I'm sure someone has thought of this before, but I haven't seen this justification (if it is one at all) for why the truth-table of the material conditional is the way it is in both literature on the subject, and on the internet.
The justification goes as follows - two points seem to make intuitive sense:
(a) The biconditional 'A↔B' is true if and only if both A and B have the same truth-value.
(b) The biconditional 'A↔B' is the same thing as saying '(A→B)&(B→A)'
Together with the truth-table for the conjunction, we get the unique truth-table the material conditional has to have for these two criteria to hold.
Does this heuristic justification hold any water?