In this paper devoted to the epistemological concepts of Jean Cavailles, regarding the formal thought and the theory of science, we shall first analyze how Cavailles's theory of mathematics, represents a severe critique of logicism and especially of the universal enterprise of Carnap, whose logical syntax is censured by the French philosopher, vis-a-vis both the question of formalism, and that which studies the relationship of mathesis formalis to physics in Carnap's epistemology. Second, given the sympathies of Cavailles for the intuitionist mathematics and a certain resonance of his epistemology with Brouwer's, we seek to underscore, based on a critical analysis by Cavailles himself, the problems that intuitionism presents. On the one hand, we shall see this in the indeterminacy of mathematics to physics, and on the other, in the danger of finding science absorbed by mathematics if one admits, with the Dutch mathematician, that it is a rational thought of the world. In the third and last part of the article we outline Cavailles's working program, his last roadmap, in favor of a constructive and refined epistemology of mathematics, perceived in its purest essence and per its praxeological relation to the natural sciences. The definitive aim is to approach the project of Cavailles, understood as a conceptual epistemology and grounded on a strictly Bolzanoan approach to what's logical, a pure theory of rational chains which at the same time addresses the determination of objects' possibilities and their possibilities of determination. We shall see how that undertaking is supported by a strong notion of necessity, whose unpredictable nature escapes the mesh of logic and is found across all mathematical praxis in its inherent temporality.
