A "fundamental" perplexity

A century before Hilbert, in his Beiträge, Bolzano proposed with astonishing prescience the autonomy of mathematics from transcendental philosophy. In a few brief, lucid paragraphs, Bolzano proposes a simple criticism of the Kantian project: not all objects that appear (to us) must have a form but only those that appear as external. Couple this observation with his definition of mathematics as the “science which deals with the general laws (forms) to which things must conform [sich richten nach] in their existence” and mathematics is effectively inoculated from the grounding mechanisms of transcendental philosophy from Kant to Heidegger.

In one sense, then, it should not be surprising that around 1961 the man who made Hilbert’s program so problematic should declare that there is something fundamentally correct about Kantian philosophy: i.e., that the construction of new mathematical theorems that cannot be derived from a finite number of axioms requires new intuitions. Yet Gödel avers here not to a Kantian notion of intuition—which he admits is unclear at best and, as Bolzano had already noted, simply false for a large part of mathematics outside geometry—but to Husserl and claims that in phenomenology philosophy for the first time meets the desiderata established by Kant. That is what should be surprising since the gulf between Kantian and Husserlian intuition seems too wide for the easy leap Gödel wishes to make.

Perhaps the missing link may in fact be Bolzano. Objects of perceptual experience, Bolzano claims, must have a form but also—unlike, for example, mathematical objects—sensible matter (as he says, something which “occupies [erfüllt] this form). Instead of the usual word “matter”, however, Bolzano asserts that these are also a priori forms (as space and time are for Kant), “except that the range to which the former relate is narrower than that of the latter, just as the form of space has a narrower range than that of time”. We are here well on the way to Husserlian hylomorphism; yet the later genetic phenomenology abandons the constitution of sense hylomorphically. As Henry has shown, for example, and as Husserl himself declares in the lectures on active and passive syntheses, hyle is ejected from its status as the blind content of the real into the life of the monad within which “a unitary nature and a world in general is constituted genetically … according to a constant process of attestation” (Husserl). Is this not the pathos of truth and the impossible ethical problem explored by Sartre insofar as, in his language, the “essence” of the for-itself is nothing other than relatedness (relation to itself, to being, and to others as three aspects of the same transcendental structure)?