sentences:  his 1904 "On the foundations of logic and arithmetic").His system is neither set theoretic nor derived directly from Russell and Whitehead.Rather, it invokes 13 axioms of logic—four axioms of Implication, six axioms of logical AND and logical OR, 2 axioms of logical negation, and 1 ε-axiom ("existence" axiom)-- plus a version of the Peano axioms in 4 axioms including mathematical induction, some definitions that "have the character of axioms, and certain "recursion axioms" that result from a general recursion schema" plus some formation rules that "govern the use of the axioms".