 Regarding the antinomies discovered at the turn of the century— such as Richard’s or Russell’s paradoxes—they are, according to Poincaré, the consequence of an abusive use of intuition with respect to abstract entities that arises from the adoption of conceptual realism (Platonism). In a definition of the form \(\exists y \forall x ((x \in y) \leftrightarrow D[x])\), the existence of the set \(y\) is intuitively postulated without any restriction for the predicate \(D[x]\). For an anti-Platonist like Poincaré was from 1906 on, intuition is not a mode for representing an object, but rather concerns our capacity to follow a rule. We see this quite clearly in Poincaré’s discussion of mathematical induction.