As important to genuine philosophical inquiry as Bayesian analysis, modal logics "and" epistemology are (an oddly redundant catch-all for you to throw into the middle of a list of specifics---but at six syllables it certainly complemented that tactical broadside of intimidating jargon!), []the default belief when presented with a claim of existence is hardly a question[/U]
Wrong. Of course, the real answer is more complicated, but as you seem to object to "tactical broadside[ S ] of intimidating jargon", I'll suffice with "this is trivially and obviously wrong."
I never liked Frost, and paraphrases or play-ons aren't any better.
(I wonder, how many people have fallen for this ploy of yours?).
Just researchers in the sciences and (less frequently) researchers outside of the sciences in fields like classics, linguistics, etc.
For starters, P cannot be "any proposition or lexeme."
Wrong. This is not only wrong, but required for mathematics and logic(s) to exist (not to mention the entirety of the science).
It's true, I didn't explicitly state this---my bad!---but all three of my examples shared a common and obvious trait (one that you shrewdly neglected in each of your counterexamples)*(EDIT: This is neither true nor fair, and I apologize. Please see footnote.)
Premise (1), clarified, is this:
1) Let [P] be any existential proposition---i.e., any claim proposing the existence of thing [N], for which the statements "[N] exists" and "[N] does not exist" are both (a) intelligible/meaningful and (b) mutually exclusive
What is an "existential proposition" (particularly given your qualifications)?
Note, as an aside, that this immediately excludes all of your fun counterexamples---they rely on grammar
None of them do. Google "construction grammar" (and don't forget to check out Hudson's work in network grammar, non-cognitive linguistic grammars such as HPSG, cognitive grammar, etc.).
whereas I'm merely using grammar as a illustrative device
You haven't demonstrated a basic understanding of grammar, let alone used it as an "illustrative device".
Because the set of all possible [N]'s (i.e. all possible things that could exist)
...doesn't address countability.
Which infinity? This is practical. See physics.
when presented with the proposed existence of any single member of that set, you have two choices:
Not according to quantum mechanics.
However, I maintain that each of my examples does reference an existential claim
Ontological claim?[/S]