Blackwell Reference Online

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The most natural and straightforward step towards the construction of a many-valued logic is to introduce logical values next to truth and falsity. Thereby one has to reject the principle of bivalence, that every proposition has exactly one of the two logical values. Another, indirect way consists in challenging the classical laws concerning the sentence connectives and introducing non-truth-functional connectives into the language, among them the modal connectives of possibility and necessity. In either case the semantics adequate is different from the classical, that is Boolean, thus the logic under consideration is non-classical.The roots of many-valued logics can be traced back to Aristotle (fourth century BC) who considered, within the modal framework, future contingents sentences. In Chapter IX of De Interpretation Aristotle provides the time-honored sentence-example representing this category: ‘There will be a sea-battle tomorrow.’ The Philosopher from Stagira emphasizes the fact that future contingents are neither actually true nor actually false, which suggests the existence of the ‘third,’ logical status of propositions.The prehistory of many-valued logic falls on the Middle Ages. More serious attempts to create non-classical logical constructions, three-valued mainly, appeared only on the turn of the nineteenth century. The evaluation to what extent these different approaches ... log in or subscribe to read full text