Topic: GENERAL LOGIC
The debate goes on: how many truth-values are necessary in Logic?
Truth, Falsity and Borderline Cases
by Miroslava Andjelkovi & Timothy Williamson
According to the principle of bivalence, truth and falsity are jointly exhaustive and mutually exclusive options for a statement. It is either true or false, and not both, even in a borderline case.
That highly controversial claim is central to the epistemic theory of vagueness, which holds that borderline cases are distinguished by a special kind of obstacle to knowing the truth -value of the statement. But this paper is not a defence of the epistemic theory. If bivalence holds, it presumably does so as a consequence of what truth and falsity separately are.
One may therefore expect bivalence to be derivable from a combination of some principles characterizing truth and other principles characterizing falsity. Indeed, such derivations are easily found. Their form will of course depend on the initial characterizations of truth and falsity, and not all such characterizations will permit bivalence to be derived. In this paper we focus on the relation between its derivability and some principles about truth and falsity . We will use borderline cases for vague expressions as primary examples of an urgent challenge to bivalence.
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For the debate of the issue, see Pelletier and Stainton?s paper On `The Denial of Bivalence is Absurd'.
Posted by Tony Marmo
at 07:39 BST
