 In Tennant (2009), the constructive logicist treatment is extended to deal with both addition and multiplication. The key innovation is a ‘logic of orderly pairing’: a system of natural-deduction rules of inference governing the formation of the ordered pair π(t,u) from existing objects t and u, and the projections λ(u) of the left, and ρ(u) of the right, member of any ordered pair u. 