The interpretive rules are repeated at the tree nodes from  section 3.1, and the result of applying the combinatory rules (with lambda-conversions where possible) are shown as well. As can be seen, the Montagovian treatment of NPs as second-order predicates leads to some complications, and these are exacerbated when we try to take account of quantifier scope ambiguity. We mentioned Montague's use of multiple parses, the Cooper-storage approach, and the unscoped-quantifier approach to this issue in section 3.1. In the unscoped-quantifier approach, with a relational interpretation of the verb, the respective interpretations of the leaf nodes (words) in Figure 4 would become Thetis, λyλx(loves(x, y), λP &lt;⟨∃P⟩&gt;), and mortal, and S′ at the root would become loves(Thetis, ⟨∃mortal⟩), to be scoped uniquely to (∃x: mortal(x) loves(Thetis, x)). It is easy to see that multiple unscoped quantifiers will give rise to multiple permutations of quantifier order when the quantifiers are brought to the sentence level. Thus we will have multiple readings in sentences such as “Every man loves a certain woman”. 