Logic and Piaget's theory: the significant implication

Abstract

"Implication" has, as a very important referent, some deductive situation. In other word, we may say that"P1, P2, ..., Pn imply C" whenever C is a conclusion that follows from the premisses Pi (i = 1, 2, ...,n). Implication, in such cases (and in similar inferential situations), admits reading with the help of"If .... then.,.". Very often, the same locution is used to read the expression"p ? q", constructed with the horseshoe of prepositional calculus (the"philonical juntor", as we may call it, homage to Philon, of Megara). It's not unusual to associate this horseshoe with some type of dedution - a serious mistake, if it is used as a simple operator from the calculus. Besides, the"If,.., then..." has a relevant role in explanations (including causal ones). Identifying the various forms of use of the expression"If..., then..." we come to an appropriate characterization of the meaning to give to the term 'significant implication', as it was considered by Jean Piaget. At the same time, sugestion is made as for the way of understanding the"operations-causality" dichotomy.