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Single Idea 9770

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

Full Idea

With a three-value approach, if P is 'blob is pink' and R is 'blob is red', then P&P is indefinite, but P&R is false, and P∨P is indefinite, but P∨R is true. This means the connectives & and ∨ are not truth-functional.

Gist of Idea

Logical connectives cease to be truth-functional if vagueness is treated with three values

Source

Kit Fine (Vagueness, Truth and Logic [1975], 1)

Book Ref

'Vagueness: a Reader', ed/tr. Keefe,R /Smith,P [MIT 1999], p.123

A Reaction

The point is that there could then be no logic in any way classical for vague sentences and three truth values. A powerful point.

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]
13695 Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider]
13693 A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [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]