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In the following sentence: "They are ....... wasting their time." Would "simply", "merely" and "only" be interchangeable? When I was a student of English I was taught the use of "simply" in formal writing should be restricted to its use as an adverb of "simple". That was long ago and I wonder whether this is still valid in 2014.

EDIT (2019) By formal writing I mean any e-mail or letter where you wish to sound educated, impersonal, and following the rules of etiquette. You would avoid the use of slang words, colloquialisms, or whatever constructions that would make a grammarian cringe.

I checked more than a dozen English usage and style guides from the past 100 years and found two treatments of simply that seriously discuss the merits of restricting its use. From Eric Partridge, Usage and Abusage, revised edition (1957):

simply should, in many contexts be avoided in the sense of merely (as in 'He is simply careless'), for it often sets up an ambiguity. Note, too, that 'He spoke simply' = 'in a simple, unaffected, sincere manner', whereas 'He simply spoke' = ''He only spoke; he spoke but did not act, sing, etc. etc.' As an intensive, simply is familiar English —not quite reprehensible, but to be avoided in good writing or dignified speech; 'simply too lovely for words' may be amusing, but it is also trivial.

From Bergen Evans & Cornelia Evans, A Dictionary of Contemporary English (1957):

simply conveys several ideas and needs to be used carefully to avoid ambiguity. Basically it means in a simple manner [example omitted], plainly, unaffectedly [example omitted], artlessly [example omitted].

Three further uses need to be handled with care. Simply may mean merely, only (I was simply trying to keep you you out of trouble), but it may also mean unwisely, foolishly (Simple Simon has become a symbol of men who who behave simply). This last use is now obsolete. Or simply can, and in colloquial use as a vague intensive all too often does, mean absolutely (She looked simply lovely). This is one of those terms which may seem trivial in writing but which its meaning indicated by the proper emphasis, can be quite meaningful.

After 1957, however, I don't find any mention of simply except glancingly by Barbara Wallraff in Word Court (2000), where a New York Times reader argues that it is a superfluous emphasis word in the phrase "simply and more clearly." But in addressing it as part of a wall of complaining sound from readers about modifiers that may or may not be superfluous, Wallraff quickly loses track of it in the mass of examples. At least I think she does. An alternative theory is that she slyly dismisses such criticism by using simply in the disapproved way in the final sentence of her comment:

But surely our linguistic pockets are deep enough for us to spend a few words frivolously, on things beyond the bare necessities—because these things may bring our listeners or our readers closer to us, or simply because it pleases us to spend them.

The overwhelming majority of style and usage guides since 1957 don't address the question of simply at all. From this profound silence, I infer that at some point after 1957—perhaps in 1958—idiomatic usage of simply in the sense of "only" or "merely" became so commonplace that people in the style and usage game stopped worrying about whether using it in that way would doom listeners and readers to needless struggles with ambiguity.

The concerns that Partridge and Evans & Evans expressed about simply do not seem to trouble their present-day counterparts. Today, you can use simply to mean "in a simple way" or you can use it to mean "merely" or you can use it to mean "absolutely"—and in each instance, practically no one will flinch at the informality of the usage, and almost everyone will follow your meaning unerringly.

While they technically all mean the same general thing, each has a slightly different connotation.

They are simply wasting their time.

This could be used to indicate that the people being referred to are being foolish by wasting time. This could occur as follows:

Person 1: Hey, did you hear how Mike and Joe signed up for the tennis team even though they have never played before in their lives?

Person 2: Those fools, I don't know what's gotten into them. They are simply wasting their time.

The people being referred to have made a mistake, so the word "simply" indicates their bad decision.

They are only wasting their time.

This could be used to indicate that the people being referred to are doing nothing harmful besides the fact that they are wasting time. This could occur as follows.

Person 1: Hey, don't you think its bad that they are playing tennis?

Person 2: No way, I think it's okay. They are only wasting their time.

While what the people being referred to may be being unproductive, they haven't done anything harmful.

They are merely wasting their time.

This is the real tricky one, as its connotation could go both ways. It is all about context and inflection of the speaker for this word, which is why it can be very hard to tell what is meant in written text.

Now, it must be noted that each of these can be used interchangeably depending on how a speaker inflects his or her voice. What I have shown above is more of a guidelines for the default meanings behind each word choice, but nothing is absolute. Some of this also depends on where the speaker is from and to whom the speaker is speaking to, but the most important aspect is inflection.