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Full Idea
Modus ponens is intuitively valid, but in A,A→B|B if A is true and B is false that must be because A→B is false. So A→B is false when A is true and B is false.
Gist of Idea
Modus ponens requires that A→B is F when A is T and B is F
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 first step in showing how the truth functional account of A→B acquires its truth table. If you are giving up the truth functional view of conditionals, presumably you are not also going to give up modus ponens?
Related Ideas
Idea 14354 When A and B have the same truth value, A→B is true, because A→A is a logical truth [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] |