As far as I know all truth refers to testimony (correspondence) and we use the term ‘loosely’ for many purposes. Technically speaking logic gates output charges (1) or not (0).
We equate this to True=On (constant relation) or false=Off (inconstant). We do this to conflate the logically true (constant relations) and logically false (inconstant relations).
We do this DESPITE the fact that all logic is ternary with negative priority (1-False, 2-True, 3-Undecidable), because all premises are contingent. Since all premises are contingent, we cannot claim positives (constructions) are true, only that they are not false.
As a consequence we falsify alternatives leaving truth candidates as possibilities. This is in fact how cognition, communication, testimony, and science function: free association(some relations), hypothesis (meaning), theory(self-tested), “Law”(Market Tested). The only question is how we falsify.
In mathematics, logic, and language not all ideas can be constructed, and must be deduced by creating constructions that permit us to deduce that which we cannot construct (a heptagon being the most rudimentary problem in geometry – it cannot be constructed by ruler and compass).
Nearly all non-trivial constructions cannot be constructed (proven or testified to) they can only be described by the process of elimination.
Mathematics is an extremely simple logic since it consists of only one dimension: position. Models are constructed of just that one relation – but in large numbers. Language consists of many kinds of measurements. And is far harder to test. What we intuit as constant relations may be in our brains, but not in reality.
This isn’t something that’s open to opinion. Words consists of constant relations. There is simply much higher density that simple reductio models in more primitive grammars (logics).