 Can formalism be developed in such a way as to surmount these two crucial objections, the problem of applicability and the problem of the metatheory, as I will call it? (Not that these are the only objections to formalism, but they are two fundamental ones.) Because Frege’s critique did not quash all formalistic impulses in later philosophers of mathematics, we shall look, now, at future developments, to see how they fare.