Ontological commitments of each side are to be judged relative to the restricted language whose vocabulary is just sufficient to form the sentence in question

For reservations about this claimed result, however, see Boolos (1997). The main objection with which the HP-er needs to contend is that Hume’s Principle is neither a logical nor an analytic truth. It cannot be logical, so the objection would go, because it has such a huge ledger of ontological commitments: for every concept, its alleged number. And it cannot be analytic, because the two sides of the biconditional have different ontological commitments: the right-hand side has no commitments to