So believing trivial truths would add nothing to cognitive value.
Still, one could argue for a weaker claim and merely say that it is prima facie or pro tanto finally good to believe the truth (cf. David 2005; Lynch 2009), where cases of trivial truths such as those just given are simply cases where, all things considered, it is not good to believe the truth.
It also seems counterintuitive to think that the appropriate epistemic goal is to have few false beliefs, for that goal could be satisfied by believing only obvious and trivial truths such as 1 + 1 = 2; that you exist; that your name is such-and-such; and so on.
That move, however, transforms what purports to be a factual claim about human motivation into a trivial definitional truth.
The converse of Theorem 5 is trivial (if truth entails possibility), so Fitch goes most of the way toward erasing any logical difference between the existence of contingent ignorance and the existence of necessary unknowability.
However, the "non-trivial mathematical truths" alluded to above will then have to be expressed by meta-language quantification over dyadic predicates rather than by object language quantification over dyadic relations.
Many will urge that such an approach is problematic, both because it is very difficult to establish non-trivial conceptual truths about controversial concepts, and because our actual usage for the last few centuries of words like disease, illness, or malady do not correspond well with such purported definitions.
Using this definition, Frege 1879 proves some non-trivial mathematical truths, such as that the ancestral R* is transitive and that, for any functional relation R, the R-ancestors of any object are R*-comparable (that is, he proved: Functional(R) & xR*y & xR*z → yR*z ∨ zR*y).
This fact implies that the generation process is cumulative and becomes saturated at a certain point, thus yielding consistent non-trivial interpretations for truth and membership.
After all, one might be interested not so much in accepting or believing such non-classical proposals, but rather in using such proposals to model various naive but non-trivial theories — naive truth theory, naive set theory, semantical property theory, naive denotation theory, etc.
