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It has been one of the strange and unexamined features of contemporary philosophy that philosophical as well as technical concern with the formal sciences — formal logic and mathematics, formal syntax and semantics — has been taken to be an ally of a positivistic, formalistic and (narrowly) analytic philosophical perspective. I believe that upon further questioning, this alleged alliance breaks down, and the prima facie neutrality of the conecrn with formalism leaves room for a great diversity of philosophical standpoints — from a Platonic to a Kantian, to name two familiar contrasting positions. It is also a philosophically unexamined point of view, which requires that an understanding of the nature of the formal sciences must itself be formalistic, that you truely understand the nature of a formal discipline when you embed it in a meta-discipline of the same nature. There is certainly a sense of "understanding" in which this is the case. But there is a sense of "understanding," a sense that is of central importance to philosophy, in which one can ask questions about the formal sciences which do not permit any nontrivially formalised answer. The purpose of the present essay is not merely to bring to the forefront the relevance of the phenomenological perspective for philosophy of the formal sciences, but to open the doors for questioning that taken-for-granted alliance and for the possibility of radically other approaches. Let us only remember that Frege was a sort of Platonist-cum-neo-Kantian (despite the efforts of the believers in that alliance to show that he was a hidden nominalist), David Hilbert a Kantian, Hermann Weyl a sort of Husserlian. Where to place Gödel and Hao Wang? Panini and Chomsky? Or, let us think of our friends Jaakko Hintikka and Carlos Rota.

DOI: 10.1007/978-94-017-2113-4_3

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