You're now reading a blog post. Consider the sentence you just read. I wrote it once. But you read it, and other readers read it. To each reader, it expressed a different proposition. To Heath it expressed the proposition that Heath was reading a blog post, while to Dagmara it expressed the proposition that Dagmara was reading it. I was somehow responsible for asserting all these propositions.
Suppose that instead I wrote: "This is the best philosophy post you've read so far today." Then to some people, I would have expressed a truth (say, the ones who haven't read any other philosophy posts today yet), but to many others, I would have expressed a falsehood. And I know that this would be so. I'd be telling the truth to some readers and lying to others. Moreover, if you read this post more than once, then whether I told you the truth or lied might have changed between your readings.
Notice another curiosity. In the first sentence of this post, I probably expressed over hundred propositions, one per reader (my posts generally get over 150 hits, though some are no doubt bots). But apart from a handful of regulars (hi, Heath; hi, Dagmara), I didn't know who they would be. But I did know that they would all be reading a blog post while reading the sentence, so I was safe writing "You're now reading a blog post." I knew I wasn't lying to any of you. I wasn't BS-ing either. Yet many of the propositions that I expressed were ones I didn't believe. To each of my lurkers, I said something true when I said: "You're now reading a blog post." But the proposition I expressed is a proposition I don't believe, since I don't know who my lurkers are.
It seems that the first sentence of this post is an assertion. After all, if it's not assertion then neither would it have been a lie had I written "You're now reading the best blog post ever written", but of course that would have been a lie. For only assertions are lies. So it's an assertion, and a responsible one, even though I didn't know which propositions I was asserting when I asserted it. (Had I known which propositions I was asserting, I could have counted them, and thus known ahead of time how many people would read this post!)
The norm of assertion, thus, can neither require me to believe what I am asserting nor even to have a belief as to what it is that I am asserting. The truth norm is what best coheres with these strictures.
Maybe, though, I am not asserting in my first sentence?