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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 closer questioning, this alleged alliance breaks down, and the prima facie neutrality of the concern 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 non-trivially formalised answer.

DOI: 10.1007/978-94-011-2580-2_7

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