The respondents to a recent CNN poll did a less than encouraging job of estimating how the Federal budget is allocated. One detail that gained widespread attention, in light of recent attempts by Congressional Republicans to eliminate Federal funding for National Public Radio, was the respondents’ median estimate of how much of the Federal budget is devoted to public broadcasting: they estimated 5%, which is equivalent to about $178 billion.

While the equivalency just noted happens to be true, it is not obvious or automatic: we have to know the actual size of the Federal budget and do multiplication in order to derive it. Much of the media response to the poll, of course, was an extended lament of the poll respondents’—and, by extension, most Americans’—inability to perform either of these tasks. While we are perfectly able to understand and recognize the two figures—5% of the Federal budget, $178 billion—the equivalency between the two remains opaque to most people.

Opaque equivalencies of this sort have been studied extensively by linguists and philosophers. In particular, there is a well-known connection between referential opacity and belief. Predicates that express propositional attitudes, such as believe or think or, in this case, estimate, are sensitive to the beliefs of the attitude holder (the believer, or thinker, or estimater). Importantly, sentences containing such predicates are often ambiguous between a de dicto interpretation, in which we refer to some term relative to the attitude holder’s beliefs, and a de re interpretation, in which we refer to the term relative to the facts of the actual world (which may differ substantially from the attitude holder’s beliefs).

The media response to the budget poll shows the importance of propositional attitudes in political rhetoric and reporting. For example, Talking Points Memo offered the following headline: “Poll: Americans Wrongly Estimate $178 Billion In Fed. Budget Goes To Public Broadcasting.” Of course, the poll respondents did no such thing: they were asked for percentage estimates, not absolute values. In this context, anything other than a de dicto report of the respondents’ estimate (i.e., “5%”) is misleading: their presumed inability to grasp the equivalency between 5% of the Federal budget and $178 billion makes a de re report (i.e., “$178 billion”) an inaccurate statement of their beliefs, even if it is a true statement about the actual-world value of their estimate. Of course, there are any number of reasons for putting a de re report in a headline like this: shock value, highlighting of general ignorance and innumeracy, and so on. Examples like this remind us that propositional attitudes and their associated ambiguities are ripe for rhetorical exploitation.