For example, consider Kripke's modal arguments.
Precisely, modal constructions of proper names do not behave like descriptions. For Kripke, proper names are rigid designators and descriptions (in general) are not.
If 'Superman' abbreviates the description 'is the flying man with a red cape' then take the sentences:
- necessarily Superman is the flying man with a red cape.
- necessarily the flying man with a red cape is the flying man with a red cape.
The former is false and the latter (identity statement) is, of course, true. In a possible world, there might have been another 'flying man with a red cape' who is Uberman, instead. (There could even be a similar man in the very same world.)
Analogously, here:
- 'Superman = Superman' is necessary.
- 'Superman = flying man with a red cape' is not.
Thus, the conclusion is that the proper name and the description are doing different things here, they aren't equivalent. For Kripke, rigid designators 'tag' the same thing in every world, (hence they designate "rigidly"). Descriptions, on the other hand, pick out different objects in different worlds.
Kripke attacks descriptivism in 'Naming and Necessity' at length. There are two major examples in there:
1. Feynman's speaker:
Consider Richard Feynman, to whom many of us are able to refer. He is
a leading contemporary theoretical physicist. Everyone here can state
the contents of one of Feynman’s theories so as to differentiate from
Gell-Mann. However, the man in the street, not possessing these
abilities, may still use the name “Feynman.” When asked he will say:
well he’s a physicist or something. He may not think that this picks
out anyone uniquely. I still think he uses the name “Feynman” as a
name for Feynman.
2. Gödel's incompleteness theorem:
Suppose that Gödel was not in fact the author of this theorem. A man
named ‘Schmidt’, whose body was found in Vienna under mysterious
circumstances many years ago, actually did the work in question. His
friend Gödel somehow got hold of the manuscript and it was thereafter
attributed to Gödel. On the view in question, then, when our ordinary
man uses the name ‘Gödel’, he really means to refer to Schmidt,
because Schmidt is the unique person satisfying the description, ‘the
man who discovered the incompleteness of arithmetic’… So, since the
man who discovered the incompleteness of arithmetic is in fact
Schmidt, we, when we talk about ‘Gödel’, are in fact always referring
to Schmidt. But it seems to me that we are not.