### 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.

## 2 Comments:

I'm not sure why you want to get a formal definition of "p is part of the meaning of q"... I miss the connection between that and "truth versus assertibility".

"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."

I guess I'm not a realist then... weird, I didn't realize that. I think part of the problem is that you make statements like "heliocentrism was rationally assertible, despite the fact that it turned out to be false". (I'll ignore the typo - you probably meant geocentrism.) According to Einstein, geocentrism never turned out to be false, it is as valid a framework as heliocentrism. (In fact, he considered as significant *and solved* the problem of lunar-centrism, so to speak - if the Moon is in the center of the universe - again, as valid a framework as any - why does the Earth - which pretty much stays in the same position in its sky - not fall down?)

What I want to say is - our statements are only about our opinion about facts, not directly about the facts themselves. "2 > 1" - to the best of my knowledge. "I am a human being - to the best of my knowledge". I cannot figure out a way it would make sense to claim that these are objectively true statements - independently of my beliefs. Not even "God exists", as much as I consider it to be true, is guaranteed to actually be true.

Happy New Year Alan,

1. Let's start with a positive argument against the claim that assertability is a guide to meaning. It starts with the following premises:

1a) There is at least one sentence of the form p->q which is synthetic a priori, whose constituents are contingent and, depending on what the world is like, can be both rationally asserted or denied. (so: there is a possible world, where it is rational to deny p, there is a possible world where it is rational to deny q, there is a possible world where it is rational to assert p, there is a possible world where it is rational to assert q, there is a possible world where p is true, there is a possible world where q is true, there is a possible world where p is false, there is a possible world where q is false).

1b) Synthetic a priori sentences aren't rationally deniable.

1c) If one rationally believes p and p->q isn't rationally deniable, then one is committed to q. [or, as you may put it, one has to believe q in order rationally to assert p].

You can see how it goes now. Take the sentence p->q mentioned in 1a). It is not rationally deniable (by 1b)). By 1a), q is a proposition that someone could rationally deny, and p is a proposition that someone could rationally assert. Also, by 1c) anyone must believe q in order rationally to assert p. This means that p and q satisfy your condition (3). But, by the assumption that 1a) is

synthetica priori, q is not part of the meaning of p.Now, what do we make of these premises? 1a) clearly depends on whether you think that there are synthetic a priori sentences. Well, you can try to drop this assumption, but then you have to be aware that your criterion of meaning seem to imply that there are no synthetic a priori with the properties mentioned in 1a).

1b) depends on how you understand rational deniability. But it seems quite plausible that if x is rational, and p->q is a conditional that has the properties mentioned in 1a) then x cannot rationally deny p->q.

1c) sort of relies on the dispositional account of commitment (if x believed p and were aware of the content of p->q, then one would believe that p->q [because p->q is a priori], and then one would be rationally commited to q).

2. But are synthetic a priori of the sort mentioned in 1a) the only sentences that you can run the argument with? Well, not really. Consider this:

1a) There is at least one sentence of the form p->q which is

pragmatically a priori, that is, it is pragmatically undeniable that p->q, everyone who understands `p->q' cannot rationally deny it, q is not part of the meaning of p, p and q are contingent and, depending on what the world is like, can be both rationally asserted or denied.1b) pragmatically a priori sentences aren't rationally deniable.

1c) If one rationally believes p and p->q isn't rationally deniable, then one is committed to q. [or, as you may put it, one has to believe q in order rationally to assert p].

Then you run the argument pretty much as we did before.

Now, do we have decent examples of sentences mentioned in 1a)? It seems that we do. Let's take:

If [every taurus is stubborn] then [astrology, at least with respect to what it says about taurus, is reliable].

Let's call the first sentence T and the second A.

- There are possible worlds where T is true. In some of them, T is also rationally assertible.

- There are possible worlds where T is false (I believe we're in one). In some of them (well, in ours) T is also rationally deniable.

- There are possible worlds where A is true. In some of them, A is rationally assertible.

- There are possible worlds where A is false. In some of them, A is rationally deniable.

- A is not part of the meaning of T.

- If T then A is not pragmatically deniable. Anyone who asserts T does that in the framework of astrology, so they have to believe that astrology is at least with respect to the content of T, reliable.

3. In other words, the problem seems to be that there might be other conditions that may enforce conditional committment than just those that are meaning-generated.

4. So, it seems, the counterexample I used before is not domain-specific, and nothing hangs on your acceptance of mathematical fictionalism (although, note that for the example to work it's enough that it is possible that there are rational mathematical fictionalists, it's not necessary for you to be one).

I'm wondering what you think about sentences with properties described in 1a) or 2a). Would you deny that there are such sentences? or would you point to some other problem with the arguments?

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