Generalized Truth Values and Many-Valued Logics: Suszko’s Thesis
According to Suszko’s Thesis, there are but two logical values, true and false. In this chapter, we consider and critically discuss Roman Suszko’s, Grzegorz Malinowski’s, and Marcelo Tsuji’s analyses of logical two-valuedness. Another analysis is presented which favors a notion of a logical system as encompassing possibly more than one consequence relation. Moreover, in light of these considerations, we will point out that the relation between the notion of a truth value and the notion of entailment is even more intimate than the connection emerging from the interaction between properties of entailment relations and truth values. In some cases it is possible to draw a strong analogy between them, namely to interpret entailment relations as a kind of truth value, and such an interpretation seems to be both natural and promising.