Would it be provable that it can or cannot be given? What literature would you recommend me for looking into various theories of truth? Thanks.

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    You can find a good overview of the subject in Theories of Truth: A Critical Introduction by Richard Kirkham.
    – Eliran
    Dec 19 '16 at 22:16
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    "Deflationary Truth" is a collection of many of the most important papers on this topic. books.google.com/books/about/…
    – user20153
    Dec 19 '16 at 23:22
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    The problem is not with giving such a definition, but that there are too many given, all of them controversial. Look also at Tarski's undefinability theorem, stated and proved by Alfred Tarski's undefinability of truth theorem which roughly states that the notion of truth in a first order language (consistent and containing arithmetic) can not be defined within it.
    – Conifold
    Dec 20 '16 at 2:00

Which sense of trivial? In the non-pejorative sense, truth is trivial, mundane, quotidian. Truth is merely a condition of propositions satisfied when what is said is corresponds with (matches, fits, etc.) what is. See chapter 9 for Searle's presentation and defense of the correspondence theory of truth.

Also, see here for references to the works of William James's "pragmatic" approach to truth.

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