Bergson and the Kantian Concept of Intensive Magnitude

ABSTRACT

Bergson’s critique of intensive magnitude in Time and Free Will mainly targets Kant’s “Anticipations of Perception”, in which the Kantian distinction between matter and form is lowered. Bergson praises precisely this distinction for safeguarding sensation as something extra-intellectual. As the concept of intensity is the main tool of neo-Kantian intellectualism, in which the whole of reality is determined by the intellect, younger Bergson forcefully rejects intensive magnitude. However, his relation towards Kant changes. In Creative Evolution, Bergson proposes a genetic correction to Kantianism in which the distinction between matter and form is weakened. By comparing Bergson’s theory with the genetic Kantianism of Salomon Maïmon, who heavily relies on the concept of intensity, I argue that the concept fits his later project of renewing the Kantian theory. I thus demonstrate how the critique of intensive magnitude merely belongs to a provisional stage of Bergson’s relation to Kant.

KEYWORDS:

• Bergson
• intensive magnitude
• Kant
• Maïmon
• genetic Kantianism
• differential calculus‌

Notes

1 For references to the works of Bergson I use the following abbreviations: “TFW” for Time and Free Will, “MM” for Matter and Memory, “CE” for Creative Evolution, “CM” for Creative Mind and “Œ” for Œuvres.

2 Vermeiren, “Bergson and Intensive Magnitude”. For a similar position see Riquier, Archélologie de Bergson, and Lacey, Bergson.

3 In fact, Bergson himself says that the first chapter of Time and Free Will was added to it in the hope of pleasing the jury and rendering his dissertation more relevant to the contemporary debates concerning neo-Kantianism (and psychophysics) (Œ 1542); Psychophysics is, in fact, rooted in the neo-Kantianism of the Marburg School (see Giovanelli, Reality and Negation, 162–178).

4 A possible point of criticism on this strategy could be that Maïmon’s theory is idealistic and thereby incomparable to Bergson’s philosophy. However, as I have argued elsewhere, Maïmon should not be simply classified as an idealistic philosopher (“Radical Immanence of Thought”, 283–289). He himself argues that his theory unifies idealism and materialism (Essay, 110). In infinite understanding every distinction between concept and object, or mind and matter, disappears. Furthermore, both subjectivity and consciousness are seen as a secondary result, just as material things, of pure thought (denken). The latter is an unlocalizable function rather than a mode of being. As I will argue in section 2 and 3, Maïmon’s position is thus not incomparable to Bergson’s position, which also escapes the classic opposition of idealism and realism (see MM, ch. 1).

5 This praise of the Kantian distinction between matter and form is only provisional in Creative Evolution. The value of the distinction if only relative: it leaves room for the supra-intellectual. Afterwards Bergson explains that we should overcome this distinction to further relativize the forms of the intellect. This will be discussed in the next section.

6 This is also argued by Husson, L’intellectualisme de Bergson, 130.

7 Although this is true for the Critique of Pure Reason, in his earlier essay “An Attempt to Introduce the Concept of Negative Quantities into Philosophy” Kant uses the concept of intensive magnitude precisely to distinguish sensation from understanding. Intensive magnitude is there conceptualized as a form of opposition in sensation that differs from logical opposition in understanding. The concept can therefore also be used to grasp the particularity of sensibility and thus counters Leibniz’s conception of sensibility as merely confused understanding. This is just one proof of the somewhat ambiguous nature of the concept of intensity, to which we will return in Section 4.

8 Kant, Critique of Pure Reason, B 207.

9 Ibid., A143/B182.

10 Ibid., A167/B209.

11 See Giovanelli, Reality and Negation, ch. 4.

12 Philonenko, Bergson, 65.

13 Vermeiren, “Bergson and Intensive Magnitude”, 7.

14 This is also argued by Husson, L’intellectualisme de Bergson, 130–131.

15 For a more extensive discussion of this critique and Maïmon’s genetic transcendentalism see Vermeiren, “Radical Immanence of Thought”.

16 Maïmon, Essay, 35–38.

17 Ibid., 38.

18 Guéroult, La philosophie transcendentale de Salomon Maïmon, 131.

19 Maïmon, Essay, 36.

20 Bergson’s concern for the foundation of knowledge proves that his philosophy is not an anti-intellectualism. He criticizes Kant’s intellectualism for making knowledge relative and limited to the forms of discursive understanding. Bergson wants to free knowledge of this Kantian limitations and thus broaden our intelligibility of reality rather than rejecting it. Knowledge is unmediated for Bergson, as he makes experience and perception immanent to reality (see Bergson, “L’évolution de l’intelligence géométrique”, p 31). This is very explicit at the beginning of Matter and Memory where matter is equated with image and perception: “Consciousness and matter, body and soul, were thus seen to meet each other (entraient en contact) in perception” (MM 119) Intellect and intuition are not distinguished as mediated and unmediated forms of knowledge. Both forms of knowledge are unmediated; they only differ in which part of reality they know. Intellect knows matter; intuition knows life. The former is a dilated form of knowledge; the latter is a contracted form of knowledge. For an extensive analysis of Bergson’s theory of knowledge, see Husson, L’intellectualisme de Bergson.

21 “In the Kantian system, namely where sensibility and understanding are two totally different sources of our cognition, this question is insoluble as I have shown; on the other hand in the Leibnizian-Wolffian system, both flow from one and the same cognitive source (the difference lies only in the degree of completeness of this cognition) and so the question is easily resolved.” (Maïmon, Essay, 38)

22 Ibid., 187–188.

23 Ibid., 59.

24 René Berthelot examines how classic Aristotelian logic bears on the same relations of exteriority and containment as classical mechanics does. He argues that the notions of “extension” and “comprehension” with which Aristotelian logic understands concepts, correspond to the pure spatial relations to which Cartesian mechanics reduced physical objects (Berthelot, Le Pragmatisme chez Bergson, 189–192).

25 Gilles Deleuze, who is influenced by both Bergson and Maïmon, understands this in a similar way as the double genesis of quantity and quality: “Extensity and quality are the two forms of generality.” (Difference and Repetition, 295) “The one [quality] profits from what has disappeared in the other [quantity], but the true difference belongs to neither. Difference becomes qualitative only in the process by which it is cancelled in extension.” (Ibid., 298)

26 See Philonenko, L’Œuvre de Kant I, 196–202.

27 Kant, Critique of Pure Reason, A166/B208.

28 Maïmon, Essay, 21–23; 68–69.

29 As Maïmon says, “dx = 0, dy = 0 etc.; however, their relations are not = 0” (Ibid., 21).

30 Simon Duffy argues that the method of integration that Maïmon refers to is the Taylor series expansion, which represents a function as the infinite sum of successive derivatives evaluated at a singular point (Duffy, “Maïmon’s Theory of Differentials”, 241; Duffy, Deleuze and the History of Mathematics, 70)

31 For a more detailed discussion of this process see Vermeiren, “Radical Immanence of Thought”; Duffy, “Maïmon’s Theory of Differentials”; and Thielke “Intuition and Diversity”.

32 Although some authors have related Bergson to Maïmon, the similarities of their theories, which go well beyond what I have discussed, have not been thoroughly examined (e.g. Lapoujade, Power of Time: Versions of Bergson, 23–25; Duffy, Deleuze and the History of Mathematics, 89).

33 This is one of the central challenges that Creative Evolution tackles. On the one hand, Bergson describes the genesis of the intellect and dismisses classic philosophies for merely taking the intellect as a given. On the other hand, he rejects the “monistic” philosophies who understand the whole of reality as a degradation of one idea or principle (see Arnaud, “Ce que Bergson entend par ‘monisme’”). He wants to understand the genesis of intellect not as a degradation of a divine intellect but as the creation of a new form of order. Note that this is in accordance with Maïmon’s theory where infinite understanding is of a radically different (we could say ‘supra-intellectual’) nature than finite understanding.

34 Bergson initially defends the distinction between matter and form for space but not for time. Space is an empty homogeneous form or schema being submitted to the matter of experience. Time, however, should not be understood as an empty form indifferent to its content, as time is essentially heterogeneous (TFW 234). Creative Evolution revokes this asymmetry of space and time, and abandons the distinction between matter and form also for space. Extended matter is no longer seen as an empty homogeneous form that is indifferent to its content, but as the dilation and thus homogenization of duration. See Worms, “L’intelligence gagnée par l’intuition”.

35 Cohen, Kant's Theorie der Erfahrung; For a discussion of the central role that the Anticipation of Perception and the theory of intensive magnitude plays in Cohen’s philosophy see Giovanelli, Reality and Negation.

36 Jean Ullmo argues that the exceptional strength of differential calculus lies in its ability to grasp the mobility and the generative character of reality (“Les Mathématiques”).

37 Deleuze, “Class on Leibniz”.

38 Péguy, Note sur m. Bergson, 49.

39 Bergson sometimes invokes Leibniz’s principle of sufficient reason and the principle of identity of indiscernibles to argue for the non-extensive heterogeneity of reality underlying extensive difference (e.g. TFW 95). These principles drive Leibniz into a philosophy in which there is no repetition, no generality and only singular substances whose identity contains its differentiation with the infinity of other substances.

40 Husson, L’intellectualisme de Bergson.

41 Particularly Newton’s description of the method fits this description: “Mathematical quantities I here consider not as consisting of least possible parts, but as described by a continuous motion. Lines are described and by describing generated not through the apposition of parts but through the continuous motion of points; surface-areas are through the motion of lines. […] I was led to seek a method of determining quantities out of the speed of motion or increment by which they are generated; and, naming these speeds of motion or increment “fluxions”, and the quantities so born “fluents”.” (Newton, “On the Quadrature of Curves”, 123)

42 Berthelot, Le Pragmatisme chez Bergson, 174–189; See, for example, how he takes the quantitative character of mathematics as its inevitable limitation of which it should be freed in order to fully grasp mobile reality: “Modern mathematics [differential calculus] is precisely an effort to substitute for the ready-made what is in process of becoming, to follow the growth of magnitudes, to seize movement no longer from outside and in its manifest result, but from within and in its tendency towards change, in short, to adopt the mobile continuity of the pattern of things. It is true that it contents itself with the pattern, being but the science of magnitudes. […] It is therefore natural that metaphysics should adopt the generative idea of our mathematics in order to extend it to all qualities, that is, to reality in general. In so doing, it will in no way proceed to universal mathematics, that chimera of modern philosophy. Quite the contrary, as it makes more headway it will meet with objects less and less translatable into symbols. But it will at least have begun by making contact with the continuity and mobility of the real exactly where this contact happens to be the most utilisable. It will have looked at itself in a mirror which sends back an image of itself no doubt very reduced, but also very luminous. It will have seen with a superior clarity what mathematic procedures borrow from concrete reality, and it will continue in the direction of concrete reality, not of mathematical methods. Let us say, then, with all due qualifications to what might seem either too modest or too ambitious in this formula, that one of the objects of metaphysics is to operate qualitative differentiations and integrations.” (CM 224–225)

43 Bergson’s relation to the calculus is examined by Jean Milet in Bergson et le calcul infinitesimal. He argues that Bergsonism finds its most important inspiration in a mathematical intuition found in differential calculus. The calculus, he argues, is the discovery in mathematics of a radically different way to think, which Bergson generalizes into a philosophy of duration. The long citation from An Introduction to Metaphysics (see note 42) shows how Bergson wants to model philosophy on the calculus. However, Milet somewhat neglects Bergson’s dismissal of the quantitative nature of the calculus. A true “thinking in duration” requires freeing the calculus from magnitudes, according to Bergson (CM 224–255). Bergson never truly accepts the differential as a different concept of quantity that escapes the thinking “in space”: “None of our mathematical symbols can express the fact that it is the moving body which is in motion rather than the axes or the Points to which it is referred.” (MM 105; see also CE 355); Jean Ullmo (Les Mathématiques) and Edouard le Roy (La Pensée Mathématique Pure) have also related Bergson’s philosophy with differential calculus. Several authors have associated the mathematics of Bernhard Riemann with Bergson and his concept of qualitative multiplicity (Deleuze, Bergsonism, 39–40; Durie, “The Mathematical Basis of Bergson”; Widder, “The Mathematics of Continuous Multiplicities”).

44 Deleuze might be the most prominent example (e.g. Difference and Repetition). Other examples are Gilles Chatelet (Figuring Space; L’enchantement du virtuel) and Hermann Weyl (Space-Time-Matter). Finally, we can, again, refer here to Jean Ullmo (Les Mathématiques) and Edouard le Roy (La Pensée Mathématique Pure).

45 Léon Husson demonstrates how in a very similar vein Bergson’s opposition of intuition and intellect as two radically opposed forms of knowledge is only a result of Bergson’s early reaction to Kant in which he follows the latter’s distinction and wants to make it to the advantage of intuition. Apart from this reactive position, Bergson develops a theory of knowledge in which both intellect and intuition are unmediated forms of knowledge which mutually influence each other. Relativizing the opposition between intuition and intellect, Husson argues that Bergsonism is a “broadened or transfigured intellectualism rather than an anti-intellectualism” (Husson, L’intellectualisme de Bergson, 105; my translation).

46 Matter and Memory, for example, professes a “reconciliation between the unextended and the extended, between quality and quantity” (MM 98); The breaching of the Kantian distinction between matter and form has been discussed in Section 2.

47 See Vermeiren, “Bergson and Intensive Magnitude”.

48 Worms, “L’intelligence gagnée par l’intuition?”, 457.

49 Čapek, Bergson and Modern Physics, 189.