I shall dust off some work by Bohm, on arithmetical features of combinatory logic. The natural combinators for addition, multiplication, exponentiation and nihilation of Church satisfy some pleasing algebraic laws resembling those of ordinal arithmetic. But they also satisfy and some other ''wild'' laws (resembling nothing arithmetical) in virtue of which they are combinatorially complete. Because of that, they support a notion of logarithm (with respect to a ''base''). I may add some remarks on ''exponentiality'', which says that two ''numbers'' are the same if they have the same behaviour as exponents.