 On most accounts, ultra-finitism leads, like intuitionism, to revisionism in mathematics. For it would seem that one would then have to say that there is a largest natural number, for instance. From the outside, a theory postulating only a finite mathematical universe appears proof-theoretically weak, and therefore very likely to be consistent. But Woodin has developed an argument that purports to show that from the ultra-finitist perspective, there are no grounds for asserting that the ultra-finitist theory is likely to be consistent (Woodin 2011).