A recent web draft by Australian philosopher Paul Redding — author of a nice introductory book on analytic readings of Hegel — makes quite a few interesting points about Leibniz, Kant, Hegel, J.N. Findley, and modal logic. Findley was an important 20th century philosopher with analytic training who developed a very this-worldly but still metaphysical reading of Hegel, with strong influence from Wittgenstein. Findley’s student Arthur Prior apparently developed an “actualist” alternative to the more common possible worlds approach to modal logic, which latter is usually said to have an antecdent in Leibniz. Redding argues that there is a similarity between Prior’s criticism of modal possible worlds and Hegel’s criticism of Kantian formalism in ethics.

I take the assertions of Leibniz in a more tentative way than Redding seems to, and sharply distinguish between Leibniz and his Wolffian semi-followers. Leibniz’s thought on possible worlds, though, is one of the parts of his work I agree is less attractive, even though I am sympathetic to its motivation as an alternative to theological voluntarism. It seems to me like a beautiful but very extravagant speculation, related to his thoughts on infinity. Leibniz’s youthful co-discovery of the calculus was but one aspect of a lifelong fascination with the new idea of a mathematical infinity. Explicit reliance on the assumption of this kind of “actual infinity” is removed from later presentations of mathematical analysis, which instead carefully talk about differentials and integrals in terms of limits. For what it’s worth, Aristotle argued against any actual infinity, and Hegel called it “bad infinity”.

Redding attributes to Findley criticism of an ethics of rules in favor of an ethics of values. I like this very much in general, but I make a big distinction between rules that would supposedly just tell us what to do (which I find hideous) and higher-order rules like Kant’s categorical imperative, which merely requires that we aim at universality, without presuming to tell us exactly what we should do. While taking Hegel’s criticism of Kantian formalism a bit more literally than I would, Redding nonetheless concludes that Hegel’s position is an extension of Kant’s.

Redding notes Hegel’s complaint against Kant’s advocacy at one point of “duty for duty’s sake”. I find this formula as unappealing as the categorical imperative is salutary. But it turns out that Kantian “duty” is really a stand-in for the kind of absence of material inconsistency that characterizes a unity of apperception. Redding cites Hegel in the Philosophy of Right as criticizing Kantian duty as mere “absence of contradiction”. He correctly points out that what is at issue is hardly the law of non-contradiction in the usual sense, so Kant’s argument is not really like the Wolffians’ attempt to derive a whole metaphysics from that logical law. But Redding then attributes to Hegel an emphasis on “actualized Sittlichkeit” as opposed to empty formalism. Hegel may have said the words, but I think this is way too simple. It sounds like some actually existing set of norms just taken at face value. I’d take empty formalism over that any day. (See discussion on Pippin’s concern about positivity in Mutual Recognition.) Unfortunately, Redding also moves from unity of apperception to a Fichtean self-identity of a Subject (“I = I”), from which I want to sharply separate Kant and Hegel.

The idea of building logical modality into the actual world rather talking about quantification over possible worlds seems appealing to me, but I would not want to go so far as to deny potentiality, as Kant seemed to in his more Newtonian moments, to which Redding alludes. I think Hegel went a long way toward recovering something like potentiality.