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Single Idea 15725

[filed under theme 10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals ]

Full Idea

In its unquantified form 'If p then q' the indicative conditional is perhaps best represented as suffering a truth-value gap whenever its antecedent is false.

Clarification

A 'truth-value gap' is 'neither true nor false'

Gist of Idea

Normal conditionals have a truth-value gap when the antecedent is false.

Source

Willard Quine (Word and Object [1960], §46)

Book Ref

Quine,Willard: 'Word and Object' [MIT 1969], p.226

A Reaction

That is, the clear truth-functional reading of the conditional (favoured by Lewis, his pupil) is unacceptable. Quine favours the Edgington line, that we are only interested in situations where the antecedent might be true.

The 25 ideas with the same theme [conditional truth based entirely on components]:

20789 Conditionals are false if the falsehood of the conclusion does not conflict with the antecedent [Stoic school, by Diog. Laertius]
12197 Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell]
14450 All forms of implication are expressible as truth-functions [Russell]
14305 In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap]
8948 The odd truth table for material conditionals is explained by conversational conventions [Grice, by Fisher]
13767 Conditionals might remain truth-functional, despite inappropriate conversational remarks [Edgington on Grice]
13856 Conditionals are truth-functional, but we must take care with misleading ones [Grice, by Edgington]
15725 Normal conditionals have a truth-value gap when the antecedent is false. [Quine]
14288 'If A,B' affirms that A⊃B, and also that this wouldn't change if A were certain [Jackson, by Edgington]
13769 Conditionals are truth-functional, but should only be asserted when they are confident [Jackson, by Edgington]
14289 There are some assertable conditionals one would reject if one learned the antecedent [Jackson, by Edgington]
14353 Modus ponens requires that A→B is F when A is T and B is F [Jackson]
14354 When A and B have the same truth value, A→B is true, because A→A is a logical truth [Jackson]
14355 (A&B)→A is a logical truth, even if antecedent false and consequent true, so it is T if A is F and B is T [Jackson]
13858 The truth-functional account of conditionals is right, if the antecedent is really acceptable [Jackson, by Edgington]
14361 Lewis says indicative conditionals are truth-functional [Lewis, by Jackson]
13764 Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
13765 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
14274 Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism [Edgington]
14276 The truth-functional view makes conditionals with unlikely antecedents likely to be true [Edgington]
14275 Truth-function problems don't show up in mathematics [Edgington]
14290 Doctor:'If patient still alive, change dressing'; Nurse:'Either dead patient, or change dressing'; kills patient! [Edgington]
14309 Truth-functional conditionals can't distinguish whether they are causal or accidental [Mumford]
22281 A material conditional cannot capture counterfactual reasoning [Potter]
8947 If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher]