Part of the difficulty surrounding donkey sentences, to my understanding, is about how hard they are to translate to FOL in a matter that is consistent with other translations to FOL in english.
Take "every man who owns a donkey beats it".
The knee-jerk translation would look something like this:
∀x[(MAN(x) ∧ ∃y[DONKEY(y) ∧ OWNS(y,x)]) -> BEATS(y,x)]
This is problematic because y is free in the consequent. But now say that we extend the scope of the existential quantifier so it reads as follows:
∀x(MAN(x) -> ∃y[ ([DONKEY(y) ∧ OWNS(y,x)] ∧ BEATS(y,x)) ∧ DONKEY(y) ])
∀x(MAN(x) ∧ ∃y[ ([DONKEY(y) ∧ OWNS(y,x)] ∧ BEATS(y,x)) ∧ DONKEY(y) ])
What I did here is extend the scope of the existential to encapsulate the BEATS predicate. Next, I included a conjunction that included another instance of the predicate DONKEY to make the formula more rigorous (because it would evaluate as true if we interpreted y as a pig/non-donkey object).
Finally, I moved the conditional after the MAN predicate to "tidy up" the universal and existential quantifiers.
From my intuition, the sentence "every man who owns a donkey beats it" doesn't suffer from ambiguity unless you interpret "beats it" as masturbating. So what's wrong with my translation into formal logic? Am I missing the point of donkey sentences?
Edit: I suspect that this stems from the basic fact that it's discouraged to say ∀x(Px&Qx) compared to ∀x(Px->Qx), but I'm not completely sure why asides from the fact that it's "too strong a claim".