 It is notable that mathematical truths in fields to which CPI applies are not conditional propositions without existential import. The demonstration of such a truth must be based on a particular and observable instance. Although there are standard procedures for constructing different geometrical and arithmetical objects, the rules do not suffice to deduce the properties of the result. They can be known only from an actual implementation of the rules. The relational orderings of positions in space, time, and among the numbers inevitably affect the base cases of inductive conclusions. So Shepherd maintains that the general truths of natural science which require empirical evidence are necessary and the necessary truths of arithmetic and geometry are believed on the basis of experience. In this respect, Shepherd’s theory is like that of Kant, but they differ over the reality of the entities known. 