According to the truth norm, p is assertible if and only if p is true. The truth norm is one of four main proposals for a norm of assertion:
One argument for the truth norm is that it is the only one of the four norms that survives, without modification, the counterexamples in this paper.
Another argument is this. Once you have speech acts that are governed by truth norm, you can get for free speech acts governed by all of the other three norms—or even any other imaginable norm. For if, say, some communication calls for a knowledge norm, you can assert "I know that s" instead of just asserting "s". But it is useful to have a variety of speech acts governed by different norms for different contexts. Sometimes, it is useful to have speech acts governed by the belief norm, sometimes by the knowledge norm, sometimes by an inclination norm ("I am inclined to think that s")[note 1]. And what is useful in language is likely to be realized. But it is better, theoretically, if we do not multiply fundamental illocutionary types and fundamental norms. So if we can have one norm from which the others can be derived, that's great.
Note that a similar move cannot be made with the other norms. Suppose that you think the knowledge norm is the right one. Well, you don't get to make a statement that s governed by the belief norm by saying "I believe that s", for the assertibility condition for that will then be that I know that I believe that s, and that's not the same as as the condition that I believe that s. And so on.
We can generalize the point by saying that the truth norm has a universal property with respect to the class of possible norms of assertion-like speech acts. Think of a norm of assertion as corresponding to a predicate N(x,p,C) that gives a condition for x's asserting p in context C being appropriate, say: x knows p in C (on contextualist accounts of knowledge) or just x knows p. Then our universal property is this: Given speech acts with the truth norm, one can engage in speech acts with a norm equivalent to N, simply by modifying the content of what is said.
For, if Assertion(p) is an appropriate speech act if and only if p is true, then Assertion(<N(x,p,C)>) is an appropriate speech act if and only if N(x,p,C).
Here, the notion of assertion-like speech acts is very, very broad. Consider, for instance, weak denial, which is an assertion-like speech act governed by the norm of non-belief. You can weakly deny that s simply by asserting, with the assertion governed by the truth norm, "It is not the case that I believe that s." (Again, you can't do this in terms of the other norms. For you might fail to believe that s and yet not know or believe or be justified in believing that you fail to believe that s.)
The notion of a universal property comes from Category Theory. I am using it analogously here.