This chapter discusses a concrete example of counterfactual reasoning about a mathematical explanation of physical facts, which serves a starting point for number-theoretic counterpossibles. Special attention will be given to contradictions that arise from varying the necessary properties in the antecedent. Even though a contradiction tolerant logic would be able to deal with those, this is not the only problem. Since the numbers are not closed under succession anymore, the resulting model of arithmetic will not be isomorphic to the standard interpretation.