The observation that isomorphic relations have isomorphic high frequency patterns implies some unexpected properties about the association rules. First of all, the patterns are properties of the isomorphic class, not an individual relation. Second, those countings on itemsets, association rules and etc. are invariants under isomorphism, and hence the probability theory based such countings is again a theory of the whole class, not an individual relation. On the other hand, examples show that "interesting-ness" (of association rules) are properties of an individual relation, not the whole isomorphic class. As a corollary, contrary to many authors beliefs, we conclude that interestingness cannot be characterized by such a probability theory.