[by Nick Midgley, London]
This chapter discusses ideas of the understanding, and distinguishes them from the ideas of reason that Kant introduced in the Antinomy of Pure Reason (A405/B432 ff). Maimon had already deployed this notion in chapter 2 to characterise the differentials of sensation, but here he re-introduces them with different examples and a definition of them as the material completeness of concepts, that does not straightforwardly apply to the differentials. The chapter ends with an opposition between the subjective and objective orders of the operations of the mind, very briefly expressed but very intriguing.
Kant, in his letter responding to the manuscript of the Essay (Appendix II), criticizes the argument Maimon makes in this chapter for introducing this new species of ideas. Because Kant states in the letter that he has only read the first two chapters of the Essay and because there are passages in the chapter where Maimon is clearly trying to respond to Kant’s criticisms (see my translator’s footnote 3 on p.47), it is evident that the original chapter two was rewritten and divided into chapters two and three after Maimon read Kant’s letter.
Maimon states that ideas of the understanding are the ‘material completeness’ of concepts in so far as this completeness cannot be given in intuition, whereas Kant’s ideas of reason are the ‘formal completeness’ of concepts. He also characterises the former as the ‘totality of intuitions’ and the latter as the ‘totality of conditions’. Maimon’s examples are drawn from mathematics – infinite series that represent numbers that cannot be represented more directly (root 2) and the circle whose area is equal to that of an infinite-sided polygon.
In the Introduction to the Translation (pp. l – lv) I discuss this notion of material completeness in terms of the example of the circle as infinite-sided polygon, and relate it to the notion of real definition. I won’t rehearse here what I said there, but rather assume that discussion and concentrate instead upon the difference between Kant’s ideas of reason and Maimon’s ideas of the understanding.
Kant’s ideas of reason are illegitimate applications of concepts of absolute totality or completeness to appearance. They belong to reason rather than to the understanding because it is reason that demands this completeness, for example reason demands that if the conditioned is given, then the whole sum of conditions and hence the absolutely unconditioned must be given (A409/B436). Kant claims that such use of ideas leads to antinomies, such that it can be proved that the world both must have a beginning in time and cannot have a beginning in time, must be made up of simple parts and cannot be made up of simple parts and so on. Transcendental idealism solves the antinomies by arguing that such completeness has no place in the sensible word, and that the ideas can only have regulative role in guiding the greatest possible extension of the use of the understanding with respect to objects of experience (A516/B544). They have a legitimate regulative use but no legitimate constitutive use with respect to experience.
What I want to emphasize is that Kant’s ideas of reason seek (illegitimately) to say something about appearance, i.e. about the sensible world, not about space and time as such. Maimon’s ideas on the contrary do not concern appearance but its forms, space and time. Thus, although they do have a constitutive rather than regulative role, this is not to say that for Maimon infinite synthesis can be intuited for space and time as forms are not intuitions. These ideas are what the understanding demands of space and time, but which the imagination cannot supply. This provides some insight into why Maimon speaks of space and time as both intuitions and concepts – on the side of the understanding there are concepts of space and time which the intuitions of space and time cannot fully capture.
My argument will be that there is a principle of the methodology of transcendental philosophy at stake here, one which Deleuze often insists on, viz that one must not derive the transcendental from the empirical. Here, in the case of space and time, we cannot understand space and time by means of their empirical instantiations. In the Anticipations of Perception (A169/B211) Kant characterises space and time as continuous magnitudes (using Newton’s term ‘fluent’ or flowing), of which each part is itself a space or time ad infinitum and no part is simple. This is not known from experience: as the antinomies demonstrate we cannot know whether experience has ultimate simples or not, whereas according to Kant we can know this of space and time. Transcendental philosophy opens up this gap between transcendental and empirical (think of Heidegger saying the essence of technology is not technological, Maimon could be parsed as saying the essence of space is not spatial) and raises the problem of knowledge of the transcendental. Now Kant has traditionally been read as tying arithmetic and geometry to time and space respectively in treating them as consisting of synthetic a priori judgements. This is fair enough, but it needs to be added that in (potentially) freeing space and time from the empirical Kant opens up the possibility of radically new understandings of space and time (Husserl, Einstein), because space and time are no longer understood in terms of objects in space and time but the reverse. Returning to Maimon, Maimon is true to this transcendental turn: space as continuous magnitude is precisely what the mathematics of the calculus seeks to grasp, it is what escapes intuition, what can be understood but not imagined.
So Maimon can challenge Kant by saying that the continuity of space is not an empirical property of space, it’s an idea of the understanding which the new mathematics is making rigorous in the theory of continuous functions, differentials and integrals. That is to say, Kant has himself ascribed a property to space and time that cannot be given in any intuition. Maimon in developing this property into a theory of differentials and integrals emphasizes the non-empirical character of Kantian space and time and his use of the term ‘ideas of the understanding’ precisely captures the fact that intuition can never display what the understanding knows as space and time.
‘By means of these forms the imagination relates different sensible representations to one another and lends unity to its manifold. Here once again the understanding insists on material totality; in other words, by means of this a priori form it considers an intuition to be in a succession in time and space (without which we would not have any intuition) even when the imagination does not notice any succession’ (Chap 3, s.80)
This is very Kantian in the way that it pictures the faculties interacting with one another (a main concern of the critical philosophy being to establish correct relations between the faculties and to stop them encroaching on one another’s domains, Kant would no doubt argue that Maimon, like Leibniz, allows the understanding to encroach on imagination and sensibility which have their own laws). Here Maimon describes the understanding directing the imagination. Where Kant had a discord between reason and understanding that led to antinomies (the understanding had to reign in reason), Maimon here has a discord between the imagination and the understanding where the understanding has to insist on the continuity and universality of space and time (to over-rule imagination when the latter cannot detect spatio-temporal difference). This discord is again at stake in his criticism of Kant’s pure intuition in chapter 2, and most explicitly in chapter 8 (s.134), here it is a question of preventing the understanding being misled by the imagination into positing a sort of absolute space illegitimately totalized from empirical spaces.
So, in summary, my argument is that a fruitful reading of Maimon’s account of space and time is to regard it as an immanent critique of Kant’s forms of space and time as contaminated with the empirical, and the positing of an alternative truer to the spirit of transcendental philosophy.
I have not had time to discuss the last part of the chapter on the subjective and objective orders of the operations of the mind, but would very much like the reading group to address this, so I’ll just mention a couple of points by way of prompting discussion. First its perspective is quite alien to the Critique of Pure Reason and perhaps augurs the ‘for consciousness’ versus ‘in itself’ or ‘for us’ of Hegel’s Phenomenology. Second it posits an opposition between thought and consciousness – I drew attention to this ‘unconscious thought’ at the end of my translator’s introduction. It relates to the discord between imagination and understanding that I just spoke of above, that is to say consciousness is inherently spatio-temporal but thought is not. But there are all sorts of questions to be asked here about the relation of the transcendental subject to the empirical ego and of the nature of transcendental time as difference (cf. Derrida’s thinking of differance in his reading of Husserl’s theory of time). Further there is the identification of thought with pure activity. I’ll end with this quote from note #58 to chapter 9, because it ties together the notion of thought as activity with what can be read as an insistence on the transcendental/empirical difference, and perhaps also has some bearing on the question that Jon raised in his post on chapter 2 concerning the possibility of rules for rules:
‘The principles of a thing are not the thing itself, for if they were, then the thing must already be presupposed before it has arisen. For example, the principles of an area are not areas, of a line are not lines, etc., so the principles of truths cannot already be truths. Properly speaking, truth is not a proposition produced in accordance with the laws of thought; rather truth is the operation of thought itself and the proposition is produced from this. The proposition is merely the matter or stuff out of which the form becomes actual’. (s.406)