This article recovers the epistemological project of Jean-Toussaint Desanti, which, by the use of the conceptual terminology of Husserlian phenomenology, aims at constituting a science of mathematical ideality both against itself and against the positivist enterprises. From this point of view the use of concepts such as immanent consciousness, intentional nucleus, horizon of possibilities, or stratification, is retrieved. Thereupon one attempts to show how Desanti's project is conceived as a new constitution of a field of study, which aims at exhibiting the specificity of mathematical ideality as an effect of a practice which develops by the constitution of its own norms and criteria of objectivity.
Philosophy of mathematics; Phenomenology; Act; Consciousness; Ideality; Immanence; Intentional nucleus; Stratification; Theory; Desanti