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You are right - I deliberately avoided the use of the term "useful statements" for this reason.
1) There are tautological statements
2) There are [insert word here] statements.
3) There are useful statements (these can be tautological, [insert word here], or false).
But we don't have a word for [insert word here]...well, prior to taking logic 101, laymen usually insert "true" into the slot, but for some reason we've decided to define the term "true" such that it refers to both tautologies and [insert word here], while neglecting to create a term exclusively for [insert word here].
That's my objection. Approaching [insert word here] is the goal of the sciences...we practically worship [insert word here], in a way that we do not worship tautologies. We aught to have a word that refers to it exclusively. I'd prefer that word to be "Truth", but then the mathematicians went and permanently broadened the meaning of that word, and now we can't have nice things anymore, so we need some other word.
“Empirically true statements”?
Informative?
See above discussion.
It's means: a statement which is true in our universe, but is not a tautology.
Right, I was suggesting the word 'informative'.
Oh, sorry.
Yeah, there are a few candidates - "informative", "real", etc.
The trouble is that we are smashing through the layman's definition again. If we define "informative" as [insert word here], then we must also say that a calculus textbook is not at all informative.