So, if you just look at the superficial layer, you will say that it is grammatically incorrect to split an infinitive. I mean, it's in all the books, right? So it must be wrong. A noted example of this error: "to boldly go" from the opening to Star Trek.
But, if you dig a little deeper, you will say that the prescriptive grammar rules we learned in school were mostly arbitrary decisions made by 18th century grammarians who troweled the models of Latin grammar over English usage. In Latin, the infinitive is one word and is impossible to split; these bluenosed grundies applied that rule to the two-word English infinitive just because they privileged the classic over the vernacular. The rule against splitting infinitives is poppycock! A noted example of this position: "to boldly go" has much more euphony than "to go boldly."
But, if you think about it a little longer, it gets a little more complicated. Those grammarians may indeed have been humorless prigs, but there may be something to the unity of the infinitive after all. To native ears, "to beyond the the farthest reaches of the galaxy go" has no euphony; it sounds particularly awkward, as a matter of fact. Perhaps we can't split infinitives willy-nilly after all.
But, if you let it stew around in your head for a while, you might come up with a theory: splitting infinitives is okay if you're not really splitting them. "To boldly go" can be seen as "to boldly-go": the verbal component is compact and cohesive enough to be conceptualized as boldly-going, a single verb, one integral action - at least by the hard-wiring in the language section of our brains. So, it passes, while "to beyond the farthest &c. go" does not. "To willingly destroy" property sounds right; "to with an axe chop" wood does not. We might see the first-mentioned written; we would never expect the second. We arrive soon at the point where we say there is no "rule" against splitting infinitives, but our language processor just won't let us do it anyway.
But, if you are hard-nosed rhetorician, you will still hold to the opinion that if you mean "boldly-go" and can't find a real word for it, you are a lousy writer, and that splitting infinitives may not be wrong, but it's a practice of the weak, the meek, and the simple.
As the song asks, did you ever have to finally decide?
Produced under the Who's on First license:
Bud: That's the first thing you've said right!
Lou: I don't even now what I'm talkin' about!