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Single Idea 14355

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

Full Idea

(A&B)→A is a logical truth, but A can be true and B false, so that (A&B) is false. So some conditionals with false antecedent and true consequent are true. If → is a truth function, then whenever A is false and B is true (A→B) is true.

Gist of Idea

(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

Source

Frank Jackson (Conditionals [2006], 'Equiv')

Book Ref

'Blackwell Guide to Philosophy of Language', ed/tr. Devitt,M/Hanley,R [Blackwell 2006], p.213

A Reaction

This is his third and final step in showing the truth table of → if it is truth functional.

Related Ideas

Idea 14353 Modus ponens requires that A→B is F when A is T and B is F [Jackson]

Idea 14354 When A and B have the same truth value, A→B is true, because A→A is a logical truth [Jackson]

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]