So of the simultaneity or coexistence among the conceptual symbols by which successive psychic states are counted: there is nothing in such a relation among the symbols to falsify the process of counting as a cognitive process whose meaning is a non-simultaneous relation among the psychic facts symbolized. As was noted above,[111] the quantitative determination of psychic facts depends solely on an aspect of homogeneity essential to such facts, for which aspect no better evidence is possible than that other aspect which Bergson attributes to them, of heterogeneity; for the two conceptions, instead of excluding each other, imply each other absolutely. All that is necessary, in order that psychic facts should be countable, is that they should possess an aspect of homogeneity. And for this, spatiality is unnecessary; for spatiality is a conception distinct from homogeneity.
Bergson’s identification of homogeneity with spatiality is a case of what Professor Perry calls “definition by initial predication.”[112] Space is homogeneous; therefore homogeneity is space. As if the fact that homogeneity is a character of space were anything against its being a character also of time or anything else. The following is the justification offered by Bergson for identifying homogeneity with space: “If space is to be defined as the homogeneous, it seems that inversely every homogeneous and unbounded medium will be space. For, homogeneity here consisting in the absence of every quality, it is hard to see how two forms of the homogeneous could be distinguished from one another.”[113] The first clause begs the question by defining space as “the” homogeneous. Such identification of space and homogeneity is the point to be proved. The second sentence begs the question again, where homogeneity is supposed “here” (i. e. in the case of space) to consist in the absence of every quality. Moreover, as we have noted above (p. 43), space possesses a very determinate quality, direction, which differentiates it from other homogeneity. Finally, it can be true that homogeneity is absence of quality only on the Bergsonian assumptions that quality is exclusively subjective, that homogeneity is exclusively objective, and that only the subjective is positive. Now, if quality is not objective, judgments cannot be made concerning it; but Bergson is constantly making such judgments. And to distinguish, in point of homogeneity or of positivity, between “the subjective” and “the objective” is to reify two equally abstract aspects of positive reality. The quality of the homogeneous is doubtless simple, and so indefinable. But Bergson nowhere shows how the homogeneous is less positive than the heterogeneous, although the thesis is the sum and substance of his philosophy. Lacking further light on the point, one can only invoke such experiences as the simple colors, for instance,—or, for that matter, any simple quality—for cases of reality as positive as any heterogeneity, and, obviously, no less qualified. And nothing seems easier than the distinction between redness, for instance, and spatiality. Bergson’s whole dialectic rests on reification of such correlative abstractions as homogeneity and heterogeneity, quality and relation etc. in a “purity” which not only is not concretely experienced, but is not even capable of being conceived, because each concept drags the other ineluctably into its own definition. If either space or homogeneity were indeed absence of quality, they could not be distinguished from time, nor from heterogeneity, nor from anything else; in short, they could not be conceived at all.
The present essay aims to report Bergson’s own work with a fair degree of fulness; but it is beyond my plan to follow exposition with criticism point by point in the details, even, in some cases, when these are of important and wide implication. For discussion of Bergson’s contention (based on analysis of the idea of velocity, as outlined above) that mechanics has nothing to do with time, the reader is referred to pages 255–61 of Perry’s Present Philosophical Tendencies. Perry shows, in this passage, that such a contention, again, depends on “confusing the symbol with what it means. To one who falls into this confusion, it may appear that an equation cannot refer to time because the structure of the equation itself is not temporal; because the symbols are simultaneously present in the equation. But if t is one of the terms of the equation, and t means time, then the equation means a temporal process. Furthermore, an equation may define a relation, such as =, <, or >, between temporal quantities, in which case the full meaning of the equation is still temporal. For changes, events, or even pure intervals, may stand in non-temporal relations, such as those above, without its in the least vitiating their temporality.”
Bergson’s solution of Zeno’s paradoxes is another detail of this chapter which is of a good deal of interest; but it applies no new principle to the support of the impossibility of counting psychic facts. Without a clearer conception of the commerce or intersection between time and space, which he characterizes only by the name of “simultaneity,” his reply to Zeno leaves the question of the divisibility of time as problematic as ever. Achilles out-strips the tortoise, he says, “because each of Achilles’ steps and each of the tortoise’s steps are indivisible acts in so far as they are movements, and are different magnitudes in so far as they are space.”[114] They are indivisible in the same sense in which a living organism is indivisible: if you divide them, no division is a part of that which was. But the trouble is that they are divisible also in the same sense in which the organism is divisible. It is the most extravagant of assumptions that analysis of a living body into right and left etc.—which, to be sure, is serviceable to activity upon it—is, because of its service to action, not a character of the object itself. And of motion the same sort of analysis is a patent fact of experience: there is an earlier, middle and latter phase. The possibility of this patent fact is the crux of the problem. No extant answer to Zeno is satisfactory to everybody. I shall refer the reader to Professor Fullerton’s treatment of the paradoxes, in Chapter XI of his System of Metaphysics, as the solution which seems to me to be at the same time the most closely related of any that I know, to Bergson’s, and free of Bergson’s error. Bergson’s solution has at least this element of truth, that Zeno confuses the space traversed with something else concerned in every case of motion. Fullerton makes a distinction between any actual experience of space or time, and the possibility of indefinitely magnified substitutes for such experience; and shows a way in which motion can be relegated to the former (“apparent” space) and denied to the latter (“real” space) without either denying reality to motion or infinite divisibility to real space and time.
Bergson’s differentiation of temporal succession from spatial seriality gets all its cogency from an exclusive attention, when consciousness is concerned, to the aspects of heterogeneity (quality) and compenetration (continuity) which consciousness shows; and, when space is concerned, to its aspects of homogeneity (quantity) and juxtaposition of parts (discreteness). As always, with correlative abstractions, Bergson reifies them: they exclude each other, for him, whereas, in truth, they imply each other, entering into each other’s definition so that each is unthinkable except by means of the other. Time is continuous, Bergson insists rightly; but jumps to the conclusion that therefore time is not discrete. Time is heterogeneous, therefore not homogeneous. Space is discrete (its parts spread out), therefore not continuous; homogeneous, therefore not heterogeneous. If any demonstration is necessary that these terms do imply each other, instead of excluding each other, the case of heterogeneity and homogeneity is only the case of resemblance and difference (cf. page 44). In regard to the heterogeneity of space, its differentiation by way of direction must not be forgotten. As for the other pair of terms, continuity can manifest itself only in extenso, and discreteness requires a separating medium.
Wherever Bergson objects to expressing time in terms of space, the real objection is to the expression of time in terms of homogeneity. This he would not only admit, but insist upon. But his demonstration that homogeneity is a character exclusively spatial is a petitio principii.[115] Of the attempt to measure a minute, he writes as follows: “I say, e. g., that a minute has just elapsed, and I mean by this that a pendulum, beating the seconds, has completed sixty oscillations. If I picture these sixty oscillations to myself all at once, by a single mental perception, I exclude by hypothesis the idea of a succession. I do not think of sixty strokes which succeed one another, but of sixty points on a fixed line, each one of which symbolizes, so to speak, an oscillation of the pendulum. If, on the other hand, I wish to picture these sixty oscillations in succession, but without altering the way they are produced in space, I shall be compelled to think of each oscillation to the exclusion of the recollection of the preceding one, for space has preserved no trace of it; but by doing so I shall condemn myself to remain forever in the present; I shall give up the attempt to think a succession or a duration.”
Notwithstanding his acuteness as a psychologist, Bergson misses the nature of the apperception both of sixty points on a line and of sixty oscillations of a pendulum. And the impossibility of counting psychic facts depends on this misapprehension. He misses the fact that an apperception of sixty points on a line includes, as an essential feature, the serial order, the here-and-there determination (a distinctive qualitative determination) of this spatial fact. And he misses the fact that an apperception of a non-spatial rhythm includes, as an essential feature, the successive order, the earlier-and-later determination, of this psychic fact. Now, seriality is not succession, if you like, except in so far as each is order. But this is no more than to say that the two orders, time and space, are distinguishable—are two, in fact. It is not the slightest obstruction to conceiving each as order, and as numerically determined. For there is no evidence except Bergson’s fundamental fallacy of “definition by initial predication,” to show why homogeneity and order, as such, are exclusively spatial. The discreteness of parts of space is thinkable only by the intervening spaces: space is as continuous (as “compenetrative”) as time.[116] On the other hand, the compenetration of time is not only nothing against its divisibility, but divisibility and compenetration (in the only rigorous meaning the word will bear, that is, continuity) are indispensable to each other, inverse aspects of each other. You can divide only what is connected, as you can connect only what is distinct. Time, then, is as discrete as space.
For every instance of temporal “compenetration,” and “solidarity,” its perfect spatial analogue is plain to the inspection of anyone who will only look that way, to anyone whose attention is not hypnotized by an ulterior purpose to its exclusion.[117] Thus the melodic phrase is present in each of its parts as much as, and no more than, the mosaic figure is present in each of its parts. The “felt four” of the clock strokes is felt as four not otherwise, I think, than a four which might figure in the pattern of a frieze. The same limitations, moreover, apply to such felt multiplicity, whether of rhythm or of pattern. It must be a relatively simple complex, to be apperceived, in either case. You could not feel fifty, and the difficulty is the same difficulty in time as in space. One measures a minute or a century just as one measures an inch or the distance from the earth to the sun: the indispensable condition is the continuity and homogeneity which belong to both quantities.
The proposition that oscillations of a pendulum measure nothing, but count simultaneities apparently means that oscillations, as physical facts, have no duration of their own, and so cannot overlie duration as a unit of measurement. This would at least be an intelligible, even if a false, representation; but, if oscillations cannot measure, how can they count? What is just that difference between counting and measuring, by virtue of which that which can count cannot measure? Simultaneity Bergson defines as the intersection of space and time. Now, counting, as well as measuring, implies a continuum. Measuring, certainly, if it is theoretically perfect, can apply only to a continuum; but counting, which obviously presupposes discreteness, then requires also the indispensable condition and correlative of discreteness, which is continuity. The intersection of space and time thus evidently involves equal continuity and discreteness in both; if they can intersect, and their intersections are countable, each is both countable and measurable. The “purely” temporal phenomena of our conscious life, although interpenetrating, “correspond individually” to an oscillation of the pendulum, which, though a “purely” spatial phenomenon, “occurs at the same time with” the former. Such “endosmotic commerce” between psychical and physical events seems to be decisive for a real community of nature between their respective forms, time and space—such, for instance, as common homogeneity and continuity.