> truth/falsehood is attached to a proposition by virtue of proving/disproving the proposition.
The thing is, this isn't necessarily the case. "Proving/disproving" a proposition can only be done starting from a set of axioms that are independently thought of as "true". But if you think of, e.g. ZFC as true, you'll also think of Con(ZFC) as true, even though the statement of Con(ZFC) can't be proven from ZFC. Similarly for Con(Con(ZFC)) and many sorts of increasingly-complex "consistency" statements.
The thing is, this isn't necessarily the case. "Proving/disproving" a proposition can only be done starting from a set of axioms that are independently thought of as "true". But if you think of, e.g. ZFC as true, you'll also think of Con(ZFC) as true, even though the statement of Con(ZFC) can't be proven from ZFC. Similarly for Con(Con(ZFC)) and many sorts of increasingly-complex "consistency" statements.