About the Mathematical Philosophy of Gaston Bachelard

ABSTRACT: How to characterize the mathematical philosophy of Gaston Bachelard? This question cannot receive a clear and quick answer. It is practically impossible in any case to study the epistemology of Gaston Bachelard without being marked by the decisive importance conferred on mathematics. Moreover, it would be more accurate to speak of an omnipresence of mathematics which leads to a quite singular mathematical philosophy. Indeed, by closely scrutinizing all the ideas that structure the mathematical thought of Gaston Bachelard, and by articulating them, we realize that there is in this author a completely new mathematical philosophy, but sometimes unnoticed. Bachelard claims his philosophy of mathematics, beyond rationalist qualifications, as being a “constructed realism” and “metaphorism”. This reflection consists of an explanatory statement of this mathematical philosophy as it comes under the little-known denomination of mathematical realism of a new kind.