A Dictionary of Philosophy, Third Edition
. True and false are known as the two main truth-values. For a two-valued logic they are in practice the only truth-values, though theoretically any two could be chosen. Three-valued and in general many-valued logics use three or more values accordingly, adding to true and false or replacing them. When they add to them, as in the first example below, or as degrees of truth do, they reject bivalence (see EXCLUDED MIDDLE).
Examples are true/false/indeterminate, known to be true/known to be false/unknown, necessarily true/necessarily false/contingent, certainly true/99 per cent probable/ …/certainly false (this last group, like that of degrees of truth, could contain infinitely many values). Sometimes a set of truth-values falls into two groups with important logical properties analogous to those of true and false respectively. Those analogous to true are then called designated values, and those analogous to false are called undesignated values.
M.Dummett, ‘Truth’, Proceedings of the Aristotelian Society, 1958–9, reprinted in G.Pitcher (ed.), Truth, Prentice-Hall, 1964, in P.F.Strawson (ed.), Philosophical Logic, Oxford UP, 1967, and in Dummett’s Truth and Other Enigmas, Duckworth, 1978. (Includes explanation of designated and undesignated values).
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