Rule: A postmodifying infinitive clause must be easily convertible to a relative clause.
Examples of errors:
(1) The child discovers its own ways and rules to develop its language.
(2) The teacher should give hints to use the structures right.
(3) The conditions to lend books should be changed.
(4) I have no idea to speak about a subject.
The semantic relationship between the postmodifying non-finite clause and the antecedent noun is quite loose, since the latter can represent a variety of syntactic functions in the underlying relative clause. For example:
The next man to arrive (= who arrived) was Bill.
The man to remember (= whom you/we/everyone should remember) is Bill.
In the first sentence, the subject of the main clause (man) is also the understood subject of the infinitive. In the second sentence, the subject of the main clause (man) is the understood direct object of the infinitive. Despite the different syntactic relationships, though, in b oth caseswe can easily convert or expand the infinitive phrases into relative clauses. But what do we do with a sentence like (1)? Is it
The child discovers its own ways to develop its language.
= The child discovers its own ways in/by/according to which it will develop its language.
Is this what the writer meant to say? If so, it is a quite complicated thought and needs further elucidation, because it is tantamount to saying: The child discovers various ways or methods which are suitable for him individually and which he will employ in order to develop his language. Did the writer really want to imply all this, and to raise all the questions it raises for the reader, did he mean simply that every child develops his own way of speaking, his own language habits?
The combination with rules compounds the problem, because the reader also has to wonder what the underlying semantic relationship is between rules and develop. Is it, parallel to ways, equivalent to
The child discovers its own rules by/according to which it will develop its language.
Does the writer really want to imply that children develop their language according to, or by using or following, rules? If this sentence were deeply embedded in a discussion of transformational grammar, it might be meaningful as a vague equivalent of something like
The child discovers the rules of language in an idiosyncratic way, and the way or order in which he acquires these rules influences the way his idiosyncratic speech habits develop.
More likely, however, the writer has simply not thought enough about the words he is using, about the relationship between ways and rules to develop. The difficulty of paraphrasing these expressions (ways to develop, rules to develop) and of readily converting them to relative clauses shows that the meaning of the sentence is not clear and has to be rewritten.
Nevertheless, there are limits to how much of the underlying clause can be ellipted in the infinitive construction. In (1). for example, ways to develop is acceptable, since we have no difficulty expanding this to ways in which the child can develop its language, but the combination of ways and rules requires us to reconstruct something like rules according to which the child can develop its language, which is not acceptable. Equally unacceptable is:
*There are rules to play this game.
for
There are rules according to which this game must be played.
Similarly, hints to use in (2) and conditions to lend in (3) are unacceptable condensations of
hints which would help the students use the structures correctly
and
conditions under which books are lent
In these cases, although the underlying relationship of the noun and the infinitive may become clear after a bit of thought, it is not transparent enough to be acceptable. A slightly different problem is presented by (4), where the author has obscured the underlying semantic relationship by mixing up two constructions, either one of which, by itself, would be acceptable, creating a kind of double exposure effect--compare:
I have no idea what subject to speak about/about which I should speak.
I have no idea (or subject) to speak about/about which I can speak.