Maimon and Coalitions
Here are some of my latest musings, somewhat in response to Ed’s recent paper. I hope you find it interesting, and I would much appreciate some feedback, especially from Ed, to see if we have similar ideas about Maimon.
Maimon’s Idea of a ‘Coalition System’ as a Possible Point of Reference Between Badiou and Deleuze
[1] What is it that makes the idea of a coalition system appealing, or interesting, in a new way? Well if the notion of a coalition, as opposed to a synthesis (Fichte, Schelling, Hegel), is to preserve some sense of an irreducible difference between the approaches of rationalism and empiricism, then this can be applied to the two different approaches of Badiou and Deleuze. Badiou is already attempting a synthesis of sorts through an introduction of category theory; a supposed phenomenology of appearance. Although not in terms of some transcendental subject, resulting from a Husserlian reduction, or epoché, but in terms of mathematical axiomatics; that is, a given minimal condition, a transcendental positing of a degree zero measure (see Hegel and the Whole, in Theoretical Writings). What these categories capture is something of the order of sets, something beyond their purely ontological or extensive nature. This distinction, between the pure cardinal extensional nature of sets and a second level which takes account of their ordering, their ordinal nature, sets up the distinction between a pure ontological foundation and the ‘appearance’ of these sets in terms of categorical distinctions. What is important is that at the most basic level set theory operates with a purely extensive notion of set, so this ‘phenomenology’ can always be reduced to extensive cardinal set theory.
[2] Deleuze never recognized the significance of Badiou’s work, and so a response to Badiou’s attempt to subsume Deleuze’s work as a phenomenological aspect of his own work, was never developed. Deleuze made no attempt at either a synthesis or a coalition, but simply rejected Badiou. But what I would like to attempt to see in these two thinkers’ work is a radically transformed repetition of the two contrasting themes of the early enlightenment; rationalism and empiricism. Deleuze often, in his early work, talks about a superior empiricism, and Badiou has been recently cast as a practitioner of aleatory rationalism (see postface to Critical Writings); this being a bizarre form of material (mathematical) formalism. So the temptation arises to bring the two together in a coalition, as opposed to a synthesis; thus paying homage to Maimon.
[3] In Maimon the existence of the infinite intellect is used as a transcendental condition, used to justify the application of intellectual categories to sensuous intuition. The de facto assumption of Kant’s, that we have experience, is replaced in Maimon by the recognition that the de facto moment can never be proved, but must be axiomatically decided for. We must readily know and assert presuppositions, or minimal determinations. Only then can the consistent rational systems which we can deduce and construct have any validity. In other words it allows us to consider intuition as an unclear ‘picture’ of a purely rational interrelation of concepts.
[4] The use of the ‘axiom’ of the infinite intellect is used to provide a dual function; initially as an axiom from which rational methods can be deployed to construct a consistent conceptual understanding of intuition. But, secondly, through the distinction between our finite intellect and the idea of an infinite intellect, it forms a separation between the finite and infinite. The infinite intellect is then used to represent a notion of ideal unified totality.
[5] The finite rational, consistent, structures we deduce from assuming that our intuition is the possible product of an infinite intellect in no way guarantees the continual correspondence between our rational constructions and intuition. There are two possible extremes; the first is that there is no rational conceptual framework underlying or producing intuition: any such appearance is simply an illusion, and what we are faced with is intuition as a pure inconsistent multiplicity. The second possibility is that provided by the idea of the infinite intellect. These two ideas are, from our perspective in the middle, unprovable they act as fictions, or regulative ideas. Each is as important as the other and they constitute the irreconcilable poles of scepticism and rationalism. Deleuze’s innovation is to redeem the sceptical pole, and not see it as simply a break, or check, on an otherwise rampant rationalism. But to revive it, and see it as productive in its own right, thinking is motivated to create as much through the idea of inconsistent multiplicity as it is through a notion of an infinite intellect. But I get ahead of myself, I will return to this point latter, first I must finish talking explicitly about Maimon.
[6] This lack of a guaranteed correspondence between our finite rational concepts and the intuitions to which they apply leads to a possible disruption of the process of rationally modelling our intuitions from two directions. Each side (either the conceptual, or that of intuition) could make the other redundant, or collapse its validity or stability. Our conceptual constructions can move beyond the constraints of intuition to reach new, purer and more general heights. Take for example our conception of space, it has moved on from our initial experience of an apparently three-dimensional Euclidean space to the multiple general ideas encompassed by modern topology. Does this contemporary conception of space still fall under a single idea, or a priori intuition, which constitutes a ‘one’ as Kant claims in the transcendental aesthetic of the Critique of Pure Reason? Hence our intuition of space can be seen as a type of sketch or picture of its true rational structure. This is how Maimon’s use of Leibniz moves beyond Kant’s criticism, which held that Leibniz took intuition to be a thing-in-itself. That is, the original intuition is the monad, and is therefore the central point, or structuring idea for all subsequent productive conceptual sequences. It is essentially arboreal, with the concept as a central trunk with the concepts it produces branching from it. Maimon’s use is far more reminiscent of a rhizomatic structure. The initial intuition gives rise to a number of conceptual developments, but the initial intuition does not necessarily cover them as a single over-arching structure. In the complex production of ideas, and their interrelations the initial intuition or idea can become displaced and incorporated as part of a more developed structure. As in the previous example, our experience of space becomes a ‘picture’ of a more general and complex notion of space. Also because of the axiomatic nature of the assumption of the infinite intellect the initial intuition is not definitively thought of as being a rational structure, but only possibly a rational structure. The initial intuition is explicitly accepted as possibly being the thing-in-itself, not as actually being the thing-in-itself. Its rational development, justified by the axiom of the infinite intellect is a process of becoming, a becoming actual.
[7] Returning to the dual function of the ‘axiom’ of the infinite intellect, it only provides the justification for approaching intuition in a rational way but it also provides a transcendent model of absolute consistent rational unity. This gives an unfair bias toward the working of our finite minds by promoting the process o actualising conceptual frameworks as progressive, and sees the motivation for this articulation in a pure rational unity. This would be as opposed to the inconsistent (not-one), or pure multiplicity of a virtual impetus; something that motivates through an unconscious process of desire.
[8] This would mean that the empirical realm of multiplicities is no longer one which is pre-conceptual (the ultimate unprovable axiom of Maimon’s scepticism), but a realm of concepts that cannot be reconciled to a unique consistent systematic framework. The not-one of pure multiplicity takes over from the axiom of the infinite intellect. Nothing is pre-conceptual. It’s just that concepts are not always, or almost never, the object, or intention, of a rational consciousness, or one of its constructions. This would be something like Deleuze’s notion of a superior empiricism: ‘Empiricism is by no means a reaction against concepts, nor a simple appeal to lived experience. On the contrary, it undertakes the most insane creation of concepts ever seen or heard.’ (Difference and Repetition: pxx) What this change of direction allows is the independent existence of a multitude of sequences driven by an impetus bo become unified, consistent, or even rational. There is no longer an over-arching notion of an infinite intellect that would se these independent processes of becoming, either reconciled t each other in a totalising system, or rejected as having become false in the light of such a system.
[9] Deleuze’s use of Maimon seems to want to shift the emphasis of the fundamental axiom away from the conscious structure of the infinite intellect, and towards the pure multiplicity of intuition. Thus it is not a one way process of deciphering the rational underpinnings of pure multiplicity according to the schema of the infinite intellect, what we are interested in is the breaks and ruptures that happen to this progress/process, as the nature of pure multiplicity erupts within the framework of a becoming rational. Badiou wants to accept the notion of a rational/consistent axiom, but not through a radical separation of the finite and the infinite. Badiou uses instead the empty set axiom, rather than the infinite intellect. Then change and transformation are, like for Deleuze, no longer generated from the idea of a god-like infinite intellect, but he does not turn the other way towards pure multiplicities, or the inconsistent. Badiou’s event utilises non-constructible sets, which are in themselves consistent multiplicities.
[10] This piece doesn’t draw any conclusions about the possibility of a coalition between Badiou and Deleuze, but it is my first thoughts on the matter as I begin to examine Deleuze in more depth. I hope to be able to write a more coherent and well thought out continuation of this initial reflection soon.
Maimon’s Idea of a ‘Coalition System’ as a Possible Point of Reference Between Badiou and Deleuze
[1] What is it that makes the idea of a coalition system appealing, or interesting, in a new way? Well if the notion of a coalition, as opposed to a synthesis (Fichte, Schelling, Hegel), is to preserve some sense of an irreducible difference between the approaches of rationalism and empiricism, then this can be applied to the two different approaches of Badiou and Deleuze. Badiou is already attempting a synthesis of sorts through an introduction of category theory; a supposed phenomenology of appearance. Although not in terms of some transcendental subject, resulting from a Husserlian reduction, or epoché, but in terms of mathematical axiomatics; that is, a given minimal condition, a transcendental positing of a degree zero measure (see Hegel and the Whole, in Theoretical Writings). What these categories capture is something of the order of sets, something beyond their purely ontological or extensive nature. This distinction, between the pure cardinal extensional nature of sets and a second level which takes account of their ordering, their ordinal nature, sets up the distinction between a pure ontological foundation and the ‘appearance’ of these sets in terms of categorical distinctions. What is important is that at the most basic level set theory operates with a purely extensive notion of set, so this ‘phenomenology’ can always be reduced to extensive cardinal set theory.
[2] Deleuze never recognized the significance of Badiou’s work, and so a response to Badiou’s attempt to subsume Deleuze’s work as a phenomenological aspect of his own work, was never developed. Deleuze made no attempt at either a synthesis or a coalition, but simply rejected Badiou. But what I would like to attempt to see in these two thinkers’ work is a radically transformed repetition of the two contrasting themes of the early enlightenment; rationalism and empiricism. Deleuze often, in his early work, talks about a superior empiricism, and Badiou has been recently cast as a practitioner of aleatory rationalism (see postface to Critical Writings); this being a bizarre form of material (mathematical) formalism. So the temptation arises to bring the two together in a coalition, as opposed to a synthesis; thus paying homage to Maimon.
[3] In Maimon the existence of the infinite intellect is used as a transcendental condition, used to justify the application of intellectual categories to sensuous intuition. The de facto assumption of Kant’s, that we have experience, is replaced in Maimon by the recognition that the de facto moment can never be proved, but must be axiomatically decided for. We must readily know and assert presuppositions, or minimal determinations. Only then can the consistent rational systems which we can deduce and construct have any validity. In other words it allows us to consider intuition as an unclear ‘picture’ of a purely rational interrelation of concepts.
[4] The use of the ‘axiom’ of the infinite intellect is used to provide a dual function; initially as an axiom from which rational methods can be deployed to construct a consistent conceptual understanding of intuition. But, secondly, through the distinction between our finite intellect and the idea of an infinite intellect, it forms a separation between the finite and infinite. The infinite intellect is then used to represent a notion of ideal unified totality.
[5] The finite rational, consistent, structures we deduce from assuming that our intuition is the possible product of an infinite intellect in no way guarantees the continual correspondence between our rational constructions and intuition. There are two possible extremes; the first is that there is no rational conceptual framework underlying or producing intuition: any such appearance is simply an illusion, and what we are faced with is intuition as a pure inconsistent multiplicity. The second possibility is that provided by the idea of the infinite intellect. These two ideas are, from our perspective in the middle, unprovable they act as fictions, or regulative ideas. Each is as important as the other and they constitute the irreconcilable poles of scepticism and rationalism. Deleuze’s innovation is to redeem the sceptical pole, and not see it as simply a break, or check, on an otherwise rampant rationalism. But to revive it, and see it as productive in its own right, thinking is motivated to create as much through the idea of inconsistent multiplicity as it is through a notion of an infinite intellect. But I get ahead of myself, I will return to this point latter, first I must finish talking explicitly about Maimon.
[6] This lack of a guaranteed correspondence between our finite rational concepts and the intuitions to which they apply leads to a possible disruption of the process of rationally modelling our intuitions from two directions. Each side (either the conceptual, or that of intuition) could make the other redundant, or collapse its validity or stability. Our conceptual constructions can move beyond the constraints of intuition to reach new, purer and more general heights. Take for example our conception of space, it has moved on from our initial experience of an apparently three-dimensional Euclidean space to the multiple general ideas encompassed by modern topology. Does this contemporary conception of space still fall under a single idea, or a priori intuition, which constitutes a ‘one’ as Kant claims in the transcendental aesthetic of the Critique of Pure Reason? Hence our intuition of space can be seen as a type of sketch or picture of its true rational structure. This is how Maimon’s use of Leibniz moves beyond Kant’s criticism, which held that Leibniz took intuition to be a thing-in-itself. That is, the original intuition is the monad, and is therefore the central point, or structuring idea for all subsequent productive conceptual sequences. It is essentially arboreal, with the concept as a central trunk with the concepts it produces branching from it. Maimon’s use is far more reminiscent of a rhizomatic structure. The initial intuition gives rise to a number of conceptual developments, but the initial intuition does not necessarily cover them as a single over-arching structure. In the complex production of ideas, and their interrelations the initial intuition or idea can become displaced and incorporated as part of a more developed structure. As in the previous example, our experience of space becomes a ‘picture’ of a more general and complex notion of space. Also because of the axiomatic nature of the assumption of the infinite intellect the initial intuition is not definitively thought of as being a rational structure, but only possibly a rational structure. The initial intuition is explicitly accepted as possibly being the thing-in-itself, not as actually being the thing-in-itself. Its rational development, justified by the axiom of the infinite intellect is a process of becoming, a becoming actual.
[7] Returning to the dual function of the ‘axiom’ of the infinite intellect, it only provides the justification for approaching intuition in a rational way but it also provides a transcendent model of absolute consistent rational unity. This gives an unfair bias toward the working of our finite minds by promoting the process o actualising conceptual frameworks as progressive, and sees the motivation for this articulation in a pure rational unity. This would be as opposed to the inconsistent (not-one), or pure multiplicity of a virtual impetus; something that motivates through an unconscious process of desire.
[8] This would mean that the empirical realm of multiplicities is no longer one which is pre-conceptual (the ultimate unprovable axiom of Maimon’s scepticism), but a realm of concepts that cannot be reconciled to a unique consistent systematic framework. The not-one of pure multiplicity takes over from the axiom of the infinite intellect. Nothing is pre-conceptual. It’s just that concepts are not always, or almost never, the object, or intention, of a rational consciousness, or one of its constructions. This would be something like Deleuze’s notion of a superior empiricism: ‘Empiricism is by no means a reaction against concepts, nor a simple appeal to lived experience. On the contrary, it undertakes the most insane creation of concepts ever seen or heard.’ (Difference and Repetition: pxx) What this change of direction allows is the independent existence of a multitude of sequences driven by an impetus bo become unified, consistent, or even rational. There is no longer an over-arching notion of an infinite intellect that would se these independent processes of becoming, either reconciled t each other in a totalising system, or rejected as having become false in the light of such a system.
[9] Deleuze’s use of Maimon seems to want to shift the emphasis of the fundamental axiom away from the conscious structure of the infinite intellect, and towards the pure multiplicity of intuition. Thus it is not a one way process of deciphering the rational underpinnings of pure multiplicity according to the schema of the infinite intellect, what we are interested in is the breaks and ruptures that happen to this progress/process, as the nature of pure multiplicity erupts within the framework of a becoming rational. Badiou wants to accept the notion of a rational/consistent axiom, but not through a radical separation of the finite and the infinite. Badiou uses instead the empty set axiom, rather than the infinite intellect. Then change and transformation are, like for Deleuze, no longer generated from the idea of a god-like infinite intellect, but he does not turn the other way towards pure multiplicities, or the inconsistent. Badiou’s event utilises non-constructible sets, which are in themselves consistent multiplicities.
[10] This piece doesn’t draw any conclusions about the possibility of a coalition between Badiou and Deleuze, but it is my first thoughts on the matter as I begin to examine Deleuze in more depth. I hope to be able to write a more coherent and well thought out continuation of this initial reflection soon.
posted by Brian at 7:21 pm
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