Chicago Manual of Style Headline-Style Capitalization

In the 17th edition of the Chicago Manual of Style, §8.159, the following rules are given (among others) for headline-style capitalization:

1. Capitalize the first and last words in titles and subtitles (but see rule 7), and capitalize all other major words (nouns, pronouns, verbs, adjectives, adverbs, and some conjunctions—but see rule 4).
2. Lowercase the articles the, a, and an.
3. Lowercase prepositions, regardless of length, except when they are used adverbially or adjectivally (up in Look Up, down in Turn Down, on in The On Button, to in Come To, etc.) or when they compose part of a Latin expression used adjectivally or adverbially (De Facto, In Vitro, etc.).
4. Lowercase the common coordinating conjunctions and, but, for, or, and nor.

But then, in §8.160, the following example is given:

Four Theories concerning the Gospel according to Matthew (2,3)

In understand that the is lowercased because of Rule 2 and to is lowercased because of Rule 3, but why are concerning and according lowercased? Aren't these “major words”?

Solution 1:

There is an excellent online resource called Title Case Converter. It allows you to enter text, and it then shows you how it would be formatted in title case according to the major style guides.

It also provides an explanation for each word if you select that option.

Here is what it says about the phrase in the question, after selecting Chicago as the style guide to use:

• Four is capitalized because it is the first word of the title.
• Theories is capitalized because it is neither an article, a coordinating conjunction nor a preposition.
• concerning is not capitalized because it is probably used as a preposition (as e.g. in “news concerning the election”). However, it can also be used as an adjective (“this is quite concerning to me”) or verb (“we should be concerning ourselves with that”), in which case it must be capitalized. As a rule of thumb, when “concerning” can be replaced with “regarding,” it is a preposition and must be lowercased.
• the is not capitalized because it is an article.
• Gospel is capitalized because it is neither an article, a coordinating conjunction nor a preposition.
• according is not capitalized because it seems to be used as a preposition.
• to is not capitalized because it is probably used as a preposition or particle. However, it can also be used as an adverb (“pull the door to”), in which case it must be capitalized.
• Matthew is capitalized because it is the last word of the title or subtitle.

Note that there can be multiple reasons for a particular case. The case can also depend on the interpretation of how a word is being used, rather than just the word in isolation to everything else.

Solution 2:

Concerning and according to are used as prepositions here, and are correspondingly lowercase in Chicago style.

In other common styles, any words longer than four letters get capitalized, and it is likely that the editors choose this example precisely to illustrate their position regarding prepositions.