An Intensional Interpretation of Truth-Values

Abstract

In a profound and seminal paper of 1956 ‘Begründung einer strengen Implikation’, JSL), Wilhelm Ackermann laid the foundation for what may reasonably be called intensional logics, characterized by the presence of an intensional ‘if… then —’ connective which demands (for provability) relevance of antecedent to consequent, in a sense amenable to treatment by the tools of mathematical logic. The growing body of literature devoted to the philosophical and mathematical analysis of these systems jeopardizes a prejudice which has been an important article of faith among extensionally-minded logicians, ever since Goodman and Quine got it into the mob that no decently reared Christian gentleman of respectable ancestry would consort with propositions, or others of intensional ilk. Among the banned notions is that of relevance, and the credo reads as follows (if memory serves): “this conception, like others in the theory of meaning, is too vague, uncertain, unsettled, indefinite, visionary, undetermined, unsure, casual, doubtful, dubious, indeterminate, undefined, confused, obscure, enigmatic, problematic, questionable, unreliable, provisional, dim, muddy, nebulous, indistinct, loose, ambiguous, and mysterious to be the subject of careful logical scrutiny.”

Reprinted from Mind, n.s. vol. 81 (1972), pp. 348–371, by kind permission of the publisher and editor.