There are a number of accounts of the speech act of assertion that take it to be necessarily tied to knowledge. It's widely held that in asserting something you represent yourself as knowing it. There are a number of reasons why you might think this. For instance, if I assert something, it will often be perfectly reasonable to ask, "How do you know that?" There are also Moorean paradoxes, like saying, "The sky is blue but I don't know that the sky is blue," which are perplexing on their face.
Williamson more recently takes a strong version of this, the Knowledge Norm of Assertion, which holds that one ought to assert something only if one knows it. (This is stronger because you could hold that there are cases in which one can represent yourself as knowing when nobody would think you actually know it.) Williamson links this to authority: to assert is to give on your authority and this, he thinks, requires knowledge. Another reason one might hold the position is related to lottery paradoxes: if I have a lottery ticket with an immensely low probability of winning, we would still perhaps think it odd if we went around asserting that it was a loser before it was actually determined to be.
I doubt both the weaker and stronger forms. If I assert something, and someone asks, "How do you know that?", it is often entirely reasonable to respond, "I don't, but it does make sense, don't you think?" Moore's Paradox and lottery paradoxes seem to me to be more about implicature than assertion. And while authority is one element in our evaluation of whether to accept other people's assertions, I am unconvinced that it is usually involved in the actual asserting; nor does it seem to be such an integrally important element that we must consider it, since we seem to have situations in which authority really doesn't matter much.
Other norms have been suggested. For instance, most Knowledge Norm people have argued against the Truth Norm, that we ought to assert something only if it is true. I confess that I find the Truth Norm of Assertion to be even less plausible than the Knowledge Norm. There are also different versions of what might be called a Reasonable Belief Norm, that we ought to assert something only if it is reasonable to accept or believe, for some particular account of what it is to be reasonable. I think all three, Knowledge, Truth, and Reasonable Belief, fail to take into account the sheer variety of assertions, ranging from assertions-from-a-point-of-view (as in Hume's four essays on happiness) to jokes to lies to complicated explanations to best estimates. (It is perhaps also worth noting that since we can apparently make highly figurative assertions, Knowledge and Truth Norms both require that figurative and heavily metaphorical assertions can be true. This isn't an issue for me, since I think it is obvious that metaphorical and figurative claims can be true, but there are quite a few people who don't think that they can. This is one of the reasons why one can't handle this kind of question only by looking at a narrow range of examples, but must follow through the implications of one's suggestion all the way across the board to discover its more marginal implications.)
I think a possible problem is that all these norms make assertion itself intrinsically an assignment of modalities -- Knowledge, Truth, or Belief, usually. But if I assert P, I don't think I'm saying that I hold P with such-and-such modality, where that modality is the same everywhere.
I don't really have a rigorous alternative, but I think one candidate more promising than these is what might be called a Usable Premise Norm of Assertion. This idea is that one ought to assert things that can function as premises in reasoning. After all, logically speaking, assertion does not have the function of showing knowledge, reasonableness, or even truth. What it does have the function of doing is indicating that something can function as a premise for reasoning. Thus I think one could at least plausibly say that the appropriate norm for assertion, the appropriate rule, is that one should assert things that are appropriate for being premises in reasoning. This is different from the Knowledge Norm, since premises don't necessarily need to be known, and from the Truth Norm, since premises only need to be such that they can be posited as true in order to see what follows from them, and it is different from any of the Reasonable Belief Norms, since you don't have to believe or accept the premise for it to be useful as a premise.
In particular cases, of course, it may be the reason that something is acceptable as a premise is that one knows it, or believes it, or that it is true. And I think there are fairly obviously particular cases in which the requirements on premises are heightened for various reasons, so that in those circumstances the only acceptable premises will be those that meet a norm of knowledge or reasonable belief, or what have you. But these all seem to be a matter of additional norms arising in particular cases that affects what premises are usable, not of assertion as such.
Of course, the obvious objection that comes to mind is that this might be too weak in several ways. And that's possible, although we do have to take additional circumstance-relative norms into account before we can really say whether the objection has any bite. I also haven't considered all the other variations of all the other norms of assertion that have been proposed. But I think it has the advantages of both staying true to the reason why we have a concept of assertion at all (since it only has general importance because of its logical role) and to the sheer variety of ways in which we assert things.
