ABSTRACT
This chapter deepens the historical remarks by pointing out that, within this tradition, there is an evident precedent to inferentialism: namely, so-called axiomatism, particularly in the form advocated by Hilbert. The specific quality of a given -ism lies in the circumstance that it sees the given principles embedded into a linguistic frame as stemming from the so-called linguistic turn and the very enterprise of analytic philosophy. In the beginning, there was Hilbert's and Poincare's reaction to the phenomenon of Non-Euclidian geometries and the doubts that their emergence had cast on the role of intuition in grounding mathematical knowledge. Hilbert Frege's logic represents both the tool that makes the axiomatic approach possible and the very example of such an approach. The usual reading of Godel's results traces the following regressive pattern: they allegedly show that the idea of purely symbolic foundations for mathematics, as urged by the Hilbert program, is unsustainable.
