An argument for the material conditional account of indicatives

The material conditional account of indicatives is that "If s, then u" is true if and only if s is false or u is true or both.

1. (Premise) If the indicative conditional has the same truth values as the material conditional in the standard cases which are alleged to be counterexamples to the material conditional account, then the material conditional account is correct.
2. (Premise) The indicative conditional has mind-independent truth value.
3. (Premise) If the indicative conditional has mind-independent truth value, then it has the same truth values as the material conditional in the standard cases which are alleged to be counterexamples to the material conditional account.
4. Therefore, the material conditional account is correct.

In this argument, I am convinced of premises (1) and (3), but not sure of premise (2). Consequently, what the argument convinces me of is that either (2) is false or (4) is true. Premise (1) is not that controversial, I think. The material conditional account is simple and elegant, verifies modus ponens and contraposition, is well-defined and mind-independent. The only problem is that it appears to give the wrong answers for certain standard cases. If this appearance were undercut, the material conditional account would be the winner.

The hard work is going to be justify (3). Let us start by giving three representative alleged counterexamples, classified by the truth values of the antecedent and consequent:

5. "If I will have dinner with the queen tonight, I will eat dinner tonight in my pajamas." (Antecedent and consequent are both false.)
6. "If I will have dinner with the queen tonight, everyone that I will have dinner with tonight will be a family member." (Antecedent is false and consequent is true.)
7. "If it is snowing in the United States, it is snowing in Central Texas." (Suppose this was uttered a couple of days ago when it was snowing in Central Texas. Antecedent and consequent were both true.)

The material conditional account says that all three conditionals are true. But all three conditionals sound wrong (assuming I am not a member of the royal family and that I wouldn't wish to insult the queen).

I will argue that:

8. If the indicative conditional has mind-independent truth value, then (5)-(7) are all true.

The method of argument generalizes to all the standard counterexamples, and thus yields (3).

Here's the way I will argue for (8). Let "a" be the antecedent in the alleged counterexample. Let "c" be the consequent. Suppose I have the belief, justified or not, that at least one of "not-a" and "c" is true, and I have no further, more specific beliefs about the matters in a and in c. Since I believe that at least one of "not-a" and "c" is true, I should be able to sincerely say to someone:

9. I may not know much about the queen, dinners, pajamas, snow, etc., but I do believe that at least one of "not-a" and "c" is true. Hence, if a, then c.

This seems very reasonable.

Suppose now that I learn all the relevant facts about the queen, dinners, pajamas, snow, etc. In particular, I learn such facts as that people tend not to wear pajamas for dinner with the queen, that central Texas is one of the somewhat less likely places in the US to have snow, etc. I also learn the truth values of "a" and "c". None of the things I learn gives me reason to retract the claim that at least one of "not-a" and "c" is true. And neither have I any reason to retract the conclusion I drew, that if a, then c.

Therefore, when I said (9), I said something true. If it wasn't true, I would have reason to withdraw it. But the difference between the circumstances in my story in which I said the conditional in (9) and standard circumstances was in my beliefs—when I said (9), I lacked various beliefs that normal people in our culture have. Thus, if the indicative conditional has mind-independent true value, I have to conclude that actually the conditional "if a, then c" is also true. And so we have an argument for (8).