Question-Answer Semantics

Abstract

The present paper deals with a special kind of many-valued semantics: Question-Answer Semantics, in which logical values are products of questions about semantic predicates (‘true’, ‘false’, etc.) and corresponding answers (‘yes’, ‘no’, etc.). It purports to clarify some di_culties related to what is meant by basic speech-acts like assertion and denial. Deep disagreements occur whenever any two speakers disagree about the meaning of the words they use. In the special case of truth-values, Frege took these as the referents of propositions that are classes of sentences accepted (‘true’) or rejected (‘false’). Starting from this usual depiction of truth and falsehood, a general algebraic framework ARn/m is proposed in order to systematize the use of truth-values within a dialectical perspective of logic. A special attention is paid to two pseudo-speakers radically opposed, namely: Heraclitus, and Nagarjuna, according to whom truth-values refer to everything and nothing, respectively. In the end, a dialectical (pseudo-Hegelian) negation is sketched as a very peculiar function, namely: as an ontological object-forming operator, which is similar to the arithmetic successor-forming operator Sn+1(x) applied to integers and also matches with a generalized theory of truth-values as Millian or Kripkean proper names.