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 Reference
'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]