Speaking of common sense, it strikes me that the indicative conditional is obviously suppositional (subsection 4.3 of Edgington’s Conditionals), i.e. that “C, if A” asserts “C” iff A. Suppose I say: “The cat will sit on the mat.” Then (whatever my motives for doing so, however likely or unlikely it seemed, and however likely or unlikely it actually was), surely what I say will be literally true iff the cat sits on the mat. Similarly, if I say: “If the mat is not removed, the cat will sit on it,” then what I say will be true iff the cat sits on the mat that has not been removed.
...... If the mat is removed (for whatever reason) then my conditional prediction, while not false, failed to come true. What could make it true, given that the mat is actually removed? That the cat would have sat on it, had it not been removed? But that would only have made the corresponding subjunctive conditional true. Now, it may well have been a belief in that subjunctive (or counterfactual) conditional that made me assert the indicative conditional (about actuality), but it was the latter that I asserted, not the former. Of course, it may not have been—and indeed, the subjunctive might be known to be false (via the counterfactual probabilities) while both the antecedent and the consequent of the indicative are correctly guessed to be true.
...... The major alternative (to such a suppositional interpretation) seems to be the material conditional, but I don’t see why indicative conditionals with false antecedents should have truth-values. Are there any good reasons for thinking that they should? Even Edgington (third paragraph of subsection 2.1) calls it uncontroversial that “If that is a square, it has four sides” is true even when said of a triangle, but in fact what is clearly true is just “All squares have four sides.” Anyway, one problem for the material interpretation (first paragraph of subsection 2.5) is that according to it “It is not the case that if it is a triangle, it has four sides” ought to be false when said of a non-triangle. And while I suppose that if our logic is set-theoretical then the material interpretation is tidier, conversely if that interpretation is indeed false then that is indicative of the falsity of set theory.
...... And what about “If you disagree with me, I’ll hit you;” isn’t there some intuitive pull to the thought that I have, after all, made an assertion here? Well, the former is certainly an assertive speech-act—a threat—but what was actually said? To find that out consider that, because of the threat, I hide my disagreement and so avoid being hit—then the antecedent is true (I do disagree) but the consequent is false (I am not hit) and so the conditional is false, and yet the assertive speech-act is nonetheless successful (I do not show my disagreement). And although in a sense I complied because I believed what was said, what I believed was that if I had shown disagreement I would have been hit.
...... Mind you, that "If you disagree with me, I'll hit you" was probably intended subjunctively anyway, to mean the same as the counterfactual "Had you disagreed with me, I would have hit you" uttered later. Still, the speaker might have been (possibly correctly) a determinist, who thought (correctly) that I would not disagree, given his threat, and then there would have been no possibility of my having disagreed with him... Although clearly indicatives have the truth-conditions of material conditionals in possible world semantics, since to say if A then C is to say that the A-worlds are all in the C-worlds, which is just to say that no A-worlds are also not-C-worlds.