"He thought me incapable ..." - What is this pattern?

Solution 1:

  1. I believed him insane.

  2. He thought me incapable of doing so.

  3. I wished them dead.

Many verbs take more than one complementation pattern. These verbs above are best thought of as verbs which can take different types of complements, because there are many verbs that take infinitival clauses as complements which cannot be "reduced" in this way. For example:

  • I know him to be an idiot.
  • *I know him an idiot. (ungrammatical)

In sentences (1-3) insane, incapable of doing so and dead are predicative complements. Predicative complements are complements of the verb that describe another argument of the verb, usually the subject or the object. In this case they are adjective phrases describing the objects him, me and them.

This means we can parse the sentences like this:

  • I believed [him] [insane].

  • He thought [me] [incapable of doing so].

  • I wished [them] [dead].

Huddleston & Pullum (2002) call clauses like this which have a verb which takes both a direct object and a predicative complement complex-transitive clauses. Other such examples are:

  • I found her quite friendly.
  • I consider the proposal preposterous.

Other examples which don't have parallel infinitive clause variants are:

  • We made them angry.
  • I painted it green.

Solution 2:

The backwards construction is actually easier than you are suspecting. These are just examples of elliptical sentences: sentences which have had part removed as understood. In all of these, the ellipsis is "to be".

I believed him [to be] insane.
He thought me [to be] incapable of doing so.
I wished them [to be] dead.

Elliptical clauses are very common in English, particularly in speech. Perplexing, isn't it [perplexing]? The use of [elliptical clauses] is dependent on a great many factors, but is enabled by context. In the particular case of elliptical "to be", it is left as understood, historically probably because it is the most common of verbs. Now it is just convention.