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Single Idea 18780

[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence ]

Full Idea

If we treat disjunction in the standard way and take the negation of a statement A to mean that A is false, accepting excluded middle forces us also to accept the principle of bivalence, which is the dictum that every statement is either true or false.

Gist of Idea

Standard disjunction and negation force us to accept the principle of bivalence

Source

Edwin D. Mares (Negation [2014], 1)

Book Ref

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.181

A Reaction

Mates's point is to show that passively taking the normal account of negation for granted has important implications.

The 18 ideas with the same theme [propositions can only be true or false]:

21593 In talking of future sea-fights, Aristotle rejects bivalence [Aristotle, by Williamson]
22154 For Aristotle bivalence is a feature of reality [Aristotle, by Boulter]
21677 How can the not-true fail to be false, or the not-false fail to be true? [Cicero]
19102 Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak]
19043 Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine]
8173 Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett]
8195 Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett]
6889 Vagueness seems to be inconsistent with the view that every proposition is true or false [Mautner]
21606 'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson]
18780 Standard disjunction and negation force us to accept the principle of bivalence [Mares]
18786 Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares]
4700 A third value for truth might be "indeterminate", or a point on a scale between 'true' and 'false' [O'Grady]
4752 Deflationism must reduce bivalence ('p is true or false') to excluded middle ('p or not-p') [Engel]
9119 No attempt to deny bivalence has ever been accepted [Sorensen]
6163 If bivalence is rejected, then excluded middle must also be rejected [Rowlands]
4638 The principle of bivalence distorts reality, as when claiming that a person is or is not 'thin' [Baggini /Fosl]
23484 Bipolarity adds to Bivalence the capacity for both truth values [Morris,M]
18840 When faced with vague statements, Bivalence is not a compelling principle [Rumfitt]