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Single Idea 21602

[filed under theme 4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic ]

Full Idea

It is an illusion that many-valued logic constitutes a well-motivated and rigorously worked out theory of vagueness. ...[top] There has been a reluctance to acknowledge higher-order vagueness, or to abandon classical logic in the meta-language.

Gist of Idea

Many-valued logics don't solve vagueness; its presence at the meta-level is ignored

Source

Timothy Williamson (Vagueness [1994], 4.12)

Book Ref

Williamson,Timothy: 'Vagueness' [Routledge 1996], p.130

Related Idea

Idea 21596 Vagueness undermines the stable references needed by logic [Williamson]

The 41 ideas from 'Vagueness'

21591 Vagueness is epistemic. Statements are true or false, but we often don't know which [Williamson]
21589 When bivalence is rejected because of vagueness, we lose classical logic [Williamson]
21590 Asking when someone is 'clearly' old is higher-order vagueness [Williamson]
21592 Supervaluation keeps classical logic, but changes the truth in classical semantics [Williamson]
21596 Vagueness undermines the stable references needed by logic [Williamson]
21599 A sorites stops when it collides with an opposite sorites [Williamson]
21600 'Blue' is not a family resemblance, because all the blues resemble in some respect [Williamson]
21601 A vague term can refer to very precise elements [Williamson]
21602 Many-valued logics don't solve vagueness; its presence at the meta-level is ignored [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]
21606 'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson]
21605 Excluded Middle is 'A or not A' in the object language [Williamson]
21611 Formal semantics defines validity as truth preserved in every model [Williamson]
21612 Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [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]
21614 The 'nihilist' view of vagueness says that 'heap' is not a legitimate concept [Williamson]
21615 References to the 'greatest prime number' have no reference, but are meaningful [Williamson]
18038 The 't' and 'f' of formal semantics has no philosophical interest, and may not refer to true and false [Williamson]
21617 We can say propositions are bivalent, but vague utterances don't express a proposition [Williamson]
21616 Truth and falsity apply to suppositions as well as to assertions [Williamson]
21618 If the vague 'TW is thin' says nothing, what does 'TW is thin if his perfect twin is thin' say? [Williamson]
21619 If a heap has a real boundary, omniscient speakers would agree where it is [Williamson]
21620 The epistemic view says that the essence of vagueness is ignorance [Williamson]
21621 We can't infer metaphysical necessities to be a priori knowable - or indeed knowable in any way [Williamson]
21622 If there is a true borderline of which we are ignorant, this drives a wedge between meaning and use [Williamson]
21623 True and false are not symmetrical; false is more complex, involving negation [Williamson]
21624 It is known that there is a cognitive loss in identifying propositions with possible worlds [Williamson]
21625 The vagueness of 'heap' can remain even when the context is fixed [Williamson]
9120 Vagueness in a concept is its indiscriminability from other possible concepts [Williamson]
21626 Knowing you know (KK) is usually denied if the knowledge concept is missing, or not considered [Williamson]
21627 We have inexact knowledge when we include margins of error [Williamson]
21629 Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness [Williamson]
21630 If fuzzy edges are fine, then why not fuzzy temporal, modal or mereological boundaries? [Williamson]
21632 A river is not just event; it needs actual and counterfactual boundaries [Williamson]
21633 Nominalists suspect that properties etc are our projections, and could have been different [Williamson]
21631 To know, believe, hope or fear, one must grasp the thought, but not when you fail to do them [Williamson]