### Assertibility and Meaning (Take 2)

As I note in a comment on my previous post, I have a strong intuition that there should be some sort of systematic connection between assertibility-conditions and truth-conditions. The source of that intuition, I think, stems from the Principle of Charity, which states that, so long as it is contextually plausible to do so, one should try to interpret the statements a person makes in such a way that what they say would be rationally assertible for them. This is, I think, an essential heuristic principle of interpretation, one that connects the meaning that we impute to people's utterances to assertibility-conditions.

But it's not so easy to come up with a generalized statement of how assertibility-conditions bear on truth-conditions. There are several traps to avoid. Here are some:

- We don't want assertibility to be a necessary condition for truth, since there can be truths that are not rationally assertible for anyone (except maybe God, but let's leave him out of this). For example, there is, presumably, a truth about how many times the last emperor of China sneezed, but I doubt that anyone is in a position to assert that the number of sneezes is equivalent to any particular number.
- We don't want truth to be a necessary condition for assertibility, since there can be rationally assertible propositions that are false. For example, prior to Copernicus and Galileo, heliocentrism was rationally assertible, despite the fact that it turned out to be false.
- We don't want to epistemicize truth or to equate it with warranted assertibility, at least not if we want to take a realist approach to metaphysics.

(1) Whatever anyone must believe in order rationally to assert a proposition p is part of the meaning of p.

But as Rafal helpfully pointed out to me, this won't do. The most glaring problem, perhaps, is that there seem to be propositions that simply cannot be rationally denied, whether because they are obvious a priori truths (e.g., 1+1=2) or because denying them would land us in a performative contradiction (e.g., there are true sentences). Consequently, (1) yields the result that these propositions are part of the meaning of every proposition whatsoever. And that's just not plausible. So I went back to the drawing board and came up with a new proposal:

(2) Where q is a proposition that someone could rationally deny, if anyone must believe q in order rationally to assert p, then q is part of the meaning of p.

This gets around the problem by restricting the claim to propositions that someone could rationally deny. Rafal, however, raises two further problems. One concerns cases in which p is a proposition that cannot be rationally affirmed (e.g., 4+1=193). Given the standard semantics for counterfactuals, (2) would seem to imply that every proposition whatsoever is part of the meaning of 4+1=193. Fortunately, there is a simple revision of (2) that blocks these sorts of cases:

(3) Where q is a proposition that someone could rationally deny and p is a proposition that someone could rationally assert, if anyone must believe q in order rationally to assert p, then q is part of the meaning of p.

We're making progress toward a plausible principle, but we're not out of the woods yet, for Rafal has another counterexample, one that might rule out (3). Let p be "2+2=4". This is rationally assertible. Let q be "There are true mathematical statements". This is rationally deniable (or so mathematical fictionalists would have us think). It seems that one cannot rationally assert p without asserting q. Hence, by (3), we should conclude that q is part of the meaning of p. Yet, arguably, this is not so (at least, mathematical fictionalists would argue the point).

Now, I'm not quite sure what to make of this counterexample. I'm sufficiently skeptical of mathematical fictionalism, that I'm tempted to appeal to (3) as a reason for rejecting mathematical fictionalism. On the other hand, I don't know enough about the philosophy of mathematics to feel comfortable being so cavalier. Nor is it clear to me right now how to revise (3) in order to block this and similar counterexamples.

For the moment, then, I'm stuck. I'm not prepared yet to give up (3), but neither do I feel very certain that it's right.