I would encourage Peter's route related to Quine. A formalist in Phil of Math would say that a mathematical statement is true if it can be derived from axiomatic set theory. That is, the truth of the statement is then grounded in formal logic.
This does, of course, beg the question of what grounds our formal logic, but at least it puts basic arithmetic on more firm footing ... in Peter's words, even more deeply imbedded in our belief system.

I would encourage Peter's route related to Quine. A formalist in Phil of Math would say that a mathematical statement is true if it can be derived from axiomatic set theory. That is, the truth of the statement is then grounded in formal logic. This does, of course, beg the question of what grounds our formal logic, but at least it puts basic arithmetic on more firm footing ... in Peter's words, even more deeply imbedded in our belief system.