This short piece aims to clarify, in the light of a comparative methodology, some aspects of the philosophical topology put forward by Gaston Bachelard in one of his final epistemological works, with the objective of making clear one of the many ‘philosophical souls’ – to use an expression of Moritz Schlick – which can be found nestled in the sciences and in particular in the mathematical corpus of his time. At the same time, this piece aims to show how this need of a topology or topological reason finds analogy with that path of a more philosophical nature that characterized the final activities of Kurt Gödel in the 1950’s, as can be seen in his rich, articulate and now available Nachlass – his attempt to classify the different philosophies of mathematics.

This makes it possible to show that different paths, despite having emerged in cultural contexts far from each other, but all oriented towards under-standing the ‘reasoning of science’ of their time – to use an expression of Federigo Enriques – sometimes come to very similar results, such as the need for a new non-analytical philosophy of mathematics.

Received 15 October 2020. Revised 20 October 2020. Accepted 03 November 2020. Published online 20 December 2020

Gaston Bachelard, Epistemology, Topology, Kurt Gödel, Philosophy of Mathematics,

http://dx.doi.org/10.26106/CMBY-1492