All statements are true, false, arbitrary, or nonsensical.
I'm missing something here. Is the statement "the three angles in a triangle add up to 180 degrees" true, false, arbitrary, or nonsensical? What do you call a statement that lacks (or reveals the lack of) crucial context?
In that particular case, any proof that the angles of a triangle add up to 180 degrees has to start from the relevant axioms - and if you include the Euclidean parallel postulate then yes, that can be proved. What would the "crucial context" outside of the axioms you start with and inference steps to get from the axioms to your statement be?
The statement given is equivalent to the parallel postulate, and thus is true in a Euclidean geometry. The statement is tautologically false in a non-Euclidean geometry.
I'm missing something here. Is the statement "the three angles in a triangle add up to 180 degrees" true, false, arbitrary, or nonsensical? What do you call a statement that lacks (or reveals the lack of) crucial context?