You are right back to missing bilby's point--that declarative statements need not be either true or false. They can simply lack a binary truth value
No, I'm pretty sure I agreed to that part quite vigorously. The part I engaged with and expanded on was exactly the part that I cared to actually mention: that sometimes the application of language doesn't just lack a binary truth value, sometimes it is a completely invalid construction of language, a syntax error.
The present king of France is bald" could be true or false in a historical or fictional text, but it lacks a truth value in the context of the real world
And it can lack a truth value for two different reasons, one because it is lacking a truth value owing to not even really being a
valid application of language and one owing to not being a
complete application of language and
these are different situations.
"This sentence is itself in the form of a declarative sentence" is trivially true
Tautologies are circular references that don't make the obvious mistake. Such statements can prove anything, including that true is false, and rather isn't the sort of circular reference being referenced. The existence of tautologies doesn't counter the existence of nonsense, and aren't what I was talking about. Apparent tautologies still need to actually be tested and cannot be taken for "true" except in the presence of other axioms which test them AFAIK.
Presupposition failures are missing references, which is distinct from the problem of assigning inconsistent truth values to constants.
Then, I would assert that absolutely nothing that those who deal in with spoken language have discovered that software engineers have missed, mostly because software engineers actually have to make sure their invocations of language are complete every time, and made various machines that both discover invalid uses and flag them as both illegal and "dangerous", but when the compiler does this, it has a myriad of different reasons, not just "this symbol is not defined".
I do not think, though, that paradoxes arise from "unordinary" or "informal" language use but from "invalid language use". It's not a problem that can be resolved by making the language ordinary or ideal, and can only be resolved by not saying nonsensical things, and by not invoking disagreements of axioms.
It seems very much that the dispute between ordinary and ideal language proponents is misplaced, because the "ordinary language" seems very much to be proclaiming their "ordinary" notions which they assert, if held to, would prevent such paradoxes when this is no different from proclaiming "natural language" somehow ideal all on its own.
Either way, they're both wrong, because such paradoxes involve saying something
nonsensical and just not catching it, and which version of language you use doesn't matter when ANY version of language can be used to express nonsense statements that cannot produce an answer in the target regime, and I think this butts up against an issue I recently came aware of called "nomic exclusion", which I'm not really actually interested in discussing much.