Many copy editors around the world, particularly in the USA, still appear to believe that the split infinitive is some kind of grammatical sin (despite what nearly all the quality handbooks of grammar and style actually say), so it may be useful to provide some additional commentary here.
As we say in the book (p. 211), there are still some prescriptive grammar books around that warn against what they call the ‘split infinitive’. They mean the construction illustrated in to really succeed, where an adjunct (really) comes between the infinitival marker to and the plain form verb that is the head of the infinitival clause.
But the term ‘split infinitive’ is very misleading. English doesn't have an infinitive form of the verb in the way a language like French does. French succéder is a single word, but English to succeed is not; it's two words, one a subordinator (to) and the other a verb (the plain form of the lexeme succeed) which is the head of a verb phrase. Verb phrases often begin with the head verb (as in the imperative Be careful!), but they can also begin with an adjunct such as an adverb (as in the imperative Really be careful!). No rule of English grammar requires that a verb phrase preceded by infinitival to must begin with its head verb — that it cannot begin with an adverb. And if you can begin a verb phrase with an adverb and mark it with to, you get phrases like to really succeed:
VP / \ / \ Sub VP | / \ | / \ | Adv VP to | | | | really succeed
All the good usage manuals and scholarly grammars now recognise that phrases of this sort have occurred in English since its earliest history. They generally note that in many cases placing an adjunct between to and the verb is stylistically preferable to other orderings.
For example, there are over 650,000 occurrences of sentences on the web containing the sequence to at least try, as in The employer intended to at least try to explore possible reasonable accommodations for coping with disabled employees. They mostly change meaning or become ungrammatical if at least is shifted to a different position. Intended at least to... sounds as if it means at least intending, possibly more than intending; at least to explore sounds as if it means at least explore, possibly more than explore; if the intended meaning is about at least trying, and possibly more than just trying, the best order of words, without question, is the one that puts at least in between to and try.)
A few writers have remarked that in certain cases it is impossible to avoid placing the adjunct in that position (see this Language Log post by Arnold Zwicky for a discussion of modifiers in infinitives that must separate the to from the verb).
Yet it is still quite common to encounter people who insist that a ‘split infinitive’ is a grammatical error. There is no clear support for that in any grammar that we are aware of: even quite conservative grammar and usage books agree on this.
It may be that citing evidence is useless, since the sort of people who insist on the ungrammaticality of split infinitives would not be convinced by any amount of evidence; but huge numbers of examples of split infinitives can be found in uncontroversially respectable and widely admired literature. Here are a few, from a couple of writers that nobody regards as ignorant or inexpert, who were writing at the end of the 19th century when so many 20th-century prescriptive grammarians were growing up and becoming acquainted with literature. In each example we underline the verb that is separated by a modifier from the preceding to, and we put brackets round the VP of which that verb is the head.
1. From The Red Badge of Courage, by Steven Crane (1895), about the American civil war:
He tried to [mathematically prove to himself that he would not run from a battle].
He began to [blithely roar at his staff: "We'll wallop 'im now..."]
The youth had a thought that it would not be handsome for him to [freely condemn other men].
He waited as if he expected the enemy to [suddenly stop, apologize, and retire bowing].
2. From Dracula, the superb Victorian epistolary horror novel by Bram Stoker (1897):
I knocked gently and rang as quietly as possible, for I feared to disturb Lucy or her mother, and hoped to [only bring a servant to the door].
I said to him, "Go to Dr. Van Helsing, and ask him to [kindly come here at once].
And so we proceeded to [minutely examine them].
So well as I can remember, here it is: "I have studied, over and over again since they came into my hands, all the papers relating to this monster, and the more I have studied, the greater seems the necessity to [utterly stamp him out].
He seems to have power at these particular moments to [simply will], and her thoughts obey him.
(In that last example the verb will is not the modal verb but the ordinary lexical verb meaning something like "wish" or "exercise volition".)
For hundreds and hundreds more to set beside these eight (we simply lack the time and motivation to type them out) see George O. Curme's standard reference work Syntax (Boston: D. C. Heath and Co., 1931), section 49 2 c, especially pages 461-465.
Obligatorily split infinitives.
14 May 2004)
Split decision. (Geoff Nunberg, 23 May 2004)
Two bites of authors' remorse. Geoff Pullum, 20 September 2004)
The pointless game of Grammar Gotcha. (Geoff Pullum, 11 April 2005)
Not to or to not. (Arnold Zwicky, 7 May 2005)
Obligatorily split infinitive in real life. (Geoff Pullum, 19 May 2005)
No splitting in court. (Arnold Zwicky, 14 July 2005)
Better to X than to not Y. (Eric Bakovic, 5 November 2005)
Joe, this is for you. (Geoff Pullum, 29 March 2007)
Irrational terror over adjunct placement at Harvard. (Geoff Pullum, 29 April 2008)
Books more loved than looked in. (Geoff Pullum, 30 April 2008)
Nonintervention. (Arnold Zwicky, 2 May 2008)
Contamination. (Arnold Zwicky, 10 May 2008)
Crazies win. (Arnold Zwicky, 13 May 2008)
Heaping of catmummies considered harmful. (Mark Liberman, 21 August 2008)
Minor writers, revolt!. (Geoff Pullum, 21 August 2008)
Inconsistent Latinophilia. (Geoff Pullum, 26 September 2008)