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Single Idea 21607

[filed under theme 7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness ]

Full Idea

The supervaluationist denies bivalence but accepts excluded middle. The statement 'A or not-A' is true on each admissible interpretation, and therefore true, even if 'A' (and hence 'not-A') are true and some and false on others, so neither T nor F.

Gist of Idea

Supervaluation has excluded middle but not bivalence; 'A or not-A' is true, even when A is undecided

Source

Timothy Williamson (Vagueness [1994], 5.2)

Book Ref

Williamson,Timothy: 'Vagueness' [Routledge 1996], p.145

A Reaction

See Ideas 21605 and 21606 for the distinction being used here. Denying bivalence allows 'A' to be neither true nor false. It seems common sense that 'he is either bald or not-bald' is true, without being sure about the disjuncts.

Related Ideas

Idea 21605 Excluded Middle is 'A or not A' in the object language [Williamson]

Idea 21606 'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson]

Idea 21604 Supervaluation assigns truth when all the facts are respected [Williamson]

Idea 21676 Epicureans say disjunctions can be true whiile the disjuncts are not true [Epicurus, by Cicero]

The 30 ideas with the same theme [narrowing down the vagueness]:

23541 Supervaluation can give no answer to 'who is the last bald man' [Fine,K]
9767 A vague sentence is only true for all ways of making it completely precise [Fine,K]
9770 Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K]
9772 Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K]
9773 With the super-truth approach, the classical connectives continue to work [Fine,K]
9774 Borderline cases must be under our control, as capable of greater precision [Fine,K]
9049 Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith]
9056 Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith]
9058 Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith]
9059 The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith]
9060 Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith]
21592 Supervaluation keeps classical logic, but changes the truth in classical semantics [Williamson]
21603 You can't give a precise description of a language which is intrinsically vague [Williamson]
21604 Supervaluation assigns truth when all the facts are respected [Williamson]
21607 Supervaluation has excluded middle but not bivalence; 'A or not-A' is true, even when A is undecided [Williamson]
21608 Truth-functionality for compound statements fails in supervaluation [Williamson]
21609 Supervaluationism defines 'supertruth', but neglects it when defining 'valid' [Williamson]
21610 Supervaluation adds a 'definitely' operator to classical logic [Williamson]
21613 Supervaluationism cannot eliminate higher-order vagueness [Williamson]
16208 Supervaluation refers to one vaguely specified thing, through satisfaction by everything in some range [Hawley]
16221 Supervaluationism takes what the truth-value would have been if indecision was resolved [Hawley]
13692 A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider]
13693 A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider]
13695 Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider]
13694 We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider]
11012 A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read]
11013 Identities and the Indiscernibility of Identicals don't work with supervaluations [Read]
11019 Supervaluations say there is a cut-off somewhere, but at no particular place [Read]
15363 In the supervaluationist account, disjunctions are not determined by their disjuncts [Horsten]
15362 If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't [Horsten]