In interpreting this sentence we can take ‘Mary’ to be of type i, but we can also take it to be of type &lt;&lt;i&gt;&gt;, that is, the type of a propositional function on propositional functions of individuals. We can also raise the type of ‘eats a hamburger’ to &lt;&lt;&lt;i&gt;&gt;&gt;, a propositional function on propositional functions on propositional functions on individuals. And so on. The principle of multiple types and the principle of multiple analyses together show that a single expression or sentence can be interpreted as having a very large number of logical forms.