Knowledge, Belief, and Assertion

The traditional answer to the question what it is to make an
assertion appeals to belief (see Grice 1989 and Searle
1969). To assert something, so the analysis goes, is to
express a belief by way of uttering a sentence. Timothy
Williamson claims (1) that on the traditional analysis
assertion is constitutively governed by the truth rule (242):1
One must: assert p only if p is true.
He argues (2) that the traditional analysis is mistaken, and
(3) that assertion is constitutively governed by the
knowledge rule instead (243):
One must: assert p only if one knows p.
I will argue that all three of these claims are false.