Logic, Mathematics, Quantity

As has been previously discussed, the standard attempt to unite Logic and Mathematics, via the equating of Conjunction and Disjunction with Multiplication and Addition, respectively, depends on the problematic reduction, within Logic, of Inference to either Conjunction or Disjunction.  In contrast, without that reduction, a immediate unification is possible, via not Propositional Connectives, but via Predicate Quantification, which is the medium of Aristotelian original Logic.  Specifically, Inference, qua Entailment, consists in the relation of Greater-Than, as is plainly illustrated by Venn diagrams, and exemplified by the Universal-Particular relation of Aristotelian Logic.  But, one reason why the standard approach to uniting Logic and Mathematics is not via the apparently common concept of Quantity may be that the concept is not necessarily common to them.  For, insofar as the Quantity entails an inherent comparison of quantities, it is not a property of Pythagorean, i. e. Cardinal, Numbers, which are mutually independent.  So, if Pure Mathematics is conceived on the basis of Cardinal Numerology, then Quantity is not 'Pure', and, hence, cannot mediate the unification of Mathematics with Predicate, i. e. Quantification, Logic.