Epistemic Notions of Truth
Epistemic notions of truth are those that involve some condition of knowledge or knowability in their account of truth, or in their favorite substitute for truth. Examples from Devitt: warranted assertability, verifiability, knowability, rational acceptablity in the ideal limit of theorizing. Epistemic notions have a fundamental obstacle as explanations or parts of explanations of truth. This obstacle can be seen in the following facts.
Fact A: Logical Laws are true.
Fact B: Whatever proposition P is, the proposition that either P or not-P is true (from Fact A)
Fact B says that for any proposition P (or any "sufficiently definite" sentence S) the proposition that either P or it is not the case that P is true. ('Sufficiently definite' means that vague predicates, non-referring descriptions, and indexicals like 'here', 'it', 'now' are avoided.)
Fact C: Whenever the proposition that either P or Q is true, then either P is true or Q is true as well.
Definition: A proposition P is warrantably assertable (by someone) if the evidence in that person's possession make it much more likely that P is true than that it is not.
The Argument: Choose some sentence or proposition X such that neither X nor its negation not-X is warrantably assertable. X might say something like "There are over 100 trillion binary stars." By Fact B, the proposition or sentence that either X or not-X is true. By Fact C, it follows that either X is true or not-X is true. However, neither X nor not-X is warrantably assertable.
The Conclusion: The argument shows that warrantable assertability does not behave like truth, and the other epistemic notions probably don't either. For example, either X or not-X is knowable, since its truth is obvious (Fact B). It is entirely possible, however, that neither X is knowable nor not-X is knowable, for some X similar to that mentioned above.
Metaphysically Ambitious Notions of Truth
The following kind of argument is sometimes called an "inference to the best explanation."
Mao, for example, would probably accept such an inference. Devitt wants to allow such inferences to be made and even imply that electrons are mind-independent. In a deflationary theory, the inference may not work. It is not clear what it would mean on this theory to say that a statement is approximately true. More importantly, on the deflationary view, claims of truth say nothing about correspondence with reality. So saying E is true makes no claim other than that which would me made by assertion theory E. Whether asserting theory E requires that the entities that E appears to discuss actually exist is something that would need to be decided by further analysis of language in terms other than truth. But since truth is the usual way to discuss the relation between language and the world, we will be in the dark about this with the deflationary theory.