Ordinal Rationality and Cardinal Rationality

Often each conceived as synonymous with Rationalism, Logic and Mathematics have sometimes been made interchangeable by virtue of equating Conjunction with Multiplication, and Disjunction with Addition.  Thus, the essential Logical operation of Inference is translatable into Mathematics by virtue of the representation within Logic of it in terms of Conjunction or Disjunction.  However, that representation is susceptible to the same challenge that Kant levels at Hume's concept of Causality.  According to that challenge, Hume's rendering of Causal connection as Conjunction abstracts from the temporal ordering of Cause and Effect, i. e. the terms of a Conjunction, but not those of Causality, are interchangeable.  Likewise, a Conjunction or a Disjunction is symmetrical, and thus abstracts from the ordering of Antecedent and Consequent.  So, the attempt to unify Logic and Mathematics via that abstraction is also similar to the common reduction of Ordinal Numerology to Cardinal Numerology, as has been previously discussed, i. e. Antecedent and Consequent are essentially in a First-Second relation, irreducible to a mere juxtaposition such as that of Pythagorean Cardinal Numbers.  Thus, the preservation of Ordinality also preserves the essential distinction between Logic and Mathematics, one that is the distinction between what can be rendered as Ordinal Rationality vs. Cardinal Rationality.