3.1.1 What Are Scope Ambiguities?

What are scope ambiguities?

A scope ambiguity is an ambiguity that occurs when two quantifiers or similar expressions can take scope over each other in different ways in the meaning of a sentence. Here are some examples.

1. ``Every man loves a woman.''

2. ``Every student did not pass the exam.''

Let's look at the first sentence to see the ambiguity. The more prominent meaning of this sentence is that for every man, there is a woman, and it's possible that each man loves a different woman. But the sentence also has a second possible meaning, which says that there is one particular woman who is loved by every man. This reading becomes clearer if we continue the example by "..., namely Brigitte Bardot."

To further underline the difference, have a look at the two readings represented in first-order logic.

They are genuinely semantic...

We see that the sentence has two different meanings: it is ambiguous. Moreover, there is no good reason to assume that the ambiguity should be syntactic. So we can say that scope ambiguities are genuine semantic ambiguities. It is important to observe here that both readings are made up of the same material (the semantic representations of the quantified NPs ``every man'' and ``a woman'', and the nuclear scope ``love''). The only difference is the way in which the material is put together. We will come back to this later.

...and omnipresent!

The second example shows that not only quantifiers can give rise to scope ambiguities (if you find this particular sentence a little odd, you can play the same game with the German ``Jeder Student hat nicht bestanden.''). In this sentence, it is the relative scope of the quantifier and the negation that is ambiguous. The two readings mean that either every single student failed, or, respectively, that not everyone of the students passed. In formulae: