Yes, we have no prepositions today!
There aren’t any prepositional phrases here, because although one
typically identiﬁes the words to and for as prepositions, they
are here functioning not as prepositions but as complementizers of inﬁnitive clauses.
Your sentences 1 and 2 do not contain prepositional phrases because
they are phrasal verbs (to wait for, to arrange for) whose complements
are inﬁnitive clauses with overt subjects:
- (1) I [waited for]phrasal verb [you to come here.]inﬁnitive clause
- (2) He [arranged for]phrasal verb [me to go there.]inﬁnitive clause
Those two uses of for are no more prepositional than the two uses of to
are. You can test that those two uses of for are not prepositions by
exchanging their inﬁnitive clauses marked above for simple noun complements:
- (1a) I [waited for]phrasal verb [daylight]noun.
- (2b) He [arranged for]phrasal verb [travel]noun.
When you do that, for daylight and for travel are not prepositional
phrases because they are not syntactic constituents.
inﬁnitive clauses are not bare inﬁnitives because they have a to.
However, some matrix verbs allow for bare inﬁnitive complements
without that to marker:
- I made her come here.
- They saw me bake the cake.
Compare those with these, where you need the to:
- I forced her to come here.
- She wanted me to bake the cake.
Your sentences 3 and 4 do not contain prepositional phrases either.
They instead use for in a different way than 1 and 2 do, this time to
mark the inﬁnitive clause as the subject of the main verb:
- (3) [For him to do that]inﬁnitive clause took courage.
- (4) [For you to apologise]inﬁnitive clause is not enough.
The for there is not part of the main verb; it’s a mandatory marker of
the inﬁnitive clause being used as the the subject of a tensed verb. You
can replace both of those two subjects with the pronoun this with no
change in meaning:
- (3a) This took courage.
- (4a) This is not enough.
Pronouns can stand in for noun phrases. They cannot stand in for prepositional
phrases, and indeed a prepositional phrase “cannot” be the subject of a clause.
They can only fulﬁll modifier roles in a sentence, not substantive ones.
Because we could make that swap here, those are not prepositional phrases. Another
indication that this for is not a preposition is that you can no more exchange
it here for any other preposition than you can exchange to for one.
Lastly, if you rearrange the ﬁrst two sentences with the phrasal verbs
so that their inﬁnitive clause becomes the main verb’s subject, now you
are forced to insert an “extra” for to keep the sentence grammatical:
- (1c) For you to come here is what I waited for.
- (2c) For me to go there is what he arranged for.
Now the ﬁrst and last words are both for. You need
both. These don’t work:
- (1d) *You to come here is what I waited for.
- (2d) *Me to go there is what he arranged for.
And these are completely ungrammatical because they
are no longer the phrasal verbs from the original:
- (1e) For you to come here is what I *waited.
- (2e) For me to go there is what he *arranged.
See also this related answer by John Lawler.