhythm is not defined by periodicity or repetition, as it is usually understood. Between these patterns, there are only analogies within experience, never pure repetition. Periodicity pattern, conceived abstractly in itself, is always bound and subordinated to the passage of nature, itself ultimately defined as an event. This passage or flux is not a pure event, it is essentially rhythmical, and this is what Whitehead calls “life.”
A second conclusion is that MEA allows us to overcome the bifurcation of nature: in the first steps of the abstractive process, the passage of nature, by its own flowing in which the percipient event takes part, reveals spatio-temporal configurations, formed and bound by relations of extension, equality and congruence. The classes and elements of the MEA are proposed as the primary sense-forms produced by the passage of nature, which spread out into space-time, and are immediately apprehended by a percipient event.
Finally, the different applications of the MEA all converge towards the essential thesis which is here defended, that objects as abstract, independent and self-sufficient entities are not necessary either for an adequate conception of the passage of nature, nor for theories of the sense-experience of identity, repetition, durability, and potentiality: rhythms and abstractive elements, understood essentially as events, are enough to describe the immediate sense-apprehension of such characters in the creative advance. Given this, the Aristotelian category of substance must be relativized and reconstructed in accordance with a metaphysics of events.
 See PNK 102, although Whitehead adds that “it is not necessary here to pursue the analogy.”
 PNK 102 (“Two events ‘intersect’ when they have parts in common”). In CN, such relations are referred to as “overlapping” (77).
 Broad comments: “This means that, although all events extend over some events and are extended over by others, yet there are pairs of events which do not stand to each other either in the relation K or not-K” (1920). Cf. Lango’s paper on “Time and Extension” in this volume.
 On the relations of these three spaces, see Durand 2006, Part IV, Chapter I, and Palter 1960, 54-55: “[…] Whitehead distinguishes three general types of ‘space’: (1) the three-dimensional instantaneous (or momentary) space to which the ‘observed space of ordinary perception is an approximation’ (PNK 138); (2) the four-dimensional space-time introduced by Minkowski; (3) the time-less (or permanent) three-dimensional space corresponding to the space of physical science. The second of these types of space is unique […]; the first and third, being relative to the state of motion of the observer, are potentially infinite in number, although the third is uniquely determined for any observer in a fixed state of motion, while the first changes from instant to instant even for an observer in a fixed state of motion.”
 See PNK 190-194: “Indeed the high perceptive power of figures is at once the foundation of our natural knowledge and the origin of our philosophical errors” (192).
 Here we will not develop the theory of congruence as presented in PNK, Chapter IV and XII, and later in R, I, Chapter III. In this paper, “congruence” simply means the concordance or spatio-temporal coincidence between perceived volumes.
 PNK 186: “The climb from the sense-object to the perceptual object, and from the perceptual object to the scientific object […] is a steady pursuit of simplicity, permanence, and self-sufficiency, combined with the essential attribute of adequacy for the purpose of defining the apparent characters.”
 See especially Chapter IV and Appendix.
 I would like to express my sincere gratitude to Elie During, Michel Weber and Charlotte Yver for their help in translating this paper.
Works Cited and Further Readings
Durand G. 2005. “Le concept événementiel de nature,” in Chromatikon I. Annuaire de la philosophie en procès, edited by Michel Weber and Diane d’eprémesnil (Louvain-la-Neuve, Presses Universitaires de Louvain), 97-114.
Durand G. 2007. Des événements aux objets. La méthode de l’abstraction extensive chez Alfred North Whitehead (Frankfurt, Ontos).
Lango, John W. 2000a. “Time and Strict Partial Order,” American Philosophical Quarterly 37, 4, 373-87.
Lango, John W. 2000b. “Whitehead’s Category of Nexus of Actual Entities,” Process Studies 29, 1, 16-42.
Lango, John W. 2001. “The Time of Whitehead’s Concrescence,” Process Studies 30, 1, 3-21.
Lango, John W. 2004. “Alfred North Whitehead, 1861-1947,” in The Blackwell Guide to American Philosophy, edited by A. T. Marsoobian and J. Ryder (Oxford, Blackwell).
Lango, John W. 2006. “Whitehead’s Philosophy of Time through the Prism of Analytic Concepts,” in Durand & Weber (eds.).
Palter R. M. 1960. Whitehead’s Philosophy of Science (Chicago, The University of Chicago Press).
Russell B. 1914. Our Knowledge of the External World as a Field for Scientific Method in Philosophy. Delivered as Lowell Lectures in Boston, in March and April 1914 (Chicago, Open Court).
Département de philosophie, Université de Nantes, France
How to Cite this Article
Durand, Guillaume, “The Method of Extensive Abstraction: The Construction of Objects”, last modified 2008, The Whitehead Encyclopedia, Brian G. Henning and Joseph Petek (eds.), originally edited by Michel Weber and Will Desmond, URL = <http://encyclopedia.whiteheadresearch.org/entries/thematic/theory-of-knowledge/the-method-of-extensive-abstraction/>.