Implication and Ordinality

One of the central principles of Analytic Philosophy, the predominant school of academic American Philosophy, is Russell's thesis 'Logic is the essence of Philosophy'. Now, if Logic is the essence of Philosophy, then its treatment of one of its key connectives, Material Implication, is also of that essence. In that Logic, Material Implication, 'If P, then Q', is represented as either a Conjunction, 'Not-(P and not-Q)', or a Disjunction 'P or not-Q', which are equivalent in the System. Representing Material Implication either way suits the systematic requirement that every compound Proposition has a Truth-Value that is computed in terms of the Truth-Values of its constituents. As has been well-documented here and elsewhere, the resultant Truth-Computation of interpreting Implication as either Conjunction or Disjunction includes peculiarities such as--'If Mars is Earth, then a tree is a frog' is True. So, one feature of Analytic Philosophy is that technical coherence is more important than common-sense, which would not make it alone amongst Philosophical Systems. But one significant distinction between the 'If-then' construction and Conjunction and Disjunction is that the latter two are symmetrical relations, whereas the former is not, i. e. whereas the order of P and Q in 'P and Q' or in 'P or Q' is irrelevant, it is essential in 'If P, then Q'. In other words, this interpretation of Implication arbitrarily trivializes the distinction between Antecedent and Consequent, which bespeaks a fundamental inadequacy to Ordinality, i. e. Sequentiality, and which raises the further question of how this Logic can elsewhere insist on a distinction between Axioms and Theorems, i. e. between primitive and derived Truths. So, if inadequacy to Ordinality is a fundamental characteristic of this Logic, then it is of the essence of Philosophy, on Russell's thesis. But, there are Philosophical Systems, including Evolvementalism, in which Ordinality is an essential feature. Hence, a more accurate version of Russell's thesis is 'OUR Logic is the essence of OUR Philosophy', a qualification of its Principle to which Analytic Philosophy sometimes expresses obliviousness.