Synthetic geometry and Aufbau
From antiquity to the beginnings of the 20th century philosophers took geometry as a paradigmatic example of science. Geometry defined what was to be considered as scientific knowledge. "More geometrico" was a sign of quality for philosophical and scientific argumentation. Philosophy and science had to make a great conceptual effort to get rid of this overwhelming and sometimes depressing epistemic ideal of geometry. Today this aim has been achieved to a large extent. Geometry as a philosophical topic is of secondary importance at most. Certainly, it does not occupy centre stage in the contemporary discussion of epistemology and philosophy of science. Not even in philosophy of mathematics, geometry is considered as a hot topic. For instance, in Tymoczko's (already somewhat dated) anthology New Directions in the Philosophy of Mathematics (Tymoczko, 1985) no contribution deals with geometry in its classical or modern form. A priori there is no need to deplore this situation, geometry may belong to those topics that for good reasons are no longer on the agenda of contemporary philosophy. Be this as it may, this situation is markedly different from that of the beginning of the 20th century. For philosophers such as Russell, Cassirer or Carnap, to name but a few, the philosophical problems posed by geometry played a central role in their investigations.
Mormann, T. (2003)., Synthetic geometry and Aufbau, in T. Bonk (ed.), Language, truth and knowledge, Dordrecht, Springer, pp. 45-64.
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