sentences: "Russell and Whitehead's theory of foundations[,] ... the foundation that it provides for mathematics rests, first, upon the axiom of infinity and, then upon what is called the axiom of reducibility, and both of these axioms are genuine contentual assumptions that are not supported by a consistency proof; they are assumptions whose validity in fact remains dubious and that, in any case, my theory does not require ... reducibility is not presupposed in my theory ... the execution of the reduction would be required only in case a proof of a contradiction were given, and then, according to my proof theory, this reduction would always be bound to succeed.