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Single Idea 21615

[filed under theme 19. Language / B. Reference / 1. Reference theories ]

Full Idea

The predicate 'is a prime number greater than all other prime numbers' is necessarily not true of anything, but it is not semantically defective, for it occurs in sentences that constitute a sound proof that there is no such number.

Clarification

It is proven that there is no greatest prime number

Gist of Idea

References to the 'greatest prime number' have no reference, but are meaningful

Source

Timothy Williamson (Vagueness [1994], 6.2)

Book Ref

Williamson,Timothy: 'Vagueness' [Routledge 1996], p.168

A Reaction

One might reply that the description can be legitimately mentioned, but not legitimately used.

The 41 ideas from 'Vagueness'

21589 When bivalence is rejected because of vagueness, we lose classical logic [Williamson]
21591 Vagueness is epistemic. Statements are true or false, but we often don't know which [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]