CLASSICAL LOGIC: FORMALIZATION OF LOGICAL IMPLICATION

Abstract

The question of formulation on a pro forma basis (without analysing the specific content of variables) of the
logical implication «A⊧B» is not still finally answered. This is due to the known difficulties. Firstly, the
logical implication takes place in conditional (implicative) statements which, if they are true, may express
logical implication or may not. Secondly, conditional statements can be true even when their antecedents and
consequents are not related to each other according to their senses. Thirdly, the problem of what is called
“para-doxes of material implication” is imposed on answering the question of the logical implication: it is
known that the implication is true, as in the case if the falsity implicates the truth ("Truth follows from
anything") as in the case when the arbitrary expression is derived from the contradiction (“contradiction
(sequitur) quodlibet (ECQ)” (“A contradiction yields to completely contrary explanations”)..