Cappelen has recently defended (see a chapter here) a "no-assertion" theory on which there is no special speech act of "assertion' associated with a special norm or set of norms. Rather, there is a multitude of contextual norms that saying can fall under.
Cappelen's most powerful argument applies to any theory on which being governed by a norm like the ones discussed under the head of "the norms of assertion"—standard proposals include: don't say the false, don't say what you don't believe, don't say what you don't know, etc.—is necessary for a speech act to be an assertion. The argument starts by noting that we can imagine people who engage in a practice that is governed by a different one of the proposed norms of assertion. For instance, instead of having a large number of token speech acts governed by Williamson's prefered "don't say what you don't know" norm, they may have a practice of speech acts governed by, e.g., "don't say what you don't believe." And such a group of people is surely no less asserting than we are, assuming of course there is such a thing as assertion. Moreover, there may be such variation within our very own community, as the apparent counterexamples to particular norms of assertion show.
I want to consider several answers. I think each of them is capable of defense, and then draw some interesting connections with debates on marriage.
1. Family resemblance. On this proposal, while there is no such thing as the norm of assertion, there is a family resemblance between all the proposed norms of assertion, and any practice governed by a norm that sufficiently resembles a member of the family counts as a practice of assertion. This allows that there is such a thing as assertion, but its boundaries are vague. This is a way of partially letting Cappelen have what he wants, but without giving up on assertion altogether. I think solutions like this should be a last resort.
2. The truth norm is triumphant. If we adopt the truth norm as constitutive of assertion, we can give a coherent story about what happens in communities where they have practices governed by other norms. Namely, in those communities, they are making assertions, but the content of their assertion is not the proposition most obviously indicated by their words. For instance, take the community K where there is a common practice participants in which are allowed to say "s" only when they know that s. The truth-normer can say that when a member of K is participating in that practice and says "s", she is in fact asserting the proposition that she knows that s. The move is to reinterpret the content of the speech act, and still make it an assertion, but of a slightly different content. There will of course have to be adjustments made elsewhere, too. Thus when A says "s" and B says "That's false", B is not referring to the content of A's assertion (which on this view is the proposition that A knows that s), but B is referring to the content of what A asserted knowledge of, namely that s. Thus, B is asserting that she knows that what A asserted to have knowledge of is false. Such adjustments are awkward but can be done, and the truth-normer, and only the truth-normer, can reinterpret speech under the other norms as assertion of a more complex content. This makes it easier for her to bite the bullet on Cappelen's objection, because she does not have to say that the members of these other communities are bereft of assertion. She might even say that there can be vagueness as to the proposition that someone is expressing, and that this vagueness may correspond to a vagueness as to what norm the saying is falling under.
It seems that this move privileges the truth norm—only the truth-normer can reinterpret speech acts governed by the other norms as assertions of a different content.
3. Focal meaning. A distinctively Aristotelian view is to accept a version of the family resemblance view, but insist that one norm is focal, and speech acts governed by the other norms are assertions in a derivative sense, in virtue of the resemblance between them and the focal norm. I think working out the details of this view will require something like the "norm magnet" view from below.
4. Natural norm bundles. Consider this hypothesis. Some types of activites are strongly natural to humans, in the sense that engaging in these activities is a constitutive part of natural human flourishing. For instance, while it is possible to lead an on-balance flourishing human life without ever eating (one might always be fed intravenously), such a life would lack an aspect of natural human flourishing (admittedly, not one of the most important ones). Among the strongly natural activities, one may hypothesize, there is the engagement in certain social practices. Perhaps requesting is a strongly natural social practice. A human who never requests anything of another is lacking a constitutive part of natural human flourishing—she is failing to flourish as the kind of dependent rational being she is. Likewise, it is pretty plausible that asserting is a strongly natural social practice. Baseball and asserting-in-English are not—one can live a fully flourishing life without participating in baseball or asserting in English.
How does this help? Well, a lot of people think that to make sense of semantic phenomena, we need the notion of "reference magnets", which are "natural" entities. Rabbits are reference magnets, while undetached rabbit parts aren't, and so saying "Gavagai!" around rabbits, barring some defeating data, refers to rabbits, not undetached rabbit parts. It could be that just as there are reference magnets, there are practice magnets. Reference magnets can be pretty strong. Someone who thinks that our language of mid-sized objects refers to spacetime regions may nonetheless be referring to a rabbit with the word "rabbit", even if she thinks she's referring to a spacetime region. Likewise, a community engaging in a practice that "looks" sufficiently similar to a practice magnet is actually engaging in the practice magnet.
Suppose that the real norm of assertion is the knowledge norm. We might have a community who think that they are engaging in a practice governed by, say, the belief norm, and their censure and praise is in line with the belief norm, but in fact their practice is similar enough to assertion that it gets pulled by the practice magnetism of assertion. Thus, the members of this community are in fact governed by the knowledge norm (assuming that's the real norm of assertion), even though their actions, especially their censure and praise, is a better fit for a different norm.
The notion of a practice magnet by itself is enough to show a weakness in Cappelen's argument. But practice magnetism is still a pretty murky idea. The notion of strongly natural practices may, however, help here. It could be that it is strongly natural practices that function as practice magnets. Any sufficiently similar behavior gets pulled in under the governance of the norms associated with the strongly natural practice.
This magnetism seems spooky (though maybe no more so than reference magnetism). Maybe, though, we can somewhat de-spookify it as follows, though to non-Aristotelians what I will say will be just as bad. When we assert, we are engaging in a strongly natural norm-governed social practice. But individually or as a community we need not have much grasp of what in fact are the norms of assertion, and we might in fact have quite mistaken ideas as to what the norms are. What makes it be that the practice has the norms of the practice of assertion is that it is a practice that arises in the right way out of our tendency to fulfill our nature in such-and-such respect (here, ostend to a particular tendency built into our nature). Notice that this suggestion no longer makes the norms be what ultimately constitutes the practice.
Now, here is something that I find quite interesting about all this. Analogous questions come up for marriage. While Cappelen's "no-assertion" theory is controversial and I suspect very much a minority position among philosophers, analogous views of marriage are, I think, going to be quite common among philosophers and other thinkers. These views will hold that there is no such thing as "the norms of marriage", and that there are simply multiple contextually defined practices. To those in the grip of such a "no-marriage" view, the idea that there is a fact of the matter as whether "the" nature of marriage allows this or that is unintelligible. At most there is a family of social practices, much as in suggestion 1.
The idea that there is such a thing as "the norms of marriage", to be investigated by moral and social philosophers, is intrinsically no more problematic than the idea that there is such a thing as "the norm (or norms) of assertion", to be investigated by philosophers of language and epistemologists. Each of the solutions on the side of assertion that I considered as options 2-4 has an analogue in the case of marriage.
I find particularly plausible the idea that marriage is a strongly natural practice with a strong practice magnetism. This allows someone who thinks that the norm of marriage requires monogamy to say that a man in a polygynous culture erroneously thinks that it is possible and permissible to marry more than one person simultaneously. The potential polygamist really is referring to marriage, even if he gets wrong what the norms are.
It may of course be that if you get the norms sufficiently wrong, the practice magnatism no longer pulls you in. Thus, someone who thought that "marriage" is what happens between people whenever they co-write a physics paper, and that the norms of marriage are the norms of co-authorship, would probably be using the word "marriage" in a different sense from us. And her drive for what she calls "marriage" would not be a species of the drive for marital flourishing.
(I do want to say, however, that in fact one of the norms of marriage is that it needs a commitment that is based upon a sufficient understanding of what norms one will have to live by. What kind of understanding is sufficient is a hard question. So we could have a case of someone whose understanding of the norms is sufficiently defective that unbeknownst to him, he is unable to enter into a valid marriage, as he lacks a sufficient understanding of the norms that is needed for the right kind of commitment to them, while at the same time he really wants to get married. That is a tragic situation.)