Assertibility and Meaning
Thesis: Whatever anyone must believe in order rationally to assert a proposition p is part of the meaning of p.
Obvious case: One cannot rationally assert p unless one believes that p.
If the thesis is right, then it provides a test for whether a given proposition q is part of the meaning of p. In other words, it gives us a test for determining whether p semantically implies q.
Test: If you want to know whether q is part of the meaning of p, suppose that someone S does not believe q (or even believes not-q), and consider whether S could rationally assert p.
If "no", then q is part of the meaning of p.
If "yes", then q is not part of the meaning of p.
Example: Let's test whether the Peircean semantics for the future tense is correct. According to the Peircean, the future tense is intrinsically modal, and to assert that an event E "will" happen implies that the world is now tending strongly (probability > 0.5) toward E's happening.
Suppose, then, that S does not believe that the world is strongly tending toward E's happening. Indeed, suppose that S believes that E's happening is highly improbable. Could S believe that and, at the same time, rationally assert "E will happen"?
It seems clear to me that the correct answer is "no". Hence, it follows that the Peircean semantics for the future tense is correct.
To resist this argument, a proponent of an Ockhamist semantics for the future tense must reject my thesis. The Ockhamist believes that the future tense is not intrinsically modal. On his view, to say that E "will" happen implies nothing about its probability, save that it is non-zero. Rather, to say that E "will" happen is simply to say "E does happen subsequently", nothing more. Since I think my thesis is pretty plausible, I think it gives us a good reason for rejecting Ockhamism.
I wonder if anyone out there has an plausible counterexamples for my thesis.
posted by Alan Rhoda @ 8:11 PM
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6 Comments:
How about this. Arguably, in order to believe rationally that 2+2=4, I have to believe that there is at least one true sentence (well, I wouldn't be rational if I believed 2+2=4 and when asked whether there are true sentences, answered `no', right?) However, it doesn't seem to be a part of the meaning of `2+2=4' that at least one true sentence exists.
Hi Rafal,
Thanks for your comment. I take it that the general question you raise has to do with whether meaning implies truth and/or existence.
In response, I think your counterexample can be defused by employing the distinction between de re and de dicto beliefs.
Thus, while I cannot assert 2+2=4 unless I believe (de re) of a proposition (2+2=4) that it is true, it is not so clear that in order to assert 2+2=4 I must believe (de dicto) that 2+2=4 is a true proposition or believe (de dicto) that there are true propositions. Indeed, it is not clear that I have to even have the concept of a proposition in order to assert 2+2=4.
So, can S assert 2+2=4 if S does not believe that at least one true proposition exists? Arguably, yes. But clearly S cannot assert 2+2=4 if S does not believe that 2+2=4 is true or if S does not believe of some proposition that it is true. That's all I'm committed to.
Hello,
Well, not exactly. I don't think meaning implies truth or existence. I rather think that `rational committment' is a wider concept than entailment. The idea was rather that there is a reasonable sense of `asserts p rationally' in which it is possible that:
1. S asserts p.
2. S has to believe q, if S is to assert p rationally.
3. q, however, is not part of the meaning of p.
Thus, in this sense of `assert something rationally', it doesn't seem true in general that whatever anyone must believe in order to assert a proposition p rationally is part of the meaning of p.
Of course, lots hangs on what you mean by rational assertion and by belief. Let's grant that S is a competent language user (so we can't say he doesn't believe a sentence because he doesn't understand it - note this isn't too radical: even a priori sentences are those believed when understood, and saying that a sentence is not a priori because someone may not undestand it, is not a very compelling argument).
Next, say that S believes q if it is the case that if one were to ask S whether q is true, S would answer `yes' (say he won't lie etc.).
On this reading, the phrase:
anyone must believe that q in order to assert p rationally
I would interpret as:
For any possible world w, for any competent language user S in that world, if S asserts p, then if S doesn't believe q, S is not rational.
There is, however, no possible situation in which a rational subject who understands the language asserts that 2+2=4 and yet answers `no' to the question `are there any true sentences?'. but it seems that `there are true sentences' is not part of the meaning of `2+2=4'.
Although, I completely agree that `2+2=4' doesn't have to entail logically `a true sentence exists'.
Now, even if you don't buy into this claim, it still seems that your test of whether q is part of the meaning of p would lead to an infinite sequence of semantically ascending sentences:
`2+2=4'
`2+4=4 is true'
` `2+4=4 is true' is true'
and so on...
...which would be parts of the meaning of `2+2=4', according to your test.
But the claim that all those sentences are part of the meaning of `2+2=4' isn't exactly obvious... If you reject it, you have to reject the test you suggested. And if you accept the test, you're also commited to this claim, right? Now, what are your intuitions?
Hello Rafal,
I appreciate your challenging me on this. My driving intuition is that there should be some systematic connection between assertibility-conditions and truth-conditions. The thesis of this post was an attempt to come up with an account of that connection.
You raise a fair objection, though. To believe that q is plausibly understood as a disposition to respond affirmatively to the question "Is q true?" Now, there are cases involving some p and some q in which one who asserts p would be irrational not to affirm q, but where q does not seem to be part of the meaning of p, contrary to my thesis.
To fix this problem I propose placing restrictions on which sorts of beliefs ought to count. It's too generous, I now think, to allow whatever anyone must believe in order rationally to assert p to be part of the meaning of p.
One problem involves propositions that are performatively undeniable, such that to assert their negations would involve one in a performative contradiction. Your example "There are true sentences" is a case in point. Other examples include "There are beliefs", "Something exists", "Some sentences are meaningful", and so forth.
Another problem involves obvious necessary truths, propositions that no competent speaker of modest intelligence could rationally deny. Examples include "2+3=5", "7 is prime", "there are no square circles", "nothing can be red and green all over at the same time", and so forth.
The difficulty these cases raise is that it's very hard to see how any rational agent who understands the claims could avoid having a disposition to affirm them if asked. And if having such a disposition qualifies as a belief, then my thesis commits me to saying that these propositions are part of the meaning of every proposition. Not a plausible thing to say.
I could resist this by rejecting dispositional accounts of belief, but I think it safer to weaken my thesis by excluding propositions that are either performatively undeniable or that are obvious necessary truths. That is, I want to set aside beliefs that no one could rationally deny.
I propose the following revision:
(T*) 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 revision is not objectionably ad hoc because I only want to say that some q is part of the meaning of p when asserting p requires affirming q in virtue of p's intrinsic content, and not because q must be rationally affirmed regardless.
Perhaps T* is vulnerable to other counterexamples (I hope not), but I think it gets around the particular objection you raise.
Hello Alan,
"My driving intuition is that there should be some systematic connection between assertibility-conditions and truth-conditions."
Drawing such a connection might be tough. One of the standard problems: a priori sentences will be (pretty much) always assertable. Hence assertable in the same conditions. Prima facie, however, their meanings don't have to be connected. [this is analogous to the difficulty of telling between two necessary sentences that mean different things, if you want to do that in terms of truth-conditions].
"One problem involves propositions that are performatively undeniable, such that to assert their negations would involve one in a performative contradiction. Your example "There are true sentences" is a case in point. Other examples include "There are beliefs", "Something exists", "Some sentences are meaningful", and so forth."
Here, I think, one has to be careful about keeping two sorts of performative undeniability apart (since the distinction will play a role in further criticism of your new formulation, bear with me for a moment).
- Some sentences are performatively undeniable with respect to a sentence q in the absolute sense: if one asserts q, which is any sentence whatsoever, there will be certain sentences that will be performatively undeniable, no matter what exactly one selected as q.
-Some other sentences, however, will be only performatively undeniable in the relative sense. if one asserts q, there will be certain sentences that will be performatively undeniable, given that one asserts q, but what would make them performatively undeniable would be precisely the selection of q.
Here's an example. Say I assert `2+2+4'. A performatively undeniable sentence: `there are true sentences'. This sentence is performatively undeniable in the absolute sense: I could've assert `pigeons can fly' instead of `2+2=4', and I would be all the same performatively committed to `there are true sentences'. On the other hand, `there are true mathematical sentences' will be performatively undeniable, but only in the relative sense, because its undeniability would depend on the choice of `2+2=4'.
"I could resist this by rejecting dispositional accounts of belief."
Well, bare rejection of dispositional accounts of belief wouldn't do. You'd have to accept a certain sensible account of belief on which one wouln't believe in all those sentences. Of course, a question arises whether (i) this account would be independently plausible, and whether (ii) it wouldn't require one to have a grasp of what meaning is, independent of the test that you're suggesting.
Anyway, let's take a look at your new formulation:
"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."
See, the problem is, as I see it, that this only excludes necessary sentences and sentences that are absolutely performatively undeniable. You still will have problems with relatively performatively undeniable sentences and necessarily equivalent but not necessary sentences.
For instance, it is the case that someone could rationally deny that `there are true mathematical statements' (say someone is a fictionalist about mathematics). But (given that assertion is taken to be the assertion of truth) in order to assert `2+2=4' rationally (and literally) one has to believe that there are true mathematical statements.
This means that your new test would still entail that `there are true mathemematical statements' is part of the meaning of `2+2=4' (even though it would no longer entail that `there are true sentences' is, because `there are true sentenecs' is performatively undeniable in the absolute sense, whereas `there are true mathematical statements' isn't).
Another example involves sentences that aren't necessary. Its viability depends on your account of couterfactuals though. Say we agree with Lewis-Stalnaker account (specifically, this entails that counterfactuals with impossible antencedents are true). It also depends on what reading of your:
"anyone must believe q in order rationally to assert p"
one takes. I take it to be a necessitated and universally quantified counterfactual:
It is necessary that for any person x, [x asserts p rationally => x believes q].
where `=>' is some sort of counterfactual implication.
Now consider the sentence:
4+1=193
Call it G. Clearly, no one can assert G rationally. Thus, it is the case that:
It is necessary that for any person x, [x asserts G rationally => x believes that France is in Europe].
just because `x asserts G rationally' is impossible.
If this latter example doesn't sound quite convincing it at least emphasizes that you have to be careful with how you understand counterfactual dependence in your test.
Alan,
I wonder what you'd make of someone who said something like the following. Suppose one thinks some thing's happening is in fact very *improbable*, but that nevertheless it will happen. That is, one thinks that one has special knowledge about the future that is not available to folks in general -- perhaps one (mistakenly) thinks one's crystal ball gives one knowledge of the future or some such. Now, one says, "Of course, if you looked solely at causal features of the world right now, you'd rightly judge that X's happening is very improbable, objectively speaking. But trust me -- I know that it will happen!"
Now, this seems like a legitimate usage of 'will'. But the user explicitly *denies* that the event's happening is probable in your sense. Of course, she *does* think it is probable in another sense -- the sense having to do with *epistemic* probability and improbability. She is *certain* the event will happen, but what she is certain of is that an incredibly *improbable* event will happen.
Anyway, what do you make of someone thinking like this? Perhaps you'll say that she secretly (as it were) *does* believe that the event's happening is probable in the relevant sense. But maybe this is strained?
Take care,
Patrick
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