# What is the syntax of “second” in phrases like “the second most common problem”?

In English, words like "second", "third" etc. (also "next", I guess) can be used with a superlative to count down from the maximum.

Some dictionaries call "second" an adverb in this context (e.g. MW, AHD) but the OED covers this usage under its entry for the adjective.

It's not obvious to me how to analyze it. It does seem plausible to me that it is an adjective that modifies "most common problem" in a specialized way: (second (most common problem). This seems to be the structure given by the Link Grammar Parser by Davy Temperley, Daniel Sleator and John Lafferty:

    +--------------------------Xp--------------------------+
|              +---------------Ost---------------+     |
|              |   +--------------Ds-------------+     |
+---Wd---+-Ss*b+   +---L--+      +--EA--+----A---+     |
|        |     |   |      |      |      |        |     |

LEFT-WALL this.p is.v the second.a most common.a problem.n .

Constituent tree:

(S (NP This)
(VP is
(NP the
common)
problem))
.)


But it also seems kind of like "second" is an adverb that modifies the meaning of "most common": ([second (most common)] problem). Of course, "the second most common" can be used without any explicit following noun, but I don't know if this is relevant, since I guess that could be analyzed as a kind of ellipsis.

A third possibility that seems to feel right to some people (although I don't really get why) is "([(second most) common] problem)". I don't know if the fact that some people say things like "the most and second most important reason(s)" would support this analysis. I feel like the existence of phrases like "second oldest" or "second highest" counts as evidence against this analysis, because these examples show that "second" can be used with superlatives that don't contain the adverb "most".

Is there any published linguistic work that analyzes the syntax of this construction? If not, could someone post an answer that presents an analysis based on linguistic principles?

• It doesn't necessarily prove anything about the English syntax, but it is interesting to think about related languages where adverb uses are distinguishable from adjective uses because adjectives agree with the noun. In German it's like an adverb, whereas in French and Russian "second" agrees with the noun. – Adam Bittlingmayer Aug 11 '18 at 17:24
• @A.M.Bittlingmayer: I wondered about that. My impression is that there are some French words that are analyzed as adverbs, but that show some kind of agreement with the adjective (or its head noun). E.g. "tout". – brass tacks Aug 11 '18 at 22:09
• Example sentence? I assume you mean some equivalent to en.wiktionary.org/wiki/aller- (which is really analysable as equivalent to "von allen"), but nothing occurs to me. – Adam Bittlingmayer Aug 12 '18 at 8:14
• Anyway the German example ("zweithäufigst") ist like an adverb or prefix (like "pen-" in "penultimate"), whereas as far as I can tell from Google Translate it is more like French in Danish, Afrikaans, Dutch and Frisian for productive formations (like "third"), with some exceptions for a few special cases like "next-". I looked at those since English is somehow a combination of those but with atrophied adjective agreement. – Adam Bittlingmayer Aug 12 '18 at 8:28
• @A.M.Bittlingmayer: I'm talking about forms like "une galerie toute petite" and "des galeries toutes petites" (examples taken from "The Principle of Phonology-Free Syntax: four apparent counterexamples in French", by Miller, Pullum and Zwicky, 1996). Here, the adverb tout [tu] is inflected to [tut], showing gender agreement with the following adjective. (Miller, Pullum and Zwicky argue that the agreement in number that is present in the standard spelling (but not pronunciation) of "des galeries toutes petites" is artificial.) – brass tacks Aug 12 '18 at 17:40

The primary question was for a reference to scholarly treatment of the problem. Until somebody can deliver this, I might as well try to provoke it with a moon shot. You ask for an analysis based on indefinite "linguistic principles". As there is no agreement on definite "linguistic principles", the question is too open and cannot yield a correct answer, only opinion.

From descriptive stand point, the construction is ambiguous. Ambiguity serves a purpose, because it increases understanding across different speakers so that parsing in multiple ways works without change in meaning. This is especially important for language acquisition.

From prescriptive point of view, consider number words in a special grammatical category, e.g. the numerals. Words like "none" and "all" in various contexts are even dubbed determiners or pronouns. I don't see why this would be different for ordinals as opposed to cardinals. If there was a proper adverb, it would have to be "secondly". Why isn't it, here? You might as well wonder for the syntax of "bi-", which is just a morpheme, not even a particle.

If you compare "the second most common." (nominal adjective) or "the second most common problem" (noun phrase) the difference is minimal. It's primarily a question of processing, not production.

I understand it as "the second of the most common problems", in which second is a noun. Expanding on the idea, "second" denotes the depth of recursion, in "the most common problem of the problems that are not the most common problem ..."

Considering number words, where "two" is simply described as numeral - not as adjective, as I do not see plurality listed in the order of adjectives, but size leads the list and numerals would typically come before even that (e.g. "one small rambling answer") - number words may belong in their own syntactic category indeed. There is a difference between ordinals and cardinals in mathematics, though, and hence in grammar, too. I really do not like the frequent one-catch-all word class of the adverbs without further distinguishing. Adverbs may well be the first most fundamental word class. That's still an open issue.

Opposite to your opinion, I find that "second superlative adjective>" is the shortest analysis of the question, disregarding the rest of the sentence, so it's the general answer, but poses the question of the "most adjective" superlative. That's the real problem here. So a treatment of "second most" alone would be incomplete. Whereas there is little difference between ((second most) common) and (second (most common)). By definition there cannot be a second of the most common, because the most common is either singular, or an unordered set. But it still may work that way for you - well, I'm guessing - because from that contradiction you infer that something else is meant, you understand it in the first bracketing, but rebracket to fit your common model and employ some weird ad-hoc rational (sorry), that you are not even sure about and come here asking for, which might be (second [in the order of] (most common (problem[s]))) or even better, because it's reminiscent of naive set theory, s=max{x \in P: x \not = max(P)}, which translates to: second = (most common (problem)) of the problems that are not the most common). I cannot think of a rendering that keeps a linear structure without introducing ellipses or repetition ... except if using the initial "second most". But that may be due to confirmation bias, as I am a speaker of German where "zweitmeist" is readily lexicalized. So we have to go deeper.

The French "le plus grand" (the biggest) is completely natural except for a few idiomatic superlatives like "le meilleur" (the best). Whereas in German, this is not very common. If taking "der bekannteste" (the knownst the most famous) the superlative does denote an increase not in quality, but quantity - how many people know the person. Otherwise "bekannt" is not comparable. I may know a book better, but not more than another. I may know more _ and better _, though. I know "meist befahrene Straße" (most traveled road), but I also know that "meist" means "mostly" next to "most often".

From "Meister" - master, we can deduce, with some suspense of disbelieve, that meist and most are in the loosest sense intensifiers. Some disbelieve is necessary as Latin magister is the most commonly assumed primary source for the term, from magis, which is a doublet of maior, maius. All these are derived from proto-indo-european *megH- (big), whence also mega, with a suffix *-is, from *-yos. Whereas the -most in utmost, foremost etc. is from different morphemes, *-umo- (which is somewhat obscure) plus *-istaz (related to the former *-is?), both are superlative forming suffixes.

That is to say, if you understand second-most as "secondest", I can completely agree with your objection. Although, given first, it seems to be somewhat regular, maybe rather "seconder".

I don't understand the constituent tree you quoted. Here is my attempt, also using a parenthesis notation with indentation showing substructure:

(S (NP This)
(VP is
(NP the
most
)
common
)
problem
)
)
)


I hope the parentheses match up.

• Thanks; so you would put "second" as an adverb modifying "most"? – brass tacks Aug 16 '18 at 2:30
• Yes. ---------- – Greg Lee Aug 16 '18 at 2:33