Poincare": Mathematics Logic Intuitiont

Poincar6 often insisted existence in mathematics means logical con-sistency, and formal logic ia the sole guarantor of rigor. The paper joins thisto his view of intuition and his own mathematics. It looks at predicativity andthe infinity Poincar^'s early endorsement of the axiom of choice, and Cantor'sset theory versus Zermelo's axioms. PoincarS discussed constructivism sympa-thetically only once, a few months before his death, and conspicuously avoidedcommitting himself. We end with Poincare' on Couturat, Russell, and Hilbert.