What can Peano say about ‘2+3=5’?

Abstract In a recent paper, Mary Leng expressed her conviction that the equality `2+3=5' should be justified by its derivability from the Peano axioms. It turns out, however, that proving `2+3=5' from the Peano axioms and counting apples in the appropriate collections are essentially the same game played with different pieces. Indeed, generally, proofs of simple arithmetical equalities from the Peano axioms can be shown to be really empirical demonstrations disguised as axiomatic proofs. Moreover, the other frequently used attempt to justify such equalities in a non-empirical way also fails.