Curious George
Veteran Member
But what if you say what you don't mean?
"The King of France does not exist" is harder to analyze as is then e.g.,
"There exists no x such that if x is the King of France, then x doesn't exist"
The reason the latter is preferable is because it lends itself to formalization:
~∃(x) ( ?→ ?)
The negated existential quantifier says that there is no x such that if x is...? If we let Kx = "is the king of Franch", we are still left with a question: ~∃(x) ( Kx → ?) ("There exists no x such that if x is the king of France then...)? To say "...then x doesn't exist" doesn't work because it entails that we can use as a predicate "exists" along with the existential quantifier: "There exists an x such that x has property P (being a person) and not property E (of existing)." Or, "for all x, x doesn't exist and x is green".
To illustrate informally:.Given a year (even month) between 1776 (or at least 1781) and 1783, a loyalist might say "the American nation doesn't exist". If a loyalist was trying to explain her or his position to some member of the Indigenous American population, but that member was unfamiliar with the word "nation", the loyalist may be asked to clarify what it is that doesn't exist. The answer isn't really "the American nation", for that does exist at least in some sense from the moment independence was declared (and even more so when the war was won). What doesn't exist according to the loyalist is the legitimacy of the American nation to call itself such, as it shouldn't be considered sovereign but an extension of the British empire. In effect, the loyalist is not speaking the truth. S/he is denying what does in fact exist.
The loyalist really means that there IS an American nation but that there shouldn't be one, or perhaps that the sovereignty of the nation is illegitimate
Can you explain this differently. If I am not mistaken, Willamina's explanation works in your spoiler example demonstrates why. In your example, legitimacy is a necessary property of an existing nation, and using the construction that is easier to formalize seems to bring this issues to the forefront, where as the other phrasing the American nation does not exist, does not.