Kant's Conception of the Leibniz Space and Time Doctrine

by Mary Whiton Calkins

Kant’s Conception of the Liebniz Space and Time Doctrine.

Kant’s doctrine of space and time is formulated with such constant reference, expressed or implied, to Leibnizian theory, that it is important to discover the exact nature of the doctrine of Leibniz. Such an investigation, however, seems to me to show clearly that Kant, looking to be sure through Wolffian glasses, as he himself admits,^[1] yet, with occasional support from exceptional statements of Leibniz himself, has thoroughly misread and misunderstood him.

The clearest introduction to the discussion of Kant's criticism is an independent consideration of the doctrine of Leibniz. Such a study is, of course, greatly hampered by the fragmentary, occasional character of Leibniz’s philosophical writings. The most sustained treatment of this specific question is found in the correspondence with Clarke, and suffers from the polemical nature and aim, which of necessity shape the argument and lend over-emphasis to the points especially under discussion. The account which follows of the Leibnizian doctrine draws its material from the Nouveaux Essais, the correspondence with Clarke, some of the letters to Des Bosses, the Examen des principes de Malebranche, and a few other of the shorter writings.

It is important to clear the way for an independent consideration of Leibniz’s positive doctrine, by pointing out that his space and time are no abstractions from extra-mental monads. There are, it is true, certain ambiguous statements, which are most naturally interpreted in this way, and which formed the starting-point of the post-Leibnizian theory of space and time. Such an expression occurs in the second letter to Des Bosses:^[2] “assert that there is no part of matter which does not contain monads.” An equally forcible statement is found in the twenty-ninth Epistle:^[3] “I believe that extension no more remains when monads are taken away than numbers when things are taken away.” And in the eighth letter^[4] occurs the emphatic assertion: “For, though simple substance does not have extension in itself, it nevertheless has position, which is the foundation of extension, since extension is the simultaneous, continuous repetition of position, as we say that a line is formed by the motion (fluctu) of a point.”

The most obvious meaning of these passages clearly is that extension presupposes the spatial, side-by-side existence of monads or simple substances,—or, at least, that extension is related to the monad as the mathematical figure to the point. This is certainly the sense in which Wolff formulated the Leibnizian space theory. It is absolutely impossible, however, to suppose that Leibniz ever entertained any such material view of his monads, however easily some of his unfortunate figurative expressions may be so interpreted. The Leibnizian monads are purely incorporeal, mere centres of spiritual force, never in spatial form or relation. Not merely the whole tenor of the monad doctrine, but definite statements, prove this. The twelfth letter to Des Bosses^[5] refers expressly to the assertion just quoted—that “simple substance has position … while extension is the simultaneous, continuous repetition of position”—and explains it by the words, “extension, indeed, has its source in situation (exsurgit ex situ), but adds to situation continuity”; that is, the essence of extension is continuity, though this, like every other phenomenal reality, presupposes the existence of monads. Therefore, Leibniz goes on to say, “I agree that the number of monads increases (augeri), but not as the extension increases.”^[6] In other words, the monads are the conditions (requisita), not the ingredients (ingredienta), of body and extension. “It is no more right to say that monads are parts of bodies or touch each other, than to make this assertion about points or about souls.”^[7]

In his more detailed discussion of extension, Leibniz seems in fact to treat it much as many modern psychologists treat space-sensations. For, in the first place, he often calls extension phenomenal or phenomenon. “Extensionem et resistentiam aut phenomena,”^[8] he says in one place. “Extensio non nisi phenomenon,”^[9] is another such expression. More definitely, as in the quotation already made from the Principes de Malebranche, extension (like duration) is called an attribute of things. In the description of the nature of this attribute, we encounter some difficulties of interpretation. Leibniz insists that extension and duration are abstract attributes, that is, that there exists no merely extended thing, nothing with the single quality of extension. Or, as he expresses himself in a slightly different form, extension always supposes something which is extended. The exact words are: “Extension is none other than an abstraction (un abstrait) … and requires something which shall be extended. It needs, as duration does, a subject. It even supposes the subject to have a certain sort of antecedence; some quality which is extended, is spread out (qui s'étende, se répande).” By the ‘subject’ of the extension Leibniz seems to refer to what later in the same paragraph he calls antitypte or la matérialité, that is, resistance or impenetrability. For much of Leibniz’s discussion of extension is a criticism and refutation of Descartes’ doctrine of the identity of matter with extension; and he always insists that matter requires more than extension, that is, antitypia or passive resistance.

But the most tangible and definite part of this statement is that which virtually points out that extension is one of several qualities of a thing, an accompaniment of some other antecedent quality. As expressing this condition of extension, the word ‘diffusion’ becomes for Leibniz a favorite synonym; one can hardly call it a definition. The qualities with which extension is combined are visual or tactual. ”For example, in milk there is an extension or diffusion of whiteness; in the diamond, an extension or diffusion of reésistance.”^[10] This capacity for union with different qualities, of course, makes extension a peculiarly general quality. It is called by Leibniz “the object of the common sense, that is, of the spirit (l’esprit)”;^[11] and in several parts of the Nouveaux Essais^[12] it is clearly implied that the consciousness of these primary qualities is distinct, as over against the confused perception of the secondary qualities,—tastes, odors, and colors. Leibniz teaches, therefore, that extension is a phenomenal attribute of things, never appearing by itself, but always in connection with some other visual or tactual attribute.

But even if Leibniz were supposed to teach that extension, like duration, is what Kant calls an adstractum reale, it would not follow that this is his teaching about space and time, for one of the most significant features of his doctrine is the clear distinction of space and time from extension and duration.^[13] There are passages, it is true, especially in the Nouveaux Essais, where the words espace and étendu, temps and durée are used without discrimination, yet the opposition is very definitely made. In the fifth letter of Leibniz to Clarke, for instance, it is supported by the remark that things, while they change their time relations and their position in space, still retain their form and their duration. ”Finite space is not the extension of bodies, as time is not duration. … Everything has its own extension and its own duration, but does not have its own time, and does not occupy (ne garde point) its own space.”^[14] Another clear statement to the same effect occurs in the Examen des principes de Malebranche: “Duration and extension are the attributes of things, but time and space are regarded (sont pris) as outside of things, and serve to measure them.”^[15]

Negatively, therefore, it has been shown that Leibniz does not hold the doctrine of space and time as abstractions from real, side-by-side substances. For, in the first place, whatever expressions may be so interpreted are clearly contradicted by the whole tenor of his teaching, and by his detailed discussions; and, further, all these expressions refer to extension and to duration, which Leibniz explicitly distinguishes from space and time.

The positive doctrine of Leibniz is most frequently summarized in the statement common to the Nouveaux Essais^[16] and to the correspondence with Clarke,^[17] that space is the order of the coexistent, and time the order of the successive. This expression must be scrutinized more closely. It has been interpreted by Kant, and by others, to mean that the order (that is, the space) of things, and the order (that is, the time) of events, is secondary to the things and the events themselves,—real only in so far as they are real, as if things and events first existed and then were ordered. Now Leibniz is at pains to guard himself against this inference. In the first place he repeatedly declares that space and time are eternal truths, “founded on God, like all eternal truths.”^[18] “Time and space,” he says simply, in another chapter, “are of the nature of eternal truths.”’^[19] It is to be noticed that these statements closely codrdinate the eternal truths space and time, not only with what Leibniz calls vérités de vaison, but more specifically with innate ideas, that is, as he defines them, habits or ways of being conscious (penchants a reconnottre, or habitudes naturelles).^[20] It follows, of course, that Leibniz unequivocally asserts the necessity of geometrical truths, classing them, however, among innate ideas.^[21] The premises of Kant’s transcendental deduction are fully accepted in the Nouveaux Essats.

In another respect the Leibnizian doctrine of space and time shows an interesting correspondence with Kant’s teaching. Kant bases his doctrine of the subjectivity of space and time on the outcome of the antinomies, but Leibniz had already recognized the difficulty involved in the supposition that space and time are infinitely divisible. The point is not, he says, a part of space, nor the moment a part of time, and infinitesimals are mere mathematical abstractions: “{{lang|fr|les infiniment petits ne sont de mise que dans le calcul des géomètres.”^[22] Moreover, “a part of duration in which we observe no succession of ideas is merely a hypothesis of the vulgar mind.”^[23] So, also, Leibniz faces the dilemma of the infinite regress and the limited world, and pronounces against the reality of the boundary. ‘There never is a complete infinite (a tout imfini)” he says; and in another place he declares that “one is deceived in supposing that he imagines an absolute space which is a complete infinite composed of parts. … This is a notion which implies a contradiction.” From the puzzling nature of time, finally, Leibniz reasons, just as Kant does, to its ideality. “Everything of time,” he says, “which exists, is successive, and so perishes continually; and how can a thing exist eternally which, to speak exactly, never exists? … Only instants of time exist, and the instant is not even a part of time. Therefore time could not be anything except ideal (le temps ne saurait être qu‘une chose idéelle); and the analogical relation of time and space will make us consider one as ideal as the other.”^[24]

Leibniz is even more specific. He does not content himself with vague statements that space and time are ideal and eternal: he definitely treats space and time as relations of God’s ideas. This doctrine is closely related with the rather obscure but reiterated assertions that space order and time order are not mere relations of actualities, but of possibilities.“ Space is a relation (rapport), an order, not merely between existing things (les existans), but also between possible things,” is one of the many definite expressions of the Nouveaux Essais^[25] A parallel statement is the following: “Space, like time, is a certain order which does not merely embrace (complectitur) actual things (actualia), but also possible things.”^[26] The meaning is evident: actual things are perceived things, and space and time are said to exist independent of any actual existences, that is, space and time are more than the perceived relations of things. “Space,” he says, “without things in it (pris sans les choses) is undetermined and not even actual”; and, were things annihilated, “there would be no times nor places (ni temps ni lieux), but time and space would exist in God’s ideas as simple possibilities.’ In fact, therefore, space and time become independent of things (hors de choses),^[27] and are orderings of God’s mind, though they may be orders of things as well. They are undetermined without things, but they are even less dependent on things than Kant’s categories are dependent on the manifold of sense, because applied only to this manifold. In a word, space and time are subjective, ordering principles of the divine mind.

Kant’s criticism of Leibniz may be found in the Dissertation, the Kritik, the Prolegomena, and in those manuscript notes on the margins of Kant’s private copy of the Kritik and of his metaphysical text-books, which Erdmann has collected under the titles Nachträge and Reflexionen. The main points of this criticism have already been suggested. In the first place, Kant ranks Leibniz with Newton, as holding to the extra-mental reality of space and time. Leibniz is distinguished from Newton on the ground of his teaching that space, though real, is an ‘abstract real,’ that is, not a substance, but rather the quality of a substance. This statement occurs twice in the Dissertation,—first, in section 14, where Kant mentions “those English philosophers who assert the objective reality of time, or, as it were,a certain stream (flurum) … continuous and apart from any existing things; or those like Leibniz and his disciples, who hold that time is, as it were, a reality abstracted from a succession of internal states (adstractum reale a successtone statuum tnternorum).” And in the following section “those who hold that space is not anything objective and real, but that it is subjective and ideal” are contrasted with those who “defend the reality of space,’ while among these, “the men who regard space as an absolute and immense reservoir (receptaculum)” are distinguished from those who contend that space is “a relation of existing things which would wholly vanish if the things were taken away.”

Though Leibniz is not named in the Prolegomena, Kant evidently refers to him by the allusion to “mathematicians who were at the same time philosophers.”^[28] Leibniz is there supposed to teach that “a line in nature might well consist of physical points, so that true space in the object would be made up of simple parts.” A little further on this is characterized as the theory that space is a “quality of things in themselves (eine Beschaffenheit der Dinge-an-sich selbst)” The same criticism is made in the Aesthetik. Again Newton and Leibniz are not named, but are clearly contrasted as “mathematical investigators (Natusforscher)” and “metaphysical teachers (Naturlehrer).” These latter, Leibniz and the Wolffians, are opposed to the mathematicians, for whom space and time are two eternal and endless nothings (Undinge). To Leibniz on the other hand, Kant says, space and time are “relations”^[29] abstracted from experience, though indistinctly imagined (verworren vorgestellte). This, Kant adds, is to admit the absolute reality of space and time, but inherent (inhärirend), not substantial (subsistirend), reality. The Amphiboly, made up as it is, for the most part, of criticism on Leibniz, contains a similar comment, ending with the words: “So space and time become (to him) the intelligible form of the relation of things in themselves.”

Now it has been shown already that Leibniz does not treat space and time as either composites or relations of things in themselves. Kant’s misunderstanding is only to be explained by the reflection that he knows only, or mainly, the corrupt Wolffian form of the Leibniz doctrine, which teaches that extended matter and composite bodies are made up of monads lying, as it were, side by side. The reference in the passage already quoted from the Prolegomena to “true space in the object” as consisting “of simple parts” evidently rests on such a conception. A passage from the Amphiboly^[30] more definitely relates the space and time theory to the monad doctrine. “Leibniz,” Kant says, “assumed monads, and within them an activity of consciousness (Vorstellungskraft). … Space and time, therefore, were possible, the former through the relation of the substances, the latter through the connection of the determinations (Verknüpfung der Bestimmungen).” Now this, as has been said, though opposed to the whole trend of Leibniz’s thought, is the precise form of the Wolffian doctrine. “Bodies are only aggregates of monads,” Wolff himself says;^[31] and in Baumgarten’s Metaphysek which Kant used for years as text-book, occurs not only the statement, “every aggregate of monads is extended,”^[32] but the assertion that the parts of which bodies are composed are monads.^[33] Kant’s conception of the Leibniz space doctrine was doubtless affected also, especially in the form in which it appears in the Dissertation, by a misinterpretation of Leibniz’s repeated assertions,—that space is an order of things. Influenced by the realistic interpretation of the monad doctrine, Kant evidently supposed thing (chose) to mean extra-mental object, element, or monad. On this view the only difference between Newton and Leibniz might indeed be expressed by the statement that the first conceived space as an absolute, substantial, extra-mental reality; the second, as an abstract, that is, attribute reality.

It is clear that a large part of Kant’s space and time discussion is virtually a refutation of this theory, attributed to Leibniz and to Newton, of their external reality. The mathematical arguments of the Dissertation,^[34] Aesthetik,^[35] and Prolegomena^[36] prove the subjectivity of space and time,^[37] Kant argues, by proving their a priori nature: Leibniz and his supporters are sufficiently condemned when it is shown that they are making an open attack upon geometry (geometriae adversa fronte repugnant). The Antinomies also definitely direct themselves against the doctrine of the objective reality. But by far the largest part of Kant’s criticism relates itself to an important consequence of the doctrine that space and time are real relations of real things and events; that is, to the teaching, which Kant attributes to Leibniz, that our consciousness of space and of time is an empirical, a posteriori consciousness, a mere passive being impressed by these relations, which are external to us and independent of us. This consequence of the (supposed) Leibnizian theory is clearly recognized and opposed in the Dissertation. “The notion of time,“ Kant says, “is wretchedly defined as gained from experience.”^[38] Space,” he continues, “is not abstracted from external sensations.” In precisely similar fashion, arguments 1 and 3 of the Aesthetik refer to the conception of space as an empirical concept,^[39] derived (abgezogen) from external experience”; and again as a “general concept of the relations of things in general.” Leibniz is not named, but a marginal note in Kant’s Handexemplar connects the doctrine with him by the definite words, wie Leibniz meynt.^[40] Later, Kant characterizes the Leibniz concepts of space and time as “mere creations of imagination”;^[41] and in the Prolegomena, as “simply self-made fictions of the brain (Altrngespenste), to which no object corresponds,—at least adequately.”^[42] Against this theory, Kant upholds the a priori nature of the space and time consciousness.

There is an interesting modification of the external-reality theory which Kant attributes to Leibniz, and which, indeed, persists in the traditional reading of the Leibnizian space doctrine. This is the teaching that space and time are truly relations of things in themselves, but relations confusedly and indistinctly apprehended. “He assumes,” Kant says of Leibniz, at the end of a passage already quoted from the Amphiboly,^[43] “that we perceive things as they are in themselves, but with confused consciousness (mit verworrener Vorstellung).” Space and time are called “confusedly imaged (vorgestellte) relations,”^[44] confused objects of consciousness (Vorstellungen).”^[45] A marginal note denies that space and time “consist in this, that we are confusedly conscious of real relations,”^[46] and a passage in section 8 of the Aesthetik plainly declares that “the system of Leibniz concerning space and time was to change both into intellectual but confused concepts.”

Now it is obvious that such a doctrine is in strict harmony with Leibniz’s fundamental law of continuity. He unquestionably teaches the unity of sense and thought as mere degrees of confused and distinct consciousness, so that he could consistently assert the sense perception—that is, the confused knowledge—of things in themselves and their relations, as well as of phenomena, Such a theory, however, would really oppose the main current of his thought, for he is never very faithful to the unification of sense and understanding, virtually abandoning it when he makes his sharp contrast between the contingent vérités de fait and the necessary vérités de vaison. This necessity really separates thought from sense, in kind as well as in degree, while space and time, as relations of things in themselves, would of course be known to thought. Moreover, even if it were properly inferred from the premises of Leibniz, the doctrine of space and time, as objects of confused consciousness, would find no justification in his definite teaching. For his occasional references are to extension, not to space, as object of perception; and more than once, when he differentiates confused and distinct consciousness, as in the discussion of Locke’s primary and secondary qualities, he calls extension intelligible and “capable of distinct explanation.”

The original of Kant’s picture, however, is not far to seek. Wolff’s^[47] definition of space is precisely in the form required: “Space consists in a certain constant and mutual relation of elements to themselves as a whole, so far as this is confusedly perceived by us.”^[48] Indeed, Kant himself virtually admits the hearsay character of his evidence concerning Leibniz. His most frequent appeals are to the followers of Leibniz, not to the philosopher himself, and in the specific opposition of the Dissertation^[49] to this last theory, explicitly refers it to Wolff, without mention of Leibniz.

Kant’s persuasion that Leibniz believes space and time to be objects of confused sense-consciousness explains an apparent inconsistency in his criticism. This has presupposed almost throughout that Leibniz treats space and time as relations of things in themselves. It is therefore very misleading to meet, not infrequently, the assertion that Leibniz believes space and time to be relations of phenomena and of phenomenal states. Some of these statements may perhaps be treated as mere verbal slips,—the reference, for instance, in the first argument of the Aesthetik^[50] to the “idea (Vorstellung) of space borrowed through experience from the relation of phenomena”’; for here the word does not reappear in the parallel argument concerning time. It is hardly possible, however, to dispose of all such statements in the same way. A passage of the Erläuterung shows this clearly.^[51] Immediately after the reference to those who hold that space and time are “confusedly perceived (vorgestellte) relations of phenomena,” Newton and his school are twitted with their inability, because of the troublesome doctrine of the external reality of space and time, to deal with the higher objects of understanding,—evidently God, freedom, and immortality. The opposing school, it is said, does not meet this difficulty, a statement which can only mean that the Leibnizians are not supposed to teach the external reality of space and time.

Undeniably, then, Kant does sometimes suppose Leibniz to teach that space and time are relations of phenomena, as well as of things in themselves. The explanation of this contradiction is offered by a passage from the Amphiboly^[52] “Leibniz considered phenomena (nahm Erscheinungen) as things in themselves, and thus as intellgibilia, that is, objects of the pure understanding, although he endowed them with the name ‘phenomena’ on account of the confusedness of the consciousness of them (ihrer Vorstellungen).” The substance of this explanation may be given somewhat as follows: On Leibnizian principles the object of indistinct consciousness, or sense, is phenomenon, and the object of clear consciousness, or thought, is noumenon. The very Leibnizian definition of space, ‘confusedly apprehended relations of things-in-themselves,’ is then a contradiction in terms. Looked at from the point of view of the confusedness, space and time, whatever one call them, are really phenomenal; and it is in this way that they gain the advantage over the hopelessly fixed absolutes of the Newtonian theory. In other words, Kant declares that Leibniz really describes his related things-in-themselves as if they were phenomena, so that it is as proper to use one term as the other in describing them.^[53]

It is not within the scope of an expository paper to consider on their merits the issues involved in the Kantian polemic. The understanding of his discussion, however, is certainly lightened by keeping in mind the various forms of supposed Leibnizian doctrine which he opposes,—the belief that space and time are confusedly apprehended relations of things in themselves, and therefore known a posteriori; and the theory that space and time are relations of phenomena, which can be only confusedly known, The doctrine of Kant appears, moreover, in truer historical perspective when it is remembered that the theories he opposes are, in truth, not those of Leibniz at all; but that Leibniz probably holds, with Kant, that space and time are subjective principles, ordering forms of consciousness.

Mary Whiton Calkins.

Wellesley College.

1. Cf. Dissertation, § 7.
2. Erdmann’s edition (to which page references throughout are made), p. 36; date of letter 1707.
3. Erdmann, p. 739 (1716).
4. Ib., p. 442 (1707).
5. Ib., p. 456.
6. Ib., p. 457.
7. Ib., p. 680, Epistola xix.
8. Epistola xii (date 1708), p. 457.
9. Ib., xix (date 1712), p. 680.
10. Examen des principes de Malebranche, Erd., p. 692.
11. Nouveaux Essais, ii, c. 5, Erd., p. 230.
12. Ib., ii, c. 8, § 9 and iv, c. 6, § 7.
13. This is the point on which Dr. Dewey lays such stress in his exposition of Leibniz.
14. Clarke Correspondence, v, 46.
15. Erdmann, p. 692.
16. Bk. ii, c. 23 et alt.
17. Clarke Correspondence, iii, v, p. 29 et alt.
18. Nouv. Es., ii, c. 13, § 175 Erd., p. 240.
19. Ib., ii, c. 14, § 26, p. 242.
20. Ib., i, c. 1, § 2, p. 207.
21. Ib., i, c. 1, §§ 10, 23, pp. 211, 212.
22. Nouv. Es., ii, c. 17.
23. Ib., ii, c. 14, p. 241.
24. Kant, like most metaphysicians, follows Leibniz in this fashion of treating time and space in an analogous manner. The analogy overlooks a real distinction between the two.
25. Bk. ii, c. 13, § 17, Erd., p. 240.
26. Epis. xiii, ad Des Bosses, Erd., p. 461.
27. Examen des principes de Malebranche.
28. § 13, Anmerkung i.
29. Kritikz, edition B, p. 56.
30. Kritik, B, p. 323.
31. Psychologia Rationalis, § 106.
32. § 399, “Omme aggregatum monadum extensum est” (cf. § 394).
33. § 420, “Corpora habent partes extra partes. Partes corporum elementa … Illae monades sunt.”
34. Dissertation, §§ 12, 15, C and D.
35. B, pp. 39, 40–41.
36. §§ 6 et seq.
37. It is evident that the mathematical argument really has to do only with the a priori nature of space. Kant’s efforts to keep to the parallel treatment of space and time result in failure. His chief objection to Leibniz’s time doctrine—the charge that it leaves simultaneity out of account (Dissertation, § 14, 5)—really discloses a weakness of his own theory.
38. § 14, 1 (cf. 2).
39. The word Begriff is here evidently used in the uncritical sense.
40. Nachträge, xiv.
41. Kritik, B. p. 57.
42. § 13, Anmerkung iii.
43. B, p. 323.
44. B, p. 57.
45. Reflexionen, 414
46. Nachträge, xxviii (on B, p. 53).
47. Psychologia Rationalis, § 106, note.
48. Wolff’s words are: “Spatium vero in quadam elementorum ad se invicem relatione constante totum consistit, quatenus ea a nobis non nisi confuse perceptibilis.” Baumgarten makes the distinction between the confused and the distinct consciousness, but does not, so far as I can discover, apply it to space and time. Baumeister, on the other hand, in his Institutiones (§ 88), treats space very much after Leibniz’s own method, asserting that space is to the spaced, as number to the things numbered.
49. § 7, “Vereor ne Wolffius,” etc.
50. B, p. 38.
51. B, pp. 57.
52. B, p. 320.
53. An even clearer statement is found on another page (B, 332): “Also waren Raum und Zeit die intelligibele Form der Verknüpfung der Dinge an sich selbst. Die Dinge aber waren intelligibele Substanzen. Gleichwohl wollte er diese Begriffe für Escheinungen geltend machen, weil er der Sinnlichkeit keine eigene Art der Anschauung zugostand, sondern alle, selbst die empirische Vorstellung der Gegenstände, im Verstande suchte, und den Sinnen nichts als das verüchtliche Geschäfte liess, die Vorstellang zu verwirren und zu verunstalten.”