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Single Idea 9024

[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle ]

Full Idea

The law of excluded middle, or 'tertium non datur', may be pictured variously as 1) Every closed sentence is true or false; or 2) Every closed sentence or its negation is true; or 3) Every closed sentence is true or not true.

Clarification

A 'closed sentence' has no free variables in it

Gist of Idea

Excluded middle has three different definitions

Source

Willard Quine (Philosophy of Logic [1970], Ch.6)

Book Ref

Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.83

A Reaction

Unlike many top philosophers, Quine thinks clearly about such things. 1) is the classical bivalent reading of excluded middle; 2) is the purely syntactic version; 3) leaves open how we interpret the 'not-true' option.

Related Ideas

Idea 8709 The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend]

Idea 17924 Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]

The 25 ideas from 'Philosophy of Logic'

10014 Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes]
9012 Talk of 'truth' when sentences are mentioned; it reminds us that reality is the point of sentences [Quine]
9011 Truth is redundant for single sentences; we do better to simply speak the sentence [Quine]
9009 Single words are strongly synonymous if their interchange preserves truth [Quine]
9007 It makes no sense to say that two sentences express the same proposition [Quine]
9008 There is no rule for separating the information from other features of sentences [Quine]
9010 We can abandon propositions, and just talk of sentences and equivalence [Quine]
9013 We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine]
9015 Universal quantification is widespread, but it is definable in terms of existential quantification [Quine]
9016 Names are not essential, because naming can be turned into predication [Quine]
9014 Some conditionals can be explained just by negation and conjunction: not(p and not-q) [Quine]
9017 Predicates are not names; predicates are the other parties to predication [Quine]
9018 A physical object is the four-dimensional material content of a portion of space-time [Quine]
9019 Four-d objects helps predication of what no longer exists, and quantification over items from different times [Quine]
9020 My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]
9021 A good way of explaining an expression is saying what conditions make its contexts true [Quine]
10705 Putting a predicate letter in a quantifier is to make it the name of an entity [Quine]
10828 Quantifying over predicates is treating them as names of entities [Quine]
10012 Quantification theory can still be proved complete if we add identity [Quine]
9024 Excluded middle has three different definitions [Quine]
9025 You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]
9026 Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine]
9023 If you say that a contradiction is true, you change the meaning of 'not', and so change the subject [Quine]
9027 A sentence is logically true if all sentences with that grammatical structure are true [Quine]
9028 Maybe logical truth reflects reality, but in different ways in different languages [Quine]