Here is a standard donkey sentence:
(1) Every farmer that owns a donkey beats it.
It is often said that such sentences cannot be formulated in the language of first-order logic. There is a formulation in first-order logic that gets the correct truth conditions but it differs radically from the surface structure of (1)---most significantly it interprets the indefinite article as a universal quantifier.
(1') ∀x∀y[(farmer(x) & donkey(y) & owns(x,y)) --> beat(x,y)]
There are numerous novel semantic frameworks that attempt to deal with the problem, e.g. various dynamic semantics. But the following seems to be a reasonable formulation of the donkey sentence in first-order logic.
(1'') ∀x[(farmer(x) & ∃y(y=z & donkey(z) & owns(x,z)) --> beat(x,z)]
What's wrong with this?