We propose an interpretation of the integers as operations on permutations. Addition and multiplication of integers represent operations on these operations. It follows that an equation involving integers, addition and multiplication is valid if and only if the corresponding operations on permutations are the same. In our interpretation, the validity of the fundamental laws of calculation is an immediate consequence of well-known properties of permutations. For example, the ‘Law of signs’: (–1) x (–1) = 1, is valid because the inverse of the inverse of any permutation is the permutation itself.