ИМПЛИКАЦИЯ

Implication

The logical operation which forms a complex proposition from two propositions (for example, p and q) through a logical connective conforming to the conjunctive "if ... then": if p then q. In an implicative proposition we distinguish the antecedent preceded by the word "if" from the consequent which follows the word "then".

Mathematical logic proceeds from the concept of material implication (expressed in the form p→q or p⊃q), which is determined through the function of truth-value. Implication is false only if the antecedent (p) is true and the consequent (q) is false, and true in all other cases. This concept proved to be quite effective for the logical proof of mathematical statements.

But logicians, who treat the problem of implication as one of formalised logical sequence have discerned in it a number of properties (for example, "a true proposition follows from any proposition", "of any two propositions one implies the other") which sound paradoxical if we require implication to express the properties of logical sequence in sense, i.e., some connection in meaning between the antecedent and the consequent, as a condition of truth.

In view of this, C. I. Lewis, utilising the concept of modal logic, gave a definition of a strict implication (expressed in the form p ~→q): it is impossible for p to be true and q false (p necessarily implies q). But Lewis' system also gives rise to its own "paradoxes" similar to the case of material implication. There are other methods of eliminating these "paradoxes" (for example, Ackermann's concept of a strong implication).

Импликация

(От лат. implico - тесно связываю) одна из логических операций; в естественном языке И. соответствует связка «если..., то».