The Formal Theory of Everything: Explorations of Husserl’s Theory of Manifolds (Mannifaltigkeitslehre)

Husserl’s theory of manifolds was developed for the first time in a very short form in the Prolegomena to his Logical Investigations, §§ 69–70 (pp. 248–53), then repeatedly discussed in Ideas I, §§ 71–2 (pp. 148–53), in Formal and Transcendental Logic, §§ 51–4 (pp. 142–54), and finally in the Crisis, § 9 (pp. 20–60). Husserl never lost sight of it: it was his idée fixe. He discussed this theme over forty years, expressing the same, in principle, ideas on it in different terms and versions. His discussions of it, however, were always cut short and inconclusive, so that he never developed his theory of manifolds in detail. Main claim in this essay is that Husserl’s theory of manifolds is twofold. It is (1) a theory of theories, advanced in the good German tradition of Wissenschaftslehre, launched first by Bernard Bolzano. The latter, in turn, is an offspring of the ancient tradition of mathesis universalis, explored in the modernity by Descartes and Leibniz. Further, (2) the theory of manifolds is also a formal theory of everything. Its objective is to provide a systematic account of how the things in the world (its parts) hang together in wholes of quite different kind. It is to be noted that Husserl explicitly speaks about (1) and only implicitly about (2). In this paper we shall also show that the theory of everything is intrinsically connected with the theory of theories.