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Philosophers have defined Gaston Bachelard as a “Janus-faced person”, for his eyes, like those of the ancient Latin divinity, seem to explore two different directions, ranging from epistemology to poetics. The French scholar equally devoted his studies to these fields, developing an extremely original perspective, which inspired new interpretations of the subject of contemporary science. This peculiarity of the Bachelardian thought must also be kept in mind when examining his reflection on the concept of space, which is analyzed from the different but complementary points of view of epistemology and poetics. Bachelard’s philosophical analysis overcomes the naïve concept of space as a uniform extension, and analyses its mathematical properties, thanks to scientific speculation; while it makes use of poetical reflection to describe its emotional properties. The first pages of Le Rationalisme appliqué (1949) propose the famous “table” providing the theoretical coordinates of Bachelard’s “applied rationalism and technical materialism”, and they reconsider some traditional categories and philosophical movements. The French scholar refers to this table as a “philosophical topology”, using a problematic definition which has been widely discussed and criticized. This contribution attempts a clarification of this “philosophical topology”, by examining some aspects of its genesis, and pointing out how Bachelard, consistently with his theoretical statements, does not simply carry out a reflection on space through philosophy. Indeed, he also considers the other side of the question, proving that mathematical knowledge may affect the understanding of philosophy. The chronology of Bachelard’s works witnesses an alternation of epistemological and poetical publications, thus proving that the distinction between the two fields does not mark a boundary between two consecutive phases of his reflection, but it highlights the constant articulation of his research. This statement underlies the second part of our itinerary, which examines the “dialectics of the outside and the inside” through which La poétique de l’espace (1957) reverses the fundamental geometrical opposition between outside and inside, typical of the traditional Euclidean common sense.

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