Maimon Reading Group: Chapter 3

[by Nick Midgley, London]

Chapter 3

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)

6 thoughts on “Maimon Reading Group: Chapter 3

  1. Pingback: Maimon Reading Group (Summer 2010) « Perverse Egalitarianism

  2. This is both very enlightening and still very confusing – thanks for this summary, but I had to read it (and Chapter 3) again and again to make sense of this notion of “idea of understanding” – as you point out, for Kant, it is “intuitions-concepts-ideas” and I think Kant also insisted that concepts apply to intuitions and ideas apply to concepts – how is it that you say that “Kant’s ideas of reason are illegitimate applications of concepts of absolute totality or completeness to appearance”? Does Kant not say that ideas (including idea of completeness) must not be applied to appearances but only to concepts? I’m not clear if I’m understanding you here. For example, notions such as freedom or immortality of the soul or finitude/infinity etc etc are all discussed after the introduction of “ideas of reason” in the very beginning of Dialectic and clearly the conclusion is that we will never know whether these ideas have connection to appearances (whether we are free, finite, mortal and so on). I’m putting too many things into one comment, so let me reduce it to this question: what does Maimon have to say about Kant’s argument in Dialectic, i.e., Kant’s insistence on the ultimate finitude/limited character of cognition/thinking? Where is Maimon-the-skeptic in all of this?

    • Hi Mike, thanks for that response. Yes my expression “Kant’s ideas of reason are illegitimate applications of concepts of absolute totality or completeness to appearance”? was unclear, I merely meant that qua concepts they are illegitimate and must instead be treated as mere ideas that can only have a regulative use. I’m not going to address your final question directly at the start, rather I’ll attempt a clearer formulation of the thoughts in my previous post, and touch on scepticism/rationalism at the end.

      For Kant we have knowledge of the nature of space and time as forms of intuition. Space and time are both infinite given magnitudes that are infinitely divisible (A25/B41, A32/B47). But we can’t say the same of appearance. So we can apply concepts of totality to the forms of intuition but not to the empirical world of appearance. With respect to the phenomenal world we cannot know whether it is infinite in extent or infinitely divisible, that is to say, concepts of totality or of infinity cannot be legitimately used of the phenomenal world, they can only be posited as ideas or problems that may guide the understanding.

      But the question naturally arises as to how we know the nature of space and time, what is this knowledge that is transcendental rather than empirical? Now if space and time are concepts there is perhaps no problem, for understanding is synthesis (and concepts are syntheses), concepts are native to the understanding, but if space and time are on the contrary (pure) intuitions, if they are given, and thus at least in part passive, then a problem of knowledge seems to arise, a gap opens between the understanding and the these forms of intuition.

      Now, when Kant speaks of the infinitude of space and time, in the ‘metaphysical expositions’ of space and time in the ‘Transcendental Aesthetic’, he argues that eg. space must be an intuition rather than a concept because while a concept may contain an infinite set of possible representations under itself, only an intuition can contain an infinite set of representations within itself (A25/B40). I think Maimon derived his opposition between ideas of the understanding and ideas of reason from this Kantian opposition between under and within, so ideas of reason refer to totality and infinity with respect to concepts/conditions (a concept bringing an infinite totality under it), and ideas of the understanding refer to the totality of intuitions (an intuition of an infinite totality). But why does one need to introduce ideas of the understanding to account for the infinite totalities of space? Well, Kant himself says, in the passage just discussed that space is thought as infinite. That is to say that Kant himself seems to assign the infinity of space to the understanding, not to intuition. So Maimon is confronting Kant’s invention ‘pure intuition’ with the (Kantian) faculties of sensibility and imagination on the one hand, and understanding and reason on the other, and asking whether it belongs to the former or the latter. Infinity belongs to the latter because it can only be thought, not imagined or intuited. When you read the Transcendental Aesthetic it is apparent that it appeals to reason (there are arguments) and the understanding, not to sensibility and imagination. Maimon sees a contradiction between Kant saying that space is an infinite given magnitude and that it is thought as infinite, ‘infinite given magnitude’ is itself a contradiction in terms (infinity cannot be given). So to come back to the question, ‘why ideas of the understanding?’, they are required to bridge a gap between space as thought (or concept) and space as intuition, a gap that is present in Kant’s account (and which the notion of ‘pure intuition’ is meant to bridge but actually just represents a paradox rather than providing a solution). So with the integral calculus one has the means for rigorously thinking determinate spaces as infinite totalities, but in relation to intuition these are mere ideas that cannot be represented (eg the regular infinite-sided polygon whose area equals the circle, is a circle: polygon and circle become one as the number of sides becomes infinite).

      This means that the analogy between ideas of reason and ideas of the understanding is a complex one. Like the ideas of reason, these concepts of infinite totality cannot be applied to intuition, but the moral of this story is almost the opposite. With the ideas of reason the lesson is that reason must be reined in or it will lead to error when it tries to know what is beyond our possible experience; with the ideas of the understanding the lesson is that our understanding exceeds our powers of intuition and imagination – and that our knowledge is not and should not be limited by these faculties. (N.B. This issue comes up again in his defence of the place of the infinite in mathematics against Ben David’ in “On Symbolic Cognition and Philosophical Language”). In fact one might say that Maimon’s ideas of the understanding are more comparable with Kant’s categories than with his ideas of reason, for the categories equally cannot be intuited (as Hume says, they are not to be found in experience), yet their use of experience is justified (the understanding goes beyond what is given in intuition), and the task of CPR is to demonstrate this justification. The difference is that (1) the ideas of the understanding are not grasping the empirical world but the world of mathematical objects, so there isn’t the same ‘quid juris’ problem here. (2) it is natural to compare them with the ideas of reason rather than the categories because both kinds of idea concern the legitimate use of concepts of infinity and totality. To say something briefly about scepticism and rationalism, Kant’s categories represent his rationalism and his ideas his scepticism (limits of rationalism), Maimon’s ideas represent his rationalism and his scepticism lies in his doubts about Kant’s justification of the application of the categories to experience.

      Everything I have said above concerns only Maimon’s introduction of ideas of the understanding to deal with infinity and totality with respect to the forms of intuition, space and time. However Maimon also introduces ideas of the understanding in order to account for the matter of intuition, sensation. In the ‘Anticipations of Perception’ (A165/B207 ff), Kant says that ‘If it were supposed that there is something which can be cognized a priori in every sensation, as sensation in general, then this would deserve to be called anticipation in an unusual sense, since it seems strange to anticipate experience precisely in terms of what concerns its matter …[but] this is actually how things stand’. What can be known a priori is that ‘in all appearances the real, which is an object of the sensation, has intensive magnitude, i.e., a degree.’ Kant reasons thus:

      ‘Every sensation is capable of diminution, so that it can decrease and thus gradually disappear. Hence between reality in appearance and negation there is a continuous nexus of many possible intermediate sensations, whose difference from one another is always smaller than the difference between the given one and zero, or complete negation. That is, the real in appearance always has a magnitude, which is not, however, encountered in apprehension, as this takes place by means of the mere sensation in an instant and not through successive synthesis of many sensations, and thus does not proceed from the parts to the whole, it therefore has a magnitude but not an extensive one.’
      Kant goes on to dub such a magnitude an intensive magnitude. It is these minimal differences that Maimon calls ideas of the understanding.

      As with the thought of infinity with respect to space, one can see that Kant is not appealing to intuition or imagination here, he is using reasoning to uncover the necessary character of sensation, and again Maimon takes Kant’s lead, there is a thought or concept of sensation that cannot be presented in intuition, and such a concept it is appropriate to call an idea of the understanding. And as with space and time so with sensation, the understanding should not be reined it by the limitations of imagination and intuition, it can grasp what they cannot represent. So, again, Maimon’s doctrine here is very much an immanent critique of Kant.

  3. Mike, I am wondering as well regarding the presence/impact of Kant’s dialectic in this case (and in the whole book, although I might be wrong in my remembering). It seems that Kant’s “ideas of reason” play a role that is distinct from a simple interaction with concepts of understanding vis-a-vis completeness, they also “domesticate” wild speculations about things we cannot ever know. I’d have to think about a more detailed response here (maybe Nick will pitch in as well), but I’d like to note that Dialectic is often treated unfairly while it is, in my estimation, one of the more important sections of the first critique (and Kant’s critical philosophy as such).

    If I may recall Descartes (again), in fourth Meditation there’s a interesting discussion of the rather peculiar problem: how is it possible for me to err, considering what was said so far? This discussion of the possibility of error, I think, is more important in the case of Kant’s critique than an explicit discussion of truth (how is perception/knowledge possible), although of course two are interconnected. To put it differently, it’s Pete’s question to Harman/Bryant (of all other examples) which is not my annoying “How do you know that?” but a rather more profound “How do you know when what you say is the case is not the case?” The explanation of the possibility of false knowledge, error, mistake, misjudgment are the important issues in the first critique and I’m not sure how Maimon covers that aspect (he does discuss Antinomies and his philosophical position does propose what Bransen calls “Antinomy of Thought” but is that going far enough? Kant’s Dialectic forever strips, or attempts to, reason of any pretension of metaphysical speculation.)

  4. There is a discussion of illusion on page 108 in the short overview section, but it’s mainly about Kantian “transcendental idealism” and the distinction between things-in-themselves and appearances. Although Maimon puts his own spin on it, it’s basically a very Kantian discussion of that distinction.

  5. Nick, thanks for such a thorough and detailed response. I’m going to read the sections of CPR you reference – hopefully the rest of the Essay will also be helpful in terms of contextualizing these observations. Looking forward to reading posts on the following chapters.

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