 The ontological bill for the constructive logicist is much more modest, compared to that of the HP-er. The constructive logicist is not even committed (by the rules he lays down) to the existence of the number of all natural numbers. Commitment is incurred (by employing Frege’s trick) to the natural numbers seriatim, as necessary existents. No commitment is incurred, however, to any other cardinal numbers. 