Chapter 7: Magnitude
A short chapter this, just two pages, and rather than take up your time with a commentary longer than the original I’ve restricted myself to summarising and explaining the main arguments before offering a few questions for possible discussion. Chapter 7 continues in the vein of elaborating some key Kantian and pre-Kantian notions, the focus here being a distinction between extensive and intensive magnitude, a contrast familiar from Leibniz but also taken up by Kant and which Maimon illustrates in nicely straightforward terms.
To explain the contrast between extensive and intensive magnitude (extensive und intensive Grösse) it is perhaps simplest to use Maimon’s own examples. A raindrop can be identified as having a position in space. When we identify another raindrop in a different place (indeed difference of place/space is, as we’ve seen, a key to comprehending difference per se) we are able to bring together two homogeneous intuitions, compare them and thereby arrive at a notion of greater or lesser. Through this ‘taking together’ (Zusammennehmung – there’s no obvious one-word English equivalent) of two objects we perceive the greater extensive magnitude of say, two with regard to one. Of course using number here is question-begging because number is itself derivative of magnitude and of other processes like individuation and differentiation, but its use arguably helps create a virtuous hermeneutic circle. Maimon then cashes this out in terms of unity and plurality. Individual raindrops may be different (indeed will be different) but we abstract from their differences and class them together under the same concept.
His example of an intensive magnitude (which is also Kant’s at A169/B211) is the colour ‘red’: in identifying a determinate or specific ‘red’ (eine bestimmte Röte) we may see it as deeper than another red, as differing in degree (and here degree [Grade] is simply another word for intensive magnitude). This difference is not numerical or spatial difference as with extensive magnitude; adding redness to a red doesn’t extend space or place, but only intensifies the degree of redness. Again this can be expressed in terms of unity and plurality: “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” (Essay, 69).
Then Maimon adds the following interesting twist, and this is likely one reason for his including a chapter on magnitude here: “The extensive magnitude is, so to speak, the schema of the intensive magnitude because intensive magnitude, along with its relations, cannot be perceived directly and in itself but only by means of extensive magnitude” (69). Put simply, we often try to put numbers on intensive magnitudes, i.e. schematise them, render qualitative differences quantitative so as to make them easily perceptible. There’s something of Leibnizian ‘composite perception’ here, though Maimon’s concern is not quite the same. And he’s surely right in what he says. To take his own example of colour, cases in point would be the quantification of the palette. There’s something perhaps necessary yet also aporetic in such extensification of the intensive. Yet Maimon arguably glosses over something which Hegel will highlight in these acts, namely the Sorites Paradox which he takes up (prompted by Maimon?) in his two Logics. In a another sense Hegel will be indebted to the idea of intensive magnitude: it also informs his critique of the “bad or merely mathematical infinite” in favour of an idea of an infinity which is intensive, qualitative.
But going back a little rather than forward this chapter can be read as an elaboration of the ‘Axioms of Intuition’ in the Transcendental Analytic of the CPR (A162-167 / B202-218). At A170 Kant writes that “all appearances whatsoever are…continuous magnitudes, either in their intuition, as extensive magnitudes, or in their mere perception (sensation and thus reality) as intensive ones” (Guyer & Wood tr. p. 292). Kant is of course carrying the terms over from Leibniz, though predictably re-inscribing them in the transcendental language of ‘appearances’ which are nevertheless universally valid and necessary: “All sensations are thus, as such given only a posteriori, but their property of having a degree can be cognized a priori” (A176/B218).
Maimon’s brief chapter comes to a close with examples taken from geometry and an analogy from calculus, as we’re now familiar with, his two favoured forms of philosophical exemplification: “With quanta, intensive magnitude is the differential of the extensive, and the extensive is, in turn, the integral of the intensive” (69).
I want to just pose a few questions in response to it, that might kick-off discussion, without thereby limiting discussion to just these.
One of Maimon’s relation to Kant. Those more familiar with Kant will be able to glean more from his own treatment of intensive magnitude than I can (see Kant A166-167/B208-209,218 and for commentary Beiser, German Idealism, p. 140, 170, 187). How far, if at all, is Maimon disagreeing with Kant or taking the idea in a direction other than Kant’s intention?
Secondly, looking forward in time to Hegel’s treatment of magnitude we see both similarity (Hegel like Kant and Maimon uses the example of ‘red’ to illustrate intensive magnitude and, like Maimon, the thermometer to illustrate extensification of the intensive) and differences (a criticism of the use of solely mathematical and geometrical examples to explain this topic and a more consciously dialectical approach which plays off extensive and intensive magnitude against each other [Encyclopedia: Logic, tr. Wallace, pp. 145-161; Science of Logic, tr. Miller, pp. 187-201]). Could the latter be in part gentle swipes at Maimon?
Chapter 8: Alteration, Change, etc.
A rather more opaque chapter this, though again we can orient ourselves once we know that its title takes its cue from Kant’s discussion of the same terms, Veränderung and Wechsel, respectively, in the CPR. Alteration, as Maimon’s translators point out, is discussed by Kant at A187/B230, but I’d add it’s also explored a bit earlier too, immediately following the discussion of magnitude at A171/B213, which helps make sense of his order of presentation here. Maimon takes a little while to get to the crux here, spending the first paragraph in this chapter rehearsing earlier statements about difference and temporal sequence, but when he does the following definitions are useful:
Change means: succession of determinations one after the other in time; alteration is the relation of the determinable to these successive determinations, in other words it is the synthesis of the very same determinable with different and mutually exclusive determinations in a temporal sequence; it is derived from the logical function in disjunctive judgements but can be perceived only as in a temporal sequence (its schema). (p. 71)
Maimon is contrasting the bare succession of qualities of a thing and the relation of a thing to its successive qualities, and there’s some overlap with the discussion of subject and predicate in Chapter 4 which Nick has shed much light on.
Maimon’s next step is to show how a concept of cause is necessary for the very idea of objects of experience to work. Without such a concept there is not only no coherent notion of objects of experience but no experience per se (p. 73). Kant of course also deals with causality in his discussion of alteration: for him while alteration can be perceived its causality cannot, because alteration concerns determinations of appearances “while their cause is to be found in the unalterable” (A171/B213, Guyer and Wood, tr. p. 293). What Maimon says at the foot of p. 71/top of p.71, using an example of water in two determinations as frozen and as fluid – that we perceive first fluidity and then solidity (or vice versa) and then in a judgment (of causation) connect the fluidity with heat and solidity with cold – does not contradict Kant. Causation for both Kant and Maimon isn’t perceived but nevertheless can be the material of a judgement or a “rule of the understanding” (p. 72) which establishes its necessity.
Pages 73-4 are taken up with arguments for the importance of the ‘reflection concepts’ identity and difference (I write ‘reflection concepts’ to avoid the genitive which makes the translation a little ambiguous, as though reflection is also one of the concepts – p. 73). Identity and difference are what Maimon calls “the highest (most universal) forms of thought”. In the complementary realisations that “nothing can be thought as self-identical without being related to things different from one another” and that “I cannot attain consciousness of any individual intuition without the concept of identity” (p. 76) we get a nice, concise statement of these concepts’ perennial usefulness. What interests me here is the apparent even-handedness with which he treats the two in these pages (indeed Chapter 7 had also shown the importance of comparison and hence differentiation to identification). Even when, as seems to follow from idealist premises, we emphasise that knowledge involves a certain “unity of difference” (p. 73) this does not entail difference’s suppression. Rather, as Maimon shows quite nicely on p. 74, difference is indispensible to knowledge, the manifold remains manifold, even if we find some unity in it. All of this is an interesting foretaste of later post-Kantian preoccupations, from Fichte through early Schelling and Hegel and on to Adorno and Derrida, where a supposed imbalance between identity and difference was a reason for each to critique their forebear.
What moves centre stage in the remainder of this chapter is the concept of experience (Erfahrung). At the foot of p. 76 we get a quite programmatic definition of experience as “the perception of the very same persisting thing connected with different determinations that are changing in time.” Maimon here rather unusually but quite vividly turns the adjective beharrlich (persistent or persevering) into a noun to produce an interestingly non-human-specific substance persisting despite changing accidents, though the linkage of this point to experience underlines that this is still a question of something humanly knowable. Indeed experience, Maimon tells us, presupposes the concept of the persisting (substance) and of the changing (accident). It also presupposes a series of determined successions which we call cause and effect. Experience’s further integral characteristic of “continuity” (which, contra Hume, is not merely abstracted from constant conjunction but is a priori) leads us to “fill in the gaps in our perceptions” in order to weave the scattered material of perception into a coherent thread (78).
All this is a great read, in some places very thought-provoking.
Which leads me to my questions. Firstly, from what we’ve read so far we’re familiar with the idea that Maimon believed that not all Kant’s arguments win out over the skeptical (particularly the Humean) position. But aren’t these two chapters, particularly statements on p. 73 and the foot of p. 77 siding more clearly with Kant against Hume? How do these two chapters fit in to the larger scheme of the book? Do we look for rigid coherence or accept that some chapters are doing different things, some more expository of Kant and some mounting a subtle immanent critique of him?
Secondly, on the topic of experience which is so central to this chapter, there’s something I’ve always wondered with regard to German Idealism, and reading Maimon reminded me of it. Could it have been that what so frustrated the Germans about the philosophy of Hume was that the latter seemed basically to have misunderstood something integral to experience, something which on one level came down to an understanding of the word ‘experience’ itself. Think of the etymology of the German word Erfahrung (Kant’s, Maimon’s, Schelling’s, Hegel’s oft-used term). It comes from the same route as fahren and has similar connotations of a journey. It is also used in some cases synonymously with ‘learning’, as in “Heute erfahren wir etwas über Maimons Philosophie”. Experience as Erfahrung connotes a continuous journey of learning, a thread through what is lived and learned from, something which I would suggest already lends itself to substantiality, connotations which are simply not present in the English word ‘experience’. I sometimes wonder if Hume’s suggestion that there is nothing linking our sensations other than mere habit just seemed so alien to the German writers because of their background understanding of Erfahrung that they would never be won over by it, as if the two different word-concepts reflected (or even influenced) incommensurable worldviews.