Poincaré believed that arithmetic is synthetic. He argued that Peano's axioms cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is a priori synthetic and not analytic. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were similar to those of Immanuel Kant (Kolak, 2001, Folina 1992). He strongly opposed Cantorian set theory, objecting to its use of impredicative definitions.
poincaré believed that arithmetic is synthetic he argued that peano's axioms cannot be proven non-circularly with the principle of induction (murzi 1998) therefore concluding that arithmetic is a priori synthetic and not analytic poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic his views were similar to those of immanuel kant (kolak 2001 folina 1992) he strongly opposed cantorian set theory objecting to its use of impredicative definitions