Blackwell Reference Online

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Standard logic is a package with two parts-a formal deductive apparatus and a conception of interpretation for the language. The deductive apparatus and the semantics are mutually reinforcing and in this chapter we examine primarily the semantic assumptions that formally justify the deductive machinery. The second part of the package, the semantics of ‘standard’ logic, includes the assumptions that:•there are two and only two truth-values, True and False,•every sentence of the language has a determinate truth-value in each interpretation,•the truth-value of any sentence of the language in an interpretation is determined by the reference or extension of the parts of the sentence in that interpretation (together with the universe of discourse.)This chapter concerns three historically important forms of non-standard logics:1. Many-valued logics reject the assumption that there are only two truth-values–it explores the possiblities that some sentences may be neither true nor false. Among the reasons for rejecting the assumption are the belief that statements about the future, statements involving vague predicates or statements about quantum mechanical properties are always either true or false. Most many-valued logics begin by rejecting the law of excluded middle, though there are exceptions. The number of values ranges from 3 to various infinite sets. The nature of the further values ... log in or subscribe to read full text