 Heck (1997b) dealt with so-called ‘finite Frege arithmetic’. His treatment was classical. But Heck was concerned, as constructive logicism had been, to derive the basic laws of arithmetic while incurring ontological commitment only to the natural numbers. To this end Heck restricted Hume’s Principle to predicates with finite extensions. It is therefore natural to conjecture that constructive logicism is the intuitionistic (relevant) fragment of Heck’s finite Frege arithmetic. 