The misnamed "split infinitive" construction, where a modifier is placed immediately before the verb of an infinitival complement, has never been ungrammatical at any stage in the history of English, and no confident writer of English prose has any problems with it at all. (As the grammarian George O. Curme pointed out in 1930, it's actually the minor writers and nervous nellies, the easily intimidated, who seem to worry about it.) Quite often, placing a modifier just after to and just before the verb is exactly the right thing to do with a modifier in an infinitival complement clause (see the discussion on this page). However, that is not the same thing as saying it is always the right thing to do. Sometimes it's an absolute disaster. My colleague Bob Ladd was preparing to fly back to Edinburgh (EDI) from Munich in Germany when his airline, easyJet, sent him the following email (bafflingly, they sent it after he was in the departure lounge):
Dear DWIGHT ROBERT LADD
We are really sorry to inform you that your easyJet flight, 6914 to EDI on 24/09/2010 has been cancelled. We understand that cancelling your flight will cause you inconvenience and we are very sorry when things don't run as scheduled.
We always aim to provide the best possible experience when flying with easyJet, however from time to time situations arise which are out of our control. On this occasion we've been forced to take the decision to regrettably cancel your flight.
You can see that this is by an inexperienced writer just from penultimate sentence, with its the dangling participle (who is flying?) and classic "comma-splice" run-on sentence and mispunctuated connective adjunct however. But the placement of the adverb regrettably is a much worse mistake. It is a horrible, disastrous writing choice, genuinely leading to syntactic ill-formedness. But why, exactly?
It is not too hard to explain. Ask yourself what regrettably modifies. What exactly is being claimed to be regrettable here?
The intent seems to have been to use regrettably as what The Cambridge Grammar of the English Language would call a modal adjunct. It is supposed to convey roughly what it is regrettable that… would convey. And what is regrettable is the whole situation of easyJet being forced into this last-resort move. It's not like they were canceling the flight quite happily and had to choose between doing an ordinary cancellation or a regrettable one. The adverb regrettably is logically not supposed to be modifying the verb cancel.
Notice, the cancellation may not be regrettable at all. Suppose that an inspection of the plane on which Bob was to fly had revealed the engine number two was hanging on by two bent rivets and would drop off the wing after takeoff, dooming Bob and all the other passengers to a hideous death, and costing my department a valuable professor of linguistics and expert on intonation. Then the cancellation was exactly the right thing to do, and has saved many lives. What is regrettable is that the loose-engine condition arose, and that the cancellation was forced.
So the adverb needs to be either at the beginning of, or after the first auxiliary verb of, the part of the sentence that culminates in the key passive participle forced.
Now, the relevant sentence already has a preposed constituent (on this occasion), and conceivably the writer sensed that it would be better not to begin with two preposed non-subject constituents (to open the sentence with On this occasion, regrettably, we have been forced… would be perfectly grammatical, and I think I would have opted for it, but it might be criticized as a little clumsy); so another possibility was sought, and the terrible choice was made to delay the adverb until a point inside the cancel clause.
What the highly inexperienced message drafter wanted to say could reasonably be expressed using the post-auxiliary placement, as follows (and while I'm doing some unpaid consulting work for easyJet I might as well fix the dangling participle and the run-on as well):
We always aim to provide the best possible experience for you when you are flying with easyJet. However, from time to time situations arise which are out of our control. On this occasion we've regrettably been forced to take the decision to cancel your flight.
Notice what it is that is so stupid about the alleged rule "don't split the infinitive". First, it bars indefinitely many phrases that are entirely grammatical, like You were right to at least consider reporting it, or the other examples given here). Second, it makes some sentences impossible to write at all, because there are cases where immediately pre-verbal placement of an adjunct is obligatory, like Profits are expected to more than double (nobody with their head screwed on correctly thinks *Profits are expected more than to double is an improvement). And third, the overkill of the rule doesn't give you any clue about what is actually wrong with the easyJet message. There really are some cases in which placing a certain adverb between to and a plain-form verb leads to ungrammatical results, but if you're going to avoid them you have to see why that is: the thing to avoid is placing an adverb down in a subordinate clause when it rightfully belongs in the matrix clause containing it.
The take-home message: there certainly are rules of grammar that you shouldn't break, but it does you no good at all to have false beliefs about what the rules are.
(One further small lesson from this astonishingly fecund example of inept writing: American purists will notice that situations arise which are out of our control has an integrated (restrictive or defining) relative clause beginning with which. Most American copy editors and grammar pedants think this has to be avoided for grammatical reasons. They are wrong: see this page for discussion. Notice in any case that the message was written for a British airline, and British speakers have never been so inclined to believe in the fictive that-not-which rule that so many Americans suffer under.)
Hat tip, of course, to Bob Ladd. And welcome back, Bob. EasyJet: my fee for grammar consulting is $200 per hour or any part thereof. Just have your people send a check to my people. Or send two free open-date tickets from Edinburgh to Paris for me and Barbara. Thank you.