Based on insights from discussions on computation, the structure of natural numbers, de re knowledge of numbers and the standard interpretation of arithmetic, it is questioned whether a counterfactual account of explanation can work for number-theoretic counterpossibles. Making use of Peano arithmetic, emphasis is put on the role of the standard induction scheme, as it contains the symbol for the successor function, as such suggesting an intimate connection between Peano numerals and de re knowledge of numbers. Because of the resulting shift in context in the antecedent, the way a contexts stops an explosion of ramifications in the case of ordinary counterfactuals might not be available in the case of number-theoretic counterpossibles.