Maimon's first point with regard to space and time fits with the argument of Kant's Transcendental Aesthetic. He opens by stating that space and time are not concepts abstracted from experience as they are not parts of concepts of experience but rather the unities through which the manifold "of experiential concepts" is gathered together. Whilst Maimon's manner of putting this is slightly different from Kant's it does not appear, at this point, significant in its difference since the argument appears to repeat the first argument of Kant's metaphysical exposition of the concepts of space and time in the Transcendental Aesthetic: A23/B37 and A30/B46.
Maimon also goes on to link this first point with a second which again echoes the argument of the Aesthetic. This second point is that the parts of space and time are not possible prior to the wholes of space and time, the parts are hence "in" space and time. This seems to conflate the 3rd and 4th of the second edition arguments from the metaphysical exposition (A24-5/B39-40 and A31-2/B47-8). This conflation erases the distinction between two separate arguments Kant gave for thinking of space and time as intuitions rather than concepts. Sticking with space, as is customary, Kant first gave the argument that space is not what he calls here a "general concept of relations of things in general" by claiming that the whole of space is prior to the representation of its parts. Subsequently he gave the separate argument that space is represented as an infinite given magnitude due to the fact that the parts are all contained within it, rather than, as with concepts, being instead thought "under" it. The distinction between the arguments is of some interest since the first was intended not merely to show that space should be seen intuitively rather than conceptually but also that the kind of concept it is not is one that describes relations of things in general. The second argument, by contrast, indicates the reason why the contrast of the first argument enables not merely a reference to the kind of whole that space is but also why this kind of whole is generically distinct from that given to concepts. So why does Maimon effectively conflate these two arguments?
The answer seems to be that Maimon wishes to point in a different direction to Kant when he lists these considerations of the way to view space and time. After mentioning these arguments Maimon immediately adds that he agrees with the Kantian claim that space and time are forms of our sensibility but then adds that they are grounded in the universal forms of our thought in general. In making this claim Maimon mentions that the condition of our thought is "unity in the manifold" and seems to be connecting the claim about space and time to the argument Kant will offer in the Transcendental Deduction concerning the transcendental unity of apperception. A reason for thinking that this connection is what Maimon has in mind can be found at A105 where Kant writes:
we think a triangle as an object, in that we are conscious of the combination of three straight lines according to a rule by which such an intuition can always be represented. This unity of rule determines all the manifold, and limits it to conditions which make unity of apperception possible. The concept of this unity is the representation of the object = x, which I think through the predicates, above mentioned, of a triangle.
As will become clear in subsequent postings, Maimon has a lot to say about the triangle, and, indeed, about geometry, a subject that will have to wait for another day (or, rather, many days!). The point is, however, that in referring to this view here, Maimon seems not to allow for an independent discussion of a priori intuition that Kant aims to carry out in the Aesthetic.
Maimon next goes on to mention the characteristic ways of understanding space and time, stating that space is the "being-apart" of objects (as follows from his first characterisation of space from the externality argument of the Aesthetic) whilst time is the preceding and succeeding of objects with respect to one another. It follows from this view of time that Maimon does not regard simultaneity as a determination of time, something that would at least cut against one reading of the 3rd Analogy, suggesting it needs to be read in terms of co-existence rather than simultaneity. However, more interestingly, Maimon is explicit in pointing out that space and time are conditions of each other in terms of representations, something Kant does indeed indicate but not always as explicitly as Maimon formulates it.
The next problem addressed concerns the view that space and time are conceptual as well as intuitive and it is here that Maimon's reflections relate to those of Sellars and McDowell. The claim that space and time are, in some sense, conceptual in addition to being intuitive is often thought (by Henry Allison, for example) to underly the distinction Kant makes between "forms of intuition" and "formal intuition" at B160. For reasons that would take too long to summarise in this posting I think this is a false view of the distinction Kant is drawing at B160 but that Allison thinks it plausible is sufficient to show that within contemporary Kant scholarship there is serious consideration given to the view that space and time are, in at least some sense, conceptual. Further, the argument, on-going since Kemp Smith's commentary on the Critique was first published, to the effect that the view of the Transcendental Analytic is not entirely of a piece with that of the Transcendental Aesthetic, further points in the direction of these types of considerations.
Maimon's way of articulating the view that space is a concept does not rely, at least in chapter 1 of the Essay, on either the considerations at work for Allison or those at work for Kemp Smith. Rather, Maimon simply goes back to the claim that conceptuality involves unity in the manifold and indicates that such manifold unity is also at work in the "concept" of space. The intuition of space is traced by Maimon back to the work of the imagination. In one sense, there is an obvious move here since intuition and imagination are closely connected for Kant. However, whereas the transcendental synthesis of imagination is, for Kant, the general basis of the possibility of experience (when combined with the transcendental unity of apperception), for Maimon, by contrast, to say that intuition and imagination are connected is to say there is something problematic in the intuitive sense of space. The intuitive sense of space is understood by Maimon as arising when something relative (such as place or movement) is taken to be absolute so the intuitive sense of space is an "imaginative" sense of it.
However, whilst this intuitive sense of space is therefore, in some sense inferior to the conceptual sense of space there is an important element of this intuitive sense of space that has to be conserved. This is that it is from the intuitive sense of space, according to Maimon, that "the objects of mathematics" arise. This claim introduces a further problem in Maimon's account since the possibility of the production of these "objects of mathematics" indicates a distinction within imagination itself as he makes clear:
The validity of the principles [Grundsatze] of these fictions is based only on the possibility of their production. For example, 'a triangle arises from three lines, of which two together are longer than the third'', or 'a figure cannot arise from two lines', and the like. In this case even the imagination (as the faculty of fictions, for determining objects a priori) serves the understanding. As soon as the understanding prescribes the rules for drawing a line between two points (that is, that it should be the shortest), the imagination draws a straight line to satisfy this demand. This faculty of fictions [Erdictungsvermogen] is, as it were, something intermediate between the imagination properly so-called and the understanding....
Here we find that the imagination that is "properly so called" is apparently distinct from the "faculty of fictions" as the latter is rather placed between imagination and understanding. The understanding itself is conceived here in orthodox Kantian fashion as the faculty of rules and is understood as active whilst the imagination is presented as partly passive and partly active. The passivity of imagination is the guidance of it by association (empirical or Humean imagination) whilst the activity of imagination involves the capacity to order. This active/passive combination is what is at work for "imagination proper" whilst the faculty of fictions is distinct from this as it is "completely spontaneous" (like understanding).
At this point things get further complicated. Maimon now presents his account of synthesis and describes three different forms of it. In one respect, again, this is orthodox since Kant did this also in the A-Deduction and section 26 of the B-Deduction still includes some sense of this. However, whereas Kant distinguishes between the syntheses of apprehension, reproduction and recognition, Maimon distinguishes rather between necessary synthesis, arbitrary synthesis and spontaneous synthesis. Necessary synthesis involves the unity and the manifold being, says Maimon, "given to the understanding, but not produced by it". This type of synthesis is at work, Maimon claims, when the real in sensation is given to us. This real is not produced by the understanding as it is sensible and it is necessary since sensation can be given no other way but understanding does not produce it. This is a suggestive response to the Anticipations of Perception.
The arbitrary synthesis, by contrast, is said to be produced by the understanding (hence not like the first synthesis just given to the understanding). However, whilst the understanding is the basis of this synthesis, this does not entail for Maimon that we have here an objective law. What does this synthesis connect to? Time and space as intuitively given and hence also the "objects of mathematics". As the first appeared to relate to the Anticipations of Perception so here there appears to be an echo of the Axioms of Intuition. Certainly the general claim that mathematics involves arbitrary production has a long ancestry in Kant's thought and I treated it at length in Chapter 6 of Kant's Transcendental Imagination. Maimon gives a lapidary presentation of his general claim here:
A determined (limited) space can be arbitrarily taken as a unit [Einheit] so that an arbitrary plurality [Vielheit] emerges out of it through the successive synthesis of such units with each other (this plurality is arbitrary as much in relation to the unity that is adopted, as with respect to the ever possible continuation of this synthesis).
However, whilst this again appears orthodox enough the way Maimon turns it shows an important twist since he goes on to claim that time and space as concepts contain "as differentials of the plurality, a necessary unity in the manifold" whereas Kant makes no reference to this conception, at least, not in this way.
Maimon also adds that the distinction between treating time and space as concepts and treating them as intuitions is important for thinking about the relation of time and space to each other. Considered just as concepts time and space are exclusive of each other whereas considered as intuitions they are not. The reason why time and space are not exclusive of each other when treated intuitively is then said to be that, as so treated, they are both extensive magnitudes, a claim that takes us straight to the Axioms of Intuition, just as I already claimed.
Finally, the spontaneous synthesis is a production of understanding from an objective ground but Maimon says no more about this in the first chapter. Rather, the discussion of the second synthesis steals the stage and from it Maimon appears to derive the surprising consequence that space and time, considered as "predicates" of intuition are only empirical and not pure though what effect this has on transcendental philosophy is not so obvious from the first chapter alone.
The considerations of this chapter are already very rich and I suggested, in opening, some connections to Sellars and McDowell but suspect I will have to leave the development of these to a further posting given the length this one has already run to. I will also treat later some considerations concerning how the views presented here relate to my previous account of Kant's view of intuition as developed in my book on imagination.