 Constructive logicism is based on rules of natural deduction that are arguably analytic of the central notions zero, successor, and number. There are also rules that pin down the meaning of the number-term-forming operator #xΦ(x) (the number of Φs). In the terminology introduced above, the rules for #x amount to a single-abstraction identity principle. The remaining rules are allowed to carry only very local and modest ontological commitment, on the grounds that it is part of the very meaning of a term such as ‘0’ that its use in the language commits one to the existence of the number 0. Here, for example, are the natural-deduction rules governing zero. ‘⊥’ is the symbol for absurdity. 