Hyphen: “well defined” vs. “well-defined” [duplicate]

Solution 1:

The linked argument by Mr. West, as far as I can tell, does not address the use of "well-defined" or "well defined" in predicative position, only in attributive position. It contrasts "well defined function" with "well-defined function".

While it's hard to pin down clear rules for hyphenation, it seems to me that the "some authors" who West says "insist that because 'well' is an adverb the term should not be hyphenated" are misguided, and following a misremembered or incorrectly formulated rule.

As described in Sven Yargs's answer to the following question (Should there be a hyphen in expressions such as “currently-available X”?), hyphens are generally only avoided after the adverb very, or after any adverb ending in -ly. There is no generally observed rule that I am aware of forbidding the use of a hyphen after other kinds of adverbs, such as well, quick, hard.

There are many phrases starting with "well" that are commonly hyphenated, mostly ending in participles or departicipial adjectives, like well-read and the other example West mentions, well-known. (Examples starting with other adverbs: quick-thinking and hard-working).

The hyphenation of adjective phrases in predicative position seems to be a bit more variable than that of adjective phrases in attributive position, but using a hyphen in this kind of context is considered correct by at least some stylebooks:

But well-known is also acceptable in both sentences according to The Associated Press Stylebook (AP). The rule in AP is that "when a modifier that would be hyphenated before a noun occurs instead after a form of the verb to be, the hyphen usually must be retained to avoid confusion." AP gives this example: "The man is well-known."

So, I hope the answer is now well known to you: Both well-known and well known are correct. You choose.

–"A Well-Known Problem: Well Known", by Lynn Gaertner-Johnston, Business Writing Blog