De dicto and de re

De dicto and de re are two phrases used to mark a distinction in intensional statements, associated with the intensional operators in many such statements. The distinction is used regularly in metaphysics and in philosophy of language.
The literal translation of the phrase "de dicto" is "about what is said", whereas "de re" translates as "about the thing". The original meaning of the Latin locutions may help to elucidate the living meaning of the phrases, in the distinctions they mark. The distinction can be understood by examples of intensional contexts of which three are considered here: a context of thought, a context of desire, and a context of modality.
Context of thought.
There are two possible interpretations of the sentence "Peter believes someone is out to get him". On one interpretation, 'someone' is unspecific and Peter suffers a general paranoia; he believes that it is true that a person is out to get him, but does not necessarily have any beliefs about who this person may be. What Peter believes is that the predicate 'is out to get Peter' is satisfied. This is the "de dicto" interpretation.
On the "de re" interpretation, 'someone' is specific, picking out some particular individual. There is some person Peter has in mind, and Peter believes that person is out to get him.
In the context of thought, the distinction helps us explain how people can hold seemingly self-contradictory beliefs. Say Lois Lane believes Clark Kent is weaker than Superman. Since Clark Kent is Superman, taken "de re", Lois's belief is untenable; the names 'Clark Kent' and 'Superman' pick out an individual in the world, and a person (or super-person) cannot be stronger than himself. Understood "de dicto", however, this may be a perfectly reasonable belief, since Lois is not aware that Clark and Superman are one and the same.
Context of desire.
Consider the sentence "Jana wants to marry the tallest man in Fulsom County". It could be read either "de dicto" or "de re"; the meanings would be different. One interpretation is that Jana wants to marry the tallest man in Fulsom County, whoever he might be. On this interpretation, what the statement tells us is that Jana has a certain unspecific desire; what she desires is for "Jana is marrying the tallest man in Fulsom County" to be true. The desire is directed at that situation, regardless of how it is to be achieved. The other interpretation is that Jana wants to marry a certain man, who in fact happens to be the tallest man in Fulsom County. Her desire is for "that man", and she desires herself to marry "him". The first interpretation is the "de dicto" interpretation, because Jana's desire relates to the words "the tallest man in Fulsom County", and the second interpretation is the "de re" interpretation, because Jana's desire relates to the man those words refer to.
Another way to understand the distinction is to ask what Jana would want if a nine-foot-tall immigrant moved to Fulsom county. If she continued to want to marry the same man – and perceived this as representing no change in her desires – then she could be taken to have meant the original statement in a "de re" sense. If she no longer wanted to marry that man but instead wanted to marry the new tallest man in Fulsom County, and saw this as a continuation of her earlier desire, then she meant the original statement in a "de dicto" sense.
Context of modality.
The number of discovered chemical elements is 118. Take the sentence "The number of chemical elements is necessarily greater than 100". Again, there are two interpretations as per the "de dicto"/"de re" distinction. According to the "de dicto" interpretation, even if the inner workings of the atom could differ, the number of elements could not be 100 or less. The second interpretation, "de re", is that things could not have gone differently with the number 118 turning out to be greater than 100.
Another example: "The President of the USA in 2001 could not have been Al Gore". This claim seems false on a "de dicto" reading. Presumably, things could have gone differently, with the Supreme Court not ruling that Bush had won the election. The sentence is trivially true with a "de re" reading: "George Bush could not have been Al Gore".
Representing "de dicto" and "de re" in modal logic.
In modal logic the distinction between "de dicto" and "de re" is one of scope. In "de dicto" claims, any existential quantifiers are within the scope of the modal operator, whereas in "de re" claims the modal operator falls within the scope of the existential quantifier. For example: