A Gricean theory of indicative conditionals

The theory consists of two theses and two definitions. I will use → for indicative conditionals. And all my disjunctions will be inclusive.

1. MatCond: "p→q" expresses the same proposition as "~p or q".
2. NonTriv: A use of "p→q" normally implicates that "~p or q" is an evidentially non-trivial disjunction for the speaker.
3. Definition: "a or b" is an evidentially non-trivial disjunction for an agent x if and only if x has non-negligible evidence for the disjunction that goes over and beyond evidence for ~p and evidence for q.

I don't here commit to any particular view of evidence, and if there are non-evidential justifications, one can probably easily modify the theory.

Here is an interesting consequence of the theory which I think is just right. When my evidence that at least one of ~p and q is true is simply the evidence for ~p (or for q), I don't get to say "If p, then q." But if I tell you that at least one of ~p and q is true, then normally you get to say "If p, then q". For when I tell you that at least one of ~p and q is true, then "~p or q" comes to be an evidentially non-trivial disjunction for you: my testimony is evidence for the disjunction and this evidence does not derive for you from evidence for the one or the other disjunct.

Notice that "has non-negligible evidence for the disjunction" has some vagueness to it. Moreover, negligibility is contextual, and that is how it should be. If I tell you that at least one of the following is true: snow is not purple and 2+2=4, then "If snow is purple, then 2+2=4" does not generally become assertible for you. For while you do gain additional testimonial evidence for the disjunction that snow is not purple or 2+2=4 from my speaking to you, the gain is normally negligible over and beyond your earlier evidence that 2+2=4. But if you respond to my assertion with "So, if snow is purple, then 2+2=4", you are speaking quite correctly, since the use of "So" and the conversational context makes the evidence I just gave you salient and hence non-negligible. (Perhaps "salient" or "relevant" could be used in place of "non-negligible" in (3).)

The theory explains why it is that paradoxes of material implication can almost always be made to cease to be paradoxes of material implication as soon as one fills out the evidential backstory in a creative enough way. Take, for instance, the paradox of material implication:

4. If the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

The antecedent is false, so the material conditional is true, but (4) sure sounds bad (it sounds bad to assert and seems to be saying something bad about my manners). Yes, but now suppose that an epistemic authority has just handed me two numbered and folded pieces of paper, with a sentence written on each and folded in half, and told me that either at least the first paper contains a falsehood or they both contain truths. I puzzle out what she says, and I conclude, very reasonably:

5. If the sentence on the first piece of paper is true, the sentence on the second piece of paper is true.

I then unfold the pieces of paper, and notice that the first piece contains the sentence "The president will invite me for dinner tonight" and the second contains "I will have dinner with the president in my pajamas." And so I reasonably infer from (5):

6. So, if the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

(And, moreover, I now gain a new piece of evidence that the president won't invite me for dinner tonight—for it would be absurd to suppose I'd have dinner with him in my pajamas.) With this epistemic backstory, the paradoxical conditional is quite unparadoxical. That's because with this epistemic backstory, the corresponding disjunction

7. The president won't invite me for dinner tonight or I will have dinner with the president in my pajamas (or both)

is epistemically non-trivial. But in normal circumstances, (7) is epistemically trivial, since my only evidence for (7) is evidence for the first disjunct.

A similar kind of epistemic backstory can be given for any of the standard paradoxes of material implication, thereby turning paradoxical sentences into non-paradoxical ones (cf. this post). Our Gricean theory (1)-(3) explains this phenomenon neatly. So do theories on which indicatives are non-cognitive and ones on which they are subjective. But the Gricean theory is, I think, simpler.

Notice that in this Gricean theory we haven't brought in non-material conditionals through any back door, because we have explained the implicated content entirely in terms of disjunctions. Furthermore, (2) is basically a consequence of (1) plus the very plausible claim that disjunctive sentences normally implicate the epistemic non-triviality of the disjunction.