Induction and Material Implication

Deduction and Induction are typically distinguished by two contrasts. First, while Deduction is the derivation of a Particular from a Universal, Induction posits a Universal on the basis of observed Particular cases. Second, accordingly, Deduction proceeds with certainty, whereas Induction is, at best, only highly probable, i. e. because it cannot preclude the possibility of a future counter-example arising. Hume has suggested a third significant distinction. In Deduction, the certainty of its conclusion is an expression of its Objectivity, namely of a relation that inheres in the connected terms or statements. In contrast, on his analysis of the most prominent result of Inductive reasoning, namely Causality, a seeming Objective relation is actually only Subjective. For, he shows that while 'A causes B' seems to assert an Objective connection between A and B, it means no more than 'The perception of A has been regularly conjoined with the perception of B', a Subjective connection, regardless of how generally accepted the proposed Law might be. Kant's response to Hume is that this analysis overlooks a crucial Objective element--that in 'A causes B', the temporal precedence of A to B is inherent, independent of any perceptual experience, in which the order of A and B is arbitrary. This response to Hume sheds a similar light on the Modern Logic's Material Implication., in which 'If A, then B' is represented as 'not-(A and not-B). As has been discussed here previously, the latter formula abstracts from the Antecedent-Consequent ordering of the former, just as Humean Induction abstracts from the Objective temporal order of a Causal connection. Hence, Material Implication is basically Inductive, not Deductive, as it is generally presented. Furthermore, insofar as Material Implication is one of the cornerstones of Contemporary Logic, so too is the latter, as a whole. The notion that Contemporary Logic is fundamentally Inductive is consistent with its implicit Ontological Atomism, and is perhaps even better exposed by its concept of 'All', derived from Peirce's, meaning 'aggregation', not 'totality', as is the product of, e. g. the Formal Principle in an Ontology of Formaterial Systems.