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Single Idea 21606

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

Full Idea

The meta-logical law of excluded middle is the meta-linguistic principle that any statement 'A' in the object language is either truth or false; it is now known as the principle of 'bivalence'.

Gist of Idea

'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false

Source

Timothy Williamson (Vagueness [1994], 5.2)

Book Ref

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

A Reaction

[He cites Henryk Mehlberg 1958] See also Idea 21605. Without this way of distinguishing bivalence from excluded middle, most discussions of them strikes me as shockingly lacking in clarity. Personally I would cut the normativity from this one.

Related Idea

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

The 96 ideas from Timothy Williamson

6858 Formal logic struck me as exactly the language I wanted to think in [Williamson]
6859 Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson]
6860 How can one discriminate yellow from red, but not the colours in between? [Williamson]
6861 What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson]
6862 Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson]
6863 Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson]
19512 Don't analyse knowledge; use knowledge to analyse other concepts in epistemology [Williamson, by DeRose]
4760 Belief aims at knowledge (rather than truth), and mere believing is a kind of botched knowing [Williamson]
19526 Surely I am acquainted with physical objects, not with appearances? [Williamson]
19527 We don't acquire evidence and then derive some knowledge, because evidence IS knowledge [Williamson]
19528 Knowledge is prior to believing, just as doing is prior to trying to do [Williamson]
19529 Belief explains justification, and knowledge explains belief, so knowledge explains justification [Williamson]
19530 A neutral state of experience, between error and knowledge, is not basic; the successful state is basic [Williamson]
19531 Internalism about mind is an obsolete view, and knowledge-first epistemology develops externalism [Williamson]
19534 How does inferentialism distinguish the patterns of inference that are essential to meaning? [Williamson]
19535 Internalist inferentialism has trouble explaining how meaning and reference relate [Williamson]
19533 Inferentialist semantics relies on internal inference relations, not on external references [Williamson]
19532 Truth-conditional referential semantics is externalist, referring to worldly items [Williamson]
19536 Knowledge-first says your total evidence IS your knowledge [Williamson]
15130 If a property is possible, there is something which can have it [Williamson]
14531 Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals [Williamson, by Hale/Hoffmann,A]
14625 Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation [Williamson]
14623 Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson]
14624 Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B) [Williamson]
14626 In S5 matters of possibility and necessity are non-contingent [Williamson]
14628 Imagination is important, in evaluating possibility and necessity, via counterfactuals [Williamson]
18925 If talking donkeys are possible, something exists which could be a talking donkey [Williamson, by Cameron]
19216 Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
16536 Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson]
9592 Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson]
9593 Progress in philosophy is incremental, not an immature seeking after drama [Williamson]
9594 Correspondence to the facts is a bad account of analytic truth [Williamson]
9595 You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson]
9596 We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson]
9597 There are 'armchair' truths which are not a priori, because experience was involved [Williamson]
9598 Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson]
9599 There cannot be vague objects, so there may be no such thing as a mountain [Williamson]
9600 If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson]
9601 The realist/anti-realist debate is notoriously obscure and fruitless [Williamson]
9602 Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson]
20181 When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson]
9183 Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
9184 We can't presume that all interesting concepts can be analysed [Williamson]
15131 If metaphysical possibility is not a contingent matter, then S5 seems to suit it best [Williamson]
15133 A thing can't be the only necessary existent, because its singleton set would be as well [Williamson]
15135 If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson]
15134 The truthmaker principle requires some specific named thing to make the difference [Williamson]
15136 Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
15138 Not all quantification is objectual or substitutional [Williamson]
15137 If 'fact' is a noun, can we name the fact that dogs bark 'Mary'? [Williamson]
15140 The converse Barcan formula will not allow contingent truths to have truthmakers [Williamson]
15141 Truthmaker is incompatible with modal semantics of varying domains [Williamson]
15139 Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson]
15142 Our ability to count objects across possibilities favours the Barcan formulas [Williamson]
18492 Not all quantification is either objectual or substitutional [Williamson]
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]
21630 If fuzzy edges are fine, then why not fuzzy temporal, modal or mereological boundaries? [Williamson]
21629 Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness [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]