I'm not a fluent english speaker. While speaking this language, we usually prefer the implicit objective subordinate clauses (with subject in the accusative case, if it exists) to the corresponding explicit ones, precisely as in classic latin. (I do not know if the word "objective" is correct: I say that a subordinate clause is objective when it functions as object of the verb of the principal clause.)
For instance, we prefer:
(a) they want [me to do this]
(b) they want [that I do this]
Observe that in (a) the subject "me" of the subordinate is in the accusative case, while in (b) the subject "I" of the subordinate is in the nominative case.
My question is: is this always syntactically correct? Can we always substitute an explicit objective subordinate clause with an implicit one?
Let me present another (trickier and maybe incorrect) example. Can we use the sentence:
(c) they showed [the hypothesis to be correct]
(d) they showed [that the hypothesis is/was correct]
Observe that the subject "the hypothesis" of the subordinate does not change his form between (c) and (d), as it does not have the nominative/accusative cases. In fact, if I'm not mistaken, in the english language, the only english words still having a difference between their nominative and accusative forms are the personal pronouns. Maybe, because of this, it is the case that the implicit objective subordinate clause is eligible just when the subject of the subordinate is a pronoun. Is this true? Was it different in the so-called Old English? I expect that this syntactical construction was more frequent in Old English (or "to be more frequent in Old English", lol), as this was the case in Latin and probably in Proto-Indoeuropean as well. Again, if I'm not mistaken: I am not a linguist.