I will argue that if the indicative "If p, then q" in English has mind-independent truth value (a somewhat vague phrase, admittedly), then this truth value is the same as that of (not-p or q) (i.e., the material conditional). The way I shall argue this is as follows. Assume that "If p, then q" has mind independent truth value. Now, I will show that (i) if (not-p or q) is false, then "If p, then q" is false, and (ii) if (not-p or q) is true, then "If p, then q" is true. Claim (i) is easy. For if (not-p or q) is false, then p is true and q is false, and it clearly cannot be the case that "If p, then q" (modus ponens would be violated).
I now argue for (ii). The easiest way to do this is to specialize to the case where p and q and their denials do not tell us anything about what beliefs and credences people have (the proposition that there are dogs satisfies this constraint; the proposition that nobody believes anything does not satisfy this constraint). If (ii) holds for propositions satisfying this constraint, it will hold in general, surely (assuming "If... then..." has mind-independent truth value). Suppose that you rationally assign a probability very close to 1/2 to p as well as to q, and neither believe nor disbelieve either of these, and rationally assign a probability very close to 1 to the claim that (not-p or q), and, moreover, you know this disjunction to be true. Given the constraint on p and q, it should be quite possible to have a set of evidence that makes one have these probability assignments, and having this set of evidence should not affect the truth values of p, q or the indicative "If p, then q".
You then reflect on the following valid argument:
- p (premise)
- not-p or q (premise)
- Therefore, q.
The conclusion might be taken as a reductio of the claim that "If... then..." has mind independent truth value.