When I make a first-order claim like, "The sky is cloudy right now," is this claim implicitly accompanied by a second-order claim like, "What I just said is true/not a lie"? Or what is the difference in information between, "The sky is cloudy right now," and, "It is true/not a lie that the sky is cloudy right now"? Is there a difference?
Clearly not, because a stament could be true when it was made, but become false later when circumstances change.
You might consider the distinction between essential and accidental properties - perhaps mathematical truths have to be true because they relate to what the abstraction is, the definition; but things like the answer to 'What time is it?' is clearly accidental.
I argue truth is about matching up our expectations to reality, especially as regards outputs from mental models matching what happens, here: Why is a measured true value “TRUE”? Like a Shannon channel (world), passing data (out idea).
See also the idea of systemising our methodology of finding convergence of evidence, or consilience: How can experts disagree despite having access to the same facts? Which still leaves the problem of hypothesis generation, in regard to our lack of imagination for alterative accounts that for all the data. A dog can't be taught Relativity (yet), and true things about the world around us are beyond our current capacities, individually and collectively - but we can strive towards understanding more.
With regards to the first formulation of the issue, consider the difference between:
- The next thing I say will be a lie.
- The next thing I say will be a false sentence.
Now, if I tell you (2), then you know in advance to negate whatever my next sentence is. We actually do this kind of thing all the time in formal logic in that we assume things for the sake of deriving a contradiction (or "absurdity"), in order to negate the premises we otherwise assumed. However, per (1), our desire would have to be to trick you into believing the next thing we say, yet by announcing our desire, we would defeat the purpose of whatever we next said. Consequently, there is at least an ambient "pragmatic" sense in which any first-order claim we make encodes for a corollary representation of ourselves (as claimants) being trustworthy enough to listen to (on pain of telling someone something without the expectation that they have a truth-oriented reason to listen to us).
Concerning the alternate sense of the question, see the prosentential theory of truth, according to which the value of the truth term is as a propositional operator relating to sentences in the way that pronouns relate to nouns (i.e. as an indexical "shorthand" for antecedently given nouns).