&gt; It sounds like you&#x27;re thinking of a statement like &quot;there is a prime number&quot; being interpreted as Fa (where a purports to be the name of a number, and F means exist). But really, it should be interpreted as Ex Fx--there exists some x such that Fx.<p>This is a very low insult - to assume I don&#x27;t understand the distinction between “F(a)”, where “a” appears free, and “Ex. F(x)”, where “x” appears bound. I understand logical quantifiers and variable binding just fine, thanks.<p>&gt; The second statement is meaningful as long as F is meaningful, and whether F is meaningful is not a matter of whether there are any things such that F. A predicate can be semantically meaningful without having anything satisfy it.<p>Another very low insult - to assume that I would conflate “false” with “meaningless”. “There is a natural number that is both even and odd” is false. “There is a myppit inside the quxxit” is meaningless unless we first define: (0) what a “myppit” is, (1) what a “quxxit” is, (2) what specific “quxxit” we&#x27;re talking about.<p>The one who&#x27;s making a mistake is <i>you</i>, because “F” isn&#x27;t the same as “F(x)”, but rather “λx.F(x)”. In a context where the variable “x” isn&#x27;t bound, the the latter is meaningful, but the former is not. In other words, the judgment “Γ ⊢ F(x) : Prop”, asserting that “F(x)” is indeed a proposition in the context “Γ”, shouldn&#x27;t be derivable if “Γ” doesn&#x27;t contain “x”. But the judgment “Γ ⊢ λx.F(x) : T → Prop”, asserting that “F” is a predicate ranging over “T”s, is derivable from “Γ, x:T ⊢ F(x) : Prop”, and “Γ, x:T” is a context containing “x”.<p>&gt; And Russell&#x27;s move was to analyze the statement as claiming there is something that is the King of France, there is only one thing that is the King of France, and that thing is bald. And clearly, that is a meaningful conjunction, though there is no present King of France.<p>Unfortunately, “Bald(king)“ isn&#x27;t the same as “E!person. King(person) ∧ Bald(person)”.