Is it the underlying statement that is ambiguous, or is it that we haven't sufficiently defined the syntax?
To say that the sentence is ambiguous is precisely to say that it's not clear what the underlying statement is. The problem is, indeed, at the syntax/semantics interface; English syntax has some tools for specifying the order of quantifiers, but the given sentence doesn't use them.
Any language or sublanguage that has to use quantifiers extensively is going to have syntactic devices - precedence, grouping symbols, etc. - to deal with the problem; the jargons of mathematics and computer science do, in particular. But in everyday language, multiple quantifiers come up rarely enough that the tools just aren't there.
no subject
To say that the sentence is ambiguous is precisely to say that it's not clear what the underlying statement is. The problem is, indeed, at the syntax/semantics interface; English syntax has some tools for specifying the order of quantifiers, but the given sentence doesn't use them.
Any language or sublanguage that has to use quantifiers extensively is going to have syntactic devices - precedence, grouping symbols, etc. - to deal with the problem; the jargons of mathematics and computer science do, in particular. But in everyday language, multiple quantifiers come up rarely enough that the tools just aren't there.