unprovable assumptions, like the utiliity of induction

One might call induction an "undeniable assumption" instead: we cannot do without it; it's part of what we are. As a matter of human nature (and, indeed, the nature of all other animals (and computer programs) capable of learning), we do use induction, regardless of whether we can prove it. Some of the best evidence for induction might be rather crudely anthropic: we, who implicitly and constantly use induction, are here; creatures with anti-inductive priors are not here.