Abstract: This chapter argues that the speech act of assertion is fundamentally characterized by the rule that one should assert only what one knows to be the case. Accounts based on other rules such as that one should assert only what is true or what one reasonably believes are argued to give false predictions in various cases, such as assertions about lotteries. The connection between knowledge and assertion is shown not to be merely a matter of Grice's conversational implicature. The account is applied to the connection between assertion and proof in mathematics. The point of having such a speech act is explored through the analogy between knowledge and action.

Keywords: assertion, conversational implicature, Grice, mathematics, proof, rule, speech act,