This rejoinder is meant to add some of my observations to those already made by Utisz. Hopefully this will be helpful, these are the sorts of issues I found interesting in Chapter 7. Generally, these reflections are an attempt to tackle Utisz’ question: How far, if at all, is Maimon disagreeing with Kant or taking the idea in a direction other than Kant’s intention?
Although, as Utisz points out, chapter 7 is rather short, it’s certainly not lacking in depth. If we take extensive and intensive magnitudes as attempts not only to think about quantitative and qualitative differences, but also as a continuation of the previous discussion of the nature of cognition, then the “definition” of extensive and intensive magnitudes, it seems to me, is the central claim of the chapter:
“Magnitude is either plurality thought as unity or unity thought as plurality. In the former case the magnitude is extensive and in the latter, intensive.” [68/120]
“In an extensive magnitude plurality is given, but unity is thought (through abstraction); in an intensive magnitude, on the other hand, it is the reverse” [69/121].
“With quanta, intensive magnitude is the differential of the extensive, and the extensive is, in turn, the integral of the intensive.” [69/122]
If extensive magnitude is number/quantity and intensive magnitude is degree/quality (with all caution Utisz already indicated is needed), or rather, if extensive magnitude is the concept of quantity and intensive magnitude is the concept of quality, then our understanding of what takes place in experience (understood here as Kantian synthesis of intuitions and concepts, sensibility and understanding) is to be clarified in the following way: space and time as forms of intuition are extensive magnitudes [68/121], therefore intuitions are extensive magnitudes, however, intuitions must intuit [have form] certain material/real content [have content/matter] and therefore also have intensive magnitude. In other words, plurality is thought as unity [extensive magnitude] due to space/time being forms of intuition (Kant), but only in connection with unity thought as plurality [intensive magnitude] due to space/time being concepts of understanding (Maimon). The connection between extensive and intensive magnitudes is thus the connection between intuitions and concepts (sensibility and understanding).
I think Utisz is absolutely correct here in drawing our attention to CPR, because it’s difficult to parse Maimon’s text without the context of “Axioms of Intuition” [All intuitions are extensive magnitudes] and “Antipications of Perception” [In all appearances the real, which is an object of the sensation, has intensive magnitude]. If I may add a couple of more quotations to Utisz’ references to CPR, there is a condensed discussion of magnitude in the opening pages of Opus Postumum that might be illuminative vis-a-vis Maimon’s text:
“Magnitude is the determination of an object according to which the apprehension of its intuition is represented as possible only through the repeated postings of what is the same – elucidation by space and time as a priori magnitudes. Thus magnitude is for us merely a predicate of things as objects of our senses (for only through sense is intuition possible for us).” [21:455]
“The concept of magnitude is not a concept derived from experience. It lies a priori in the understanding, although only in experience do we develop it. What cannot be perceived in the object cannot be derived from experience either. Now the concept of magnitude contains that which the understanding performs for itself, namely, to produce an entire representation through the synthesis of repeated addition… It contains nothing further than the synthetic unity of consciousness, which is required for an object in general, and insofar is an element of knowledge, but is not yet knowledge save when applied to pure or empirical intuition.” [21:457]
In the Notes and Fragments (that’s the title of Cambridge volume in English), there are some interesting references to magnitude (extensive, intensive and protensive) as a part of formulations of Kant’s over intention in CPR:
“Transcendental principles of mathematics (not mathematical principles), namely that all intuitions and sensations are magnitudes and that the mathematical propositions about magnitude have reality, although only as of appearances.
No appearance can ever demonstrate an empty space or an empty time. Since appearances are nothing in themselves, that is, not objects subsisting for themselves, empty space is a perception of an extension without matter of appearance.
Every magnitude has a quality, i.e., continuity. Every quality has a magnitude, i.e., intensity (degree). The boundaries of extensive magnitudes are not at the same time the boundaries of intensive ones, but the latter can diminish unnoticed down to nothing. The limits of intensive magnitudes, e.g., weight, are on that account not the boundaries of extensive ones (or if the latter are equal, the former are also equal), rather the latter can grow infinitely. Against atoms and the void.” [R5636, 18:267-68]
The purpose of these quotes is simply to point out that the idea of extensive and intensive magnitude is found everywhere in Kant (even in his early aesthetic notes he talks about feeling as subjective magnitude and taste as objective magnitude). So clearly Maimon’s discussion in this context finds itself in a larger conversation. And, to address the question of similarity with Kant, Maimon’s short remarks seems to be quite in line with Kant’s general idea of magnitude.
I think another way of approaching this chapter could be to see it as a continuation of the discussion of identity and difference in Chapter 6. If identity and difference are a) relational concepts and b) only really apply to other concepts, not objects (“we can be certain that a concept is completely identical with itself, but not that an object is.”), then magnitudes might be understood in the same vein – we are not measuring things themselves, but are forming concepts of unity and plurality out of the sensations/impressions that are given to us in experience. Identity and difference are identity and difference of magnitudes (it seems fair to put it this way) – all relational concepts are defined circularly and all relational concepts “are universal forms of thought by means of which the understanding brings unity to the manifold.” [64/112]. If only concepts are self-identical, it means that at the top (if hierarchical metaphor is appropriate here) there are concepts and at the bottom there are sensations of an infinite number of objects (or an infinite number of sensations) – thinking works both up the ladder (plurality thought as unity) and down the ladder (unity thought as plurality). The picture, if it’s a fair one, again, is certainly close to Leibniz’s vision: the solution to the problem of the duality of sensibility and understanding is to get rid of sensibility as an independent domain, i.e. by making the empirical thoroughly intelligible.
A note of Hegel: is it fair to say that for Hegel the duality of sensibility (sense-perception) and intelligibility (understanding) turns into an opposition, a working opposition that through its movement achieves a higher state of the concept? I’m tempted to skim through Phenomenology, but I trust that there are better Hegelians out there…