Writing SampleInfinitesimals and Di!erentials in

Salomon Maimon’s Essay on TranscendentalPhilosophy

B Tyson GoftonUniversity of Toronto

Abstract

It has become standard in the literature on the reception of Kant’s Critique ofPure Reason to interpret Salomon Maimon as proposing a “Leibnizian” representa-tional monism (i.e., thought all the way down) in his Essay on Transcendental Philos-ophy (Maimon 2010) in order to remedy perceived limitations in the representationaldualism implied by Kant’s Transcendental Deduction. (See, for example, (Bergman1967), (Beiser 1993) and (Thielke 2003).) This now-standard reading, however, isincorrect. The misreading is based in a failure to appreciate Maimon’s distinction be-tween ‘infinitesimals’ as a term designating the actual least magnitudes that are thereal components of sensibility and ‘di!erentials’ (or ‘ideas of the understanding’, Ver-standesideen) as a term designating the intelligible or symbolic posits that are thoughtto be the fundamental components of purely intelligible representations of real de-terminations of the subject. Accordingly, Maimon does not propose a representationalmonism, but rather a intelligible dualism (concepts and ideas) that serves an epistemo-logical dualism: one that distinguishes between empirical cognition (and the skepticismthat it gives rise to) and purely ideal or symbolic knowledge (and the dogmatism thatit gives rise to). A more accurate interpretation of Maimon’s Essay on TranscendentalIdealism will help us to better understand the reception of Kant’s Critique of PureReason by the German Idealists. However, it also points to an important limitation inKant’s epistemology and proposes a solution that is worth considering in its own right.

1 Maimonian Monism

Salomon Maimon’s Essay on Transcendental Philosophy (Maimon 1790) (Maimon 2010) is

one of the most important works in the early reception of Kant’s Critique of Pure Reason.1

1For a general introduction to Salomon Maimon’s life and work, see Frederick Beiser’s The Fate of Reason(Beiser 1993, Chapter 10). For a contrasting interpretation of the orientation and significance of Maimon’swork — one closer in spirit to my own view — see Paul Franks’ All or Nothing (Franks 2005).

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1 MAIMONIAN MONISM 2

Although by no means a well-known work in its own right, it had a significant (and by

now well-documented) impact on the major figures in post-Kantian systematic philosophy

in Germany, especially Fichte, Schelling and Hegel. Moreover, Maimon’s skepticism — and

especially his doubts about the success of the Transcendental Deduction even if we concede

Kant’s premises — raised lasting doubts about the integrity of Kant’s proposal. Nevertheless,

it’s not entirely clear what Maimon actually proposed. For, the Essay on Transcendental Phi-

losophy is surely not the most perspicuously composed works of commentary ever written.2

One of the most problematic aspects of interpreting Salomon Maimon’s Essay is making

sense of his doctrine of the di!erential, since interpreting the doctrine of the di!erential

is essential to interpreting the Spinozist, Humean, Leibnizian and Kantian dimensions that

Maimon explicily avows. Only through a correct interpretation of the di!erential can we pre-

cisely define the failure of transcendental philosophy and correctly identify the idealization

of sensibility that it proposes.

Maimon introduces the di!erential — a metaphysical and mathematical concept — in

three distinct ways. The di!erential:

(a) originates in sensibility as the object of our ultimate claims to knowledge; (Maimon

2010, MW II:32)

(b) is a pure product of the understanding, or a Verstandesidee; (Maimon 2010, MW II:75)

(c) is declared to be a “limit concept (Granzebegri! )” between sensibility and thought.

(Maimon 2010, MW II:192)

It is because of the di!erence between (a) and (b) that, Maimon claims, Kant’s attempt

to resolve the quaestio quid juris fails. However, it is because of (c) that an answer is

thinkable, if merely ideally. However, it is also claims such as (c) that give the impression

that di!erentials just are the components of sensibility. Unfortunately, apart from the Essay

2The Essay contains at least four di!erent layers of commentary: the initial (short) commentary; theextensive notes and comments added to the same; the “Short Summary” that is nearly as long as thecommentary itself; and the “Appendix on Symbolic Thought”.

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Maimon nowhere makes explicit the claims and commitments of his interpretation of the

di!erential and its relation to metaphysics, epistemology or mathematics. Instead, we are

left with a handful of suggestive remarks, some unhelpful allusions to Leibniz, and a scathing

criticism of the Kantian position.

The general consensus is that Maimon’s proposal renders him a kind of monist;3 For

example, Bergman claims, that the doctrine of the di!erentials is “a doctrine designed to

reduce sensibility to silence or, at least, to diminish its excessive claims” (Bergman 1967,

59). Indeed, di!erentials, Bergman thinks, turn out to be nothing more than “laws of

the understanding” (which would seem to be categories!), since “the a"nity between the

understanding and matter can be understood only after matter has been converted into the

laws of the understanding. These laws Maimon calls di!erentials” (Bergman 1967, 59). A

similar interpretation is defended by some contemporary interpreters, for example, by Peter

Thielke:

Di!erentials of perception are to be understood as, in some sense, the productsof the understanding itself, (Thielke 2003, 117, my emphasis)

since,

what to the quotidian consciousness appears as merely given is, from a philo-sophical perspective, a product of the rule-governed but not ‘rule-understood’di!erentials of the productive understanding. (Thielke 2003, 118, my emphasis)

Maimon, then, is a Leibnizian, who claims that there is merely a conceptual distinction

between the activity of intuiting forms and the activity of understanding them; that is, that

the di!erential is the origin of both intuition and the understanding.

It’s not hard to see what motivates this reading of the Essay, for, especially in the ‘Short

Overview of the Whole Work’, Maimon makes a number of claims that suggest just such an

3The interpretation has become standard since Samuel Bergman’s The Philosophy of Solomon Maimon(Bergman 1967) and has been embraced by most commentators since then, including Samuel Atlas, PeterThielke and Fred Beiser.