Abstract
One of the first tasks in investigating imagination is to determine what kind of phenomenon it is and to work out appropriate conceptual and descriptive vocabulary for its basic features. Traditionally it has been understood as dependent on sense perception and related to memory. The skeptical empiricist David Hume (1711–1776) laid down the rule that it is impossible for us to imagine what we have not already experienced through sense. But a thought experiment he devised—showing that if we use arrays to organize phenomena we have already experienced, we can fill gaps by imagination—can generate a limitless number of exceptions to his rule. This suggests a non-Humean possibility: image-appearances are not isolated data but take place in structured fields of interconnected experience. Sensation, imagination, and memory all produce or require such fields as the experiential place necessary for the emergence of appearances. Fields can be conceptually marked and articulated, which yields a matrix or topography. It is this conceptual marking of a field—conceptual topology—that makes images describable, knowable, and systematically variable. The structure of the articulated matrix in a field can often itself be experienced as a more abstract field, so that we come to grasp phenomena in a biplanar way: one field in terms of another. This phenomenon of projective biplanar field experience is cognitively productive and also yields insight into “fields” as diverse as game playing and artistic production.
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Notes
- 1.
I am not saying that this can be resolved by armchair helminthology, without actual investigations of invertebrate physiology. Only the phenomena of memory, articulated and correlated with neurological processes and locations, can give us real purchase on strategies for answering. But drawing evolutionary boundaries based in psychology is always difficult, especially in animals taxonomically remote from homo sapiens sapiens.
- 2.
For example, Hyman 2006, 124.
- 3.
The argument occurs even earlier, in the Treatise of Human Nature (Hume 1739–1740, bk. 1, pt. 1, sect. 1, par. 10). The essential identity of the two arguments shows that Hume found no reason to reconsider it in the interval between the works. Hume (1711–1776) was a leading participant in the Scottish enlightenment and the major proponent of modern skeptical empiricism.
- 4.
Hume appears to disagree with Newton’s claim that the number of hues is limitless. If Newton were right, between any two shades of blue there would be an infinite number of intermediates. This does not invalidate the initial portion of Hume’s argument; it requires only that he say we are capable of “supplying from our imaginations” at least one specific hue between two others. But, if Newton’s claim were literally true, it would also virtually ensure that, no matter how many shades of blue we had encountered over 30 years, there would be an infinite number more that we had not. The exception to Hume’s general rule would loom even larger, then, because between every two adjacent colors we could always add more, without limit. That is, the imagination would be infinitely more productive of new colors than actual experience. Similar conclusions might be drawn concerning other color qualities. But more recent physiological and physical considerations support the notion that between any two hues there can be only a finite number of discriminable intermediates; see, for example, Raman 1968, ch. 8.
- 5.
I am leaving untouched for now the possibility that the “mental searches” of memory described in this section might be imagination-driven—that is, that we in some sense have to begin to imagine a possibility before we can interrogate our memories whether we have actually experienced it.
- 6.
An objective array heightens rather than eliminates our awareness of the limits of subjective memory. It does, however, allow us, for any specific hue we can recall, to place it in the series of colors, and to do this in a way that would typically match series produced by others.
- 7.
Is this the sequence that Hume had in mind? Or was he talking about all shades of a single hue varied by adding or taking away white light, that is, by progressing from a pale, slightly blue-tinged white to an intensely saturated blue? The principle that we can imaginatively produce an intermediate would not seem to be affected by which of these he intended.
- 8.
CIE stands for the Commission Internationale de l´Eclairage, in English the International Commission on Illumination. The original CIE chromaticity diagram was published in 1931. It is based on an averaging of the experience of very large numbers of observers with “normal” color vision. The space of color is usually conceived in three dimensions, but in the CIE diagram it is reduced to two-dimensional representation by the appropriate selection of a parameter for luminance (brightness) and then deriving two parametric equations involving the three color stimulus values (called “tristimulus values”). See Hardin 1988.
- 9.
“Blue” would be minimally abstract, although it is certainly abstract by virtue of its equal applicability to teal, azure, cerulean, navy, etc. “Color” is yet more abstract, and “sensory data” more abstract than “color.” “Sequence” is another abstraction, though not part of the series blue–color–sensory data.
- 10.
See the conversation with Burman (Descartes 1964–1976, 5: 162–163). Descartes notes that we can “imagine a triangle, a pentagon, and similar things, not so however a chiliagon, etc.”
- 11.
I have little doubt that, if a heptagonal roadsign were introduced and universally used, most people would acquire an ease in imagining heptagons. The imagination is trainable and extendable.
- 12.
Thus a genus like rodent is second-intentional, because it applies immediately to various species concepts (rat, hamster, squirrel) and only through those to the instances of those animals. The species names, on the other hand, are first-intentional. On first and second intention, see Knudsen 1982, esp. 492–493.
- 13.
At this point of the discussion there is no justification for invoking the “faculty psychology” taboo. These functions do not have to be exercised by a single faculty or a single, discrete brain organ or module.
- 14.
By now it should also be obvious that the intense attention to images we have been describing, though it clearly invokes what we habitually call reason or intellect, has a claim to be called imagination—in fact the distinctive kind of imagining that human beings do not share with other animals.
- 15.
Bachelard of course uses the term poetry broadly, in essence synonymous with ancient Greek poiēsis, “making.” If every act of imagination is poetic in the described sense, then “poetic image” would not in any significant way differ from “image.”
- 16.
If, for example, we have some kind of configurative impulse that allows us to perceive a triangle from perceptual cues—for instance, from three marked points not on a straight line—any Gestalt response has to have an intrinsic flexibility allowing it to follow these impulses in the most various circumstances. Thus Benjamin’s reflection is an elaboration, not a critique, of the presuppositions of Gestalt theory.
- 17.
Locke never provides a clear justification for calling an idea simple. Eighteenth-century rationalism, for example in the school of Wolff, simply accepted Locke’s distinction of simple and complex. This was unfortunate, for rationalism, empiricism, psychology, and epistemology.
- 18.
I am expressing this thought in a way calculated to raise possible qualms. I do not agree with Sartre that the great originators of modern rationalism and empiricism all thought this way.
- 19.
The word is in ironic quotation marks because, on the basis of radically empiricistic principles, it is not clear where the norm should be drawn from—though in immediate context I am invoking the reader’s average, everyday experience.
- 20.
Empiricism of any kind attaches imagination to a past act (e.g., Hume’s original impression) or the thing the past act experiences. Sartre’s phenomenological analysis, on the other hand, attaches it strongly to the present act of mind directed to a nonexistent intentional object. These are two extreme examples of philosophers’ reifying and overdetermining images and thus misplacing imagination.
- 21.
For instance, in theories assuming that sense perception begins with sense data—say, a flash of color corresponding to each retinal receptor, like pixels of color—the natural, original object of vision seems to be a basic unit of the color quality that, alongside all the other data perceptions, is then synthesized into macroscopic experience.
- 22.
“Relatively” is an essential rather than an approximative qualification whenever the medium of imaginative realization is different from the medium of its original. There is no degree of detail in a pencil sketch that fully realizes the pictured object’s substance; and sometimes a few strokes manage to capture and highlight features of interest better than perfect ontological replication in the same fleshly matter could.
- 23.
See the etymologies of these words in the Oxford English Dictionary.
- 24.
Here is a stricter definition: a field is “a set for which two operations, called addition and multiplication, are defined and have the properties: (i) the set is a commutative group with addition as the group operation; (ii) multiplication is commutative and the set, with the identity (0) of the additive group omitted, is a group with multiplication as the group operation; (iii) a(b + c) = ab + ac for all a, b, and c in the set.” S.v. “field” in James and James 1959. A group, in turn, is a set over a binary, associative—i.e., (a + b) + c = a + (b + c)—operation such that one of the elements in the set is an identity operator and, for each element of the set, there is an inverse element. It is possible to have noncommutative groups. It should be emphasized that the “addition” and “multiplication” of the group are not, in general, the addition and multiplication of ordinary arithmetic.
- 25.
This field of the rational numbers is infinite, but finite sets can be the domains of fields as well.
- 26.
Unpacking the implications of this sentence is key to understanding the nature of imagination. It is not just that professional mathematicians are well aware that their subject requires intense and subtle imaginative gifts that tend to be hidden from the rest of us (and even from many scientists who think of mathematics as something that is rationally-mechanically “applied” to other things). It is even more that imagination always has the dual character exhibited in mathematics: it is a way of conceiving abstractively what is more concrete, and it is also capable of taking on a more concrete character of its own. In the introduction to Chap. 1, I defined imagination (in part) as both abstractional and concretional; pointing to the imaginative character of mathematics is a first gesture toward explicating what that means. It goes almost without saying that “abstract” and “concrete” are, and thus ought to be grasped as, correlative, not absolute, terms.
- 27.
This word is not intended ironically, even if to most people the definition seems anything but concrete!
- 28.
Kant’s claim that “7 + 5 = 12” is a synthetic rather than an analytic truth rests on this distinction. That there is something unprecedented in the mathematician’s experience is clearer when we add together very large, randomly selected numbers we have never dealt with before.
- 29.
What is at issue here is easy enough to conceive more concretely by thinking of how a child learns about fractions over time. Perhaps the younger child is introduced to them in terms of “pieces” (if a pie is divided into eight equal pieces and you are given three…); next she learns to form the mathematical representation using a stroke mark between two whole numbers (3/8) and is told that this is in effect a form of division; then she learns how to treat such representations as belonging to a set, the rational numbers, the elements of which she learns to add, subtract, multiply, and divide; and after achieving a certain mastery of these operations, she begins to understand fractions and all the arithmetic operations on them as a unified field of mathematical activity, learns alternative representations as equivalent (for example, decimal fractions), and grasps the set of fractions as, first, an extension of the concept of whole numbers and the division operation, and, second, a subset of the real numbers, which are not expressible as such fractions. Thus the student progressively acquires a sense of being at home in an ever-expanding field of numbers and operations, and fractions become part of the standard furnishings of her mind. That all this field-expansive knowledge is at least as much imaginative as it is conceptual is one of the themes of this book.
- 30.
That is, I will not insist that the phenomena constitute a group in the strict sense, despite the fact that a mathematical field always implies two mathematical groups, the set over the “additive” operation and the same set, with the exclusion of addition’s identity operator, over the “multiplication” operation. What matters for the analogy is that there are structured, operational relationships that can be analogized to fields and groups.
- 31.
In this sense, an even better mathematical model might be to replace group operations with functions. But that is a complication for another day.
- 32.
This is a title given by later commentators to a group of writings that treat of formal (scientific) and informal reasoning. It includes Aristotle’s works Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, and On Sophistical Refutations, often with the inclusion of the Rhetoric, not least because it develops themes of the Topics.
- 33.
Enthymemes are usually interpreted as arguments without fully articulated logical form, in particular without all premisses of the argument being explicit. The page–column–line numbers I use for Aristotle’s works are Bekker numbers, a standard format of page marking indicated in the margins of nearly all modern editions of those works. A. I. Bekker was the editor of the Prussian Academy of Sciences nineteenth-century edition of Aristotle’s writings. “1403a18–19” means lines 18 to 19 of the first column (a) of p. 1403.
- 34.
That is, where there is the possibility of uncertainty, either actually (for instance, when one is inquiring into what one does not yet know) or formally (when, no matter how certain one may be of one’s own theory, there exist alternatives that need to be debated). Dialectic in Aristotle is the process by which we take different accounts given of a subject matter and argue out the logical consequences and conflicts.
- 35.
This is not a reductive network, of course. A reductive network—for example, a biological one that claimed plants and animals were nothing more than devices to preserve a genotype, or a chemical one that said genetic expression is nothing other than the functioning of valence bonding—might nevertheless be conceived as a kind of variation on the network I have described, with the limitation that this type of reduction aims to grasp things not as a differentiation of the genus but rather as nothing but the genus.
- 36.
Logical and mathematical formulation does not imply that these things are beyond imagination, however, as should be clear already and shall become clearer as the book goes on.
- 37.
Here and in related locutions over the next few pages, these quotation marks are of the type known as ironic. My point is that the purely conceptual, the pure abstraction, is never absolutely pure. To put it differently, these pure rational phenomena have to be understood as formed in an imaginative field.
- 38.
For example, Lévi-Strauss’s analysis of the generative logic of kinship can be, and was, extended to the shapes of storytelling and then to social structures.
- 39.
The plasticity is of course closely related to the lack of a metric. If a measuring stick were constantly to stretch or contract unpredictably along its length, we could not rely on it for fixing distances between objects. Nevertheless, we could still use it to display certain properties of continuity and coherence, since the markings on the stick would maintain the same order with respect to one another even as the stick stretched or contracted. Topology studies precisely such matters and properties.
- 40.
There are different kinds of midpoint that could be defined. I am assuming here that it is the midpoint determined by the intersection of the triangle’s angle bisectors, which yields the so-called “center of gravity” of the triangle.
- 41.
An easily imaginable example: take an equilateral triangle (all sides equal), then from one of the vertices drop a perpendicular to the side opposite. This divides the equilateral triangle (which is also equiangular, with each angle 60°) into two congruent triangles, each with angles of 30°, 60°, and 90° and with corresponding sides equal in length. The only way to make them match point for point is to flip one of them over, by rotating or lifting it out of the plane, or “folding” the two halves of the triangle upon one another along the dropped perpendicular.
- 42.
As I shall show later, however, it is highly problematic to assert without further argument (and an indispensable amount of historical investigation) that symbolic formulas are purely rational, without any admixture of or dependence on imagination. In fact the real genius of mathematics is that, in the long run, what was abstract becomes the element or field of mathematical imagining for a future generation.
- 43.
This paragraph is a simplified adaptation of Dreyfus’s discussion of the stages of learning to drive a car, which he uses to illustrate levels of progress in advancing toward mastery (Dreyfus identifies seven stages in the first edition, six in the second). See Dreyfus 2008, ch. 2.
- 44.
This is not to say that one doesn’t follow rules any more, much less violates them. Rather, they become second nature, to the point that one can attend to higher levels of structure because one no longer needs to focus on the basics. This is the most familiar experience in the world—which does not mean that it is sufficiently appreciated.
- 45.
See Wittgenstein 1967, §621, pp. 109 and 109e: “Während ich einen Gegenstand sehe, kann ich ihn mir nicht vorstellen,” “While I am looking at an object I cannot imagine it.” The translation of vorstellen by “imagine” is not entirely unproblematic.
- 46.
Note that distinguishing various ways of experiencing the space complicates defending Wittgenstein’s claim. Each agent perceives the place under a different set of abstract–and–concrete parameters.
- 47.
To accommodate those unfamiliar with the game, I will have to overdescribe. For those who hate sports and games of all kinds, I leave it to them to imaginatively construct an equivalent alternative.
- 48.
For our purposes here it is probably sufficient to point out that the court is 94 ft long and 50 ft wide, that, at both ends of the court’s long axis, baskets (hoops with netting open at the bottom) are attached to the front of a vertically oriented board, with the hoop at a height of 10 ft from the floor, that at the beginning of every quarter each team is assigned a basket and scores points by “shooting” the ball so it falls through that basket (while the other team tries to prevent it), and that when the scoring chance for one team ends, because the team scores or loses possession of the ball, the other team moves (usually very quickly) toward the other basket to make its own scoring tries. Since in basketball walking or running while holding the ball is a rules violation, a player on offense has to move the ball either by bouncing it with just one hand (“dribbling”) or by throwing it to a teammate.
- 49.
And even if one can say, for example, that the point guard is supposing that the power forward is about to make a spin move toward the basket (and so the pass will lead to a score if he is right or be intercepted if he is wrong in the supposition), that runs the risk of portraying (or parodying) the event as essentially cognitive and predictive when it is instead a dynamic situation of engaged activity. It is, moreover, quite simply wrong to say that the point guard is supposing that this side of a painted mark on the floor is in bounds and on or beyond it out of bounds, or that he is supposing that the players in differently colored uniforms are his opponents. Being in bounds or out of bounds is real, even if imaginatively real, as is also being an opponent—at least once you are in the game.
- 50.
Coaches will often tell players not to overthink a situation. But that is not the same as not thinking ever and at all. Once their experience of the game becomes habitual, it also becomes more easily imaginable—both in advance and in action.
- 51.
Kittens wrestling with one another or batting and chasing toys may be acquiring skills that will be useful in hunting, but they are not practicing, because practice has express intention toward the ultimate activity.
- 52.
I am freely adapting the notion of the instituting imagination from Castoriadis 1987 [1975].
- 53.
“Prescind” will take on a thematic role in Sect. 5.13. For the time being it can be considered a form of abstraction in which a part or feature of something is treated as though it existed apart from the whole.
- 54.
An example of the former would be a passing drill that tests how many times two players, running up and down the court at full speed, can make legal passes to one another without dropping the ball; of the latter, the game of horse, in which competitors have to make shots identical to the ones their opponents have just made—often with fanciful conditions attached—in order to avoid incurring the letters H–O–R–S–E and becoming the (losing) “horse.”
- 55.
See Sepper 1996, 49–58.
- 56.
That imagination has a template character is one of the principal conclusions Brann draws from the study undertaken in her magnificent compendium; see Brann 1991, 773–786.
- 57.
As I shall point out later in discussing Descartes, this framework provides a more exact understanding of what constitutes the ego. Descartes’s ego is mobile; insofar as it is conceived as a fixed foundation, it is misconceived.
- 58.
I say “differential unification” because an inhabitable space is always differentiated according to myriad principles and is not the uniform, infinitely extendable space of Euclid or Descartes.
- 59.
This sentence greatly oversimplifies the historical reality of Romanticism. One could begin to provide nuance beginning with Coleridge’s differentiation of fancy and imagination; see chapter 13 of the first volume of Coleridge 1907 [1817], esp.1:202. But Coleridge’s conceptions are one thing, the cultural commonplaces of the broader society’s beliefs quite another. The popularly effective romanticisms of European cultures have been blunt intellectual instruments.
- 60.
A publicly shared imagination or system of images is known as an imaginary (French imaginaire).
- 61.
See, for example, Townsend 1993, 41.
- 62.
One day an artist incorporates a plastic object into a collage. A second learns how to mold plastic to acquire greater control over the pieces added to the collage, a third starts molding plastic to serve as the ground of the entire collage, and finally someone begins producing large molded pieces as the whole work.
- 63.
These considerations suggest a path to understanding even feeling, emotion, and passion as differential responses to fields of experience—perhaps these psychological phenomena themselves can be seen as a topographical field or virtual space. Today an attempt to do this might begin with a work like Damasio 2003, especially if supplemented by a direct encounter with Spinoza and Descartes on affect. Spinoza, inspired by but radicalizing Descartes, defines passions/emotions as “the affections of the body by which the body’s power of activity is increased or diminished, assisted or checked, together with the ideas of these affections.” But previously he defines the ideas of bodily affections as the work of imagination. Thus emotions turn out to be the activity-increasing or activity-diminishing affections of the body that accompany imagination.
- 64.
If we think of the mortality rate in the past, the rigidity of social structure, and the overwhelming proportion of people engaged in agriculture, we can begin to see how different the life world would have been in the past. One does not have to be a professional anthropologist to recognize this—though it helps!
- 65.
Considering the different approaches and one-sidednesses of the sciences leads quite naturally to understanding what science does, fundamentally, as establishing rigorously constituted imaginative planes and spaces. This is not the last occasion on which I shall point to this fact, which could easily be taken up in the philosophy of science.
- 66.
If there is a second, square-bracketed date, it indicates the year the work first appeared in its original language.
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Sepper, D.L. (2013). Locating Imagination: The Inceptive Field Productivity and Differential Topology of Imagining (Plus What It Means to Play a Game). In: Understanding Imagination. Studies in History and Philosophy of Science, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6507-8_3
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