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Full Idea
(A→A) is a logical truth, so some conditionals with antecedent and consequent the same truth value are true. But if '→' is a truth function, that will be true for all cases. Hence whenever A and B are alike in truth value, (A→B) is true.
Gist of Idea
When A and B have the same truth value, A→B is true, because A→A is a logical truth
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
His second step in demonstrating the truth table for →, assuming 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 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]
| 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] |
| 14352 | '¬', '&', and 'v' are truth functions: the truth of the compound is fixed by the truth of the components [Jackson] |
| 14358 | In the possible worlds account of conditionals, modus ponens and modus tollens are validated [Jackson] |
| 14360 | Possible worlds for subjunctives (and dispositions), and no-truth for indicatives? [Jackson] |
| 14359 | Only assertions have truth-values, and conditionals are not proper assertions [Jackson] |
| 14357 | Possible worlds account, unlike A⊃B, says nothing about when A is false [Jackson] |
| 14356 | We can't insist that A is relevant to B, as conditionals can express lack of relevance [Jackson] |