 From 1905, Poincaré therefore opposed the logicist thesis that claims to be able to prove all mathematical truths without recourse to intuition, once the principles of logic are admitted. Poincaré suspected that the logicians were actually making an equivocal use of the term logic and that they no longer sought the former kind, but rather a “new logic” containing principles of synthetic proof or formations of non-logical concept. He was evidently right given that not only is the modern logic of predicates richer than the traditional (syllogistic) logic, but in order to carry out the logicist project, one is even led to expand logic again by certain set-theoretic postulates of existence.