In my study I've found that ἀτάκτως atáktōs is given the meaning of disorderly, undisciplined or out of rank. The implied meaning is of fruitlessness. And later the passage talks about those who are busybodies rather than busy working (v. 11). There seems to be an implied analogy with the discipline of a soldier, who follows instructions and is therefore a useful and productive member of the group. I find that the word "idle" doesn't encapsulate this fuller possible meaning. How do we best interpret v. 6 then?
ἀτάκτως is a very uncommon word: It only appears in the two verses you cite in 2 Thessalonians, but nowhere else in the Greek New Testament or in the Septuagint version of the Old Testament. So it is hard to look at other contexts where it is used in the Bible.
It does appear, though, in classical Greek. Herodotus used to describe troops who are not in battle order:
The Aeginetan ships found the Athenians in disarray and attacked and overcame them, taking four Athenian ships and their crews.1
Other meanings given are:
- Not at one's post (Lycurgus, Against Leocrates, XXXIX)
- Undisciplined, disorderly (Thucydides, The Peloponnesian War, VIII.10)
- (As an adverb) In an irregular manner (Thucydides, The Peloponnesian War, III.108)
It doesn't ever seem to have been used in the sense of being unoccupied, as "idle" suggests.
The root of the word is the verb τασσω, which means something like to "determine" or "originate". A related noun is τάξις, meaning "order", or "fixed succession". προστάσσω means to give a command or order. The prefix ἀ- conveys absence or opposite of something (e.g. Sin is lawlessness - ἀ-νομία; 1 John 3:4). Hence, ἀτάκτως is the opposite sense of something that is determined or ordered.
In 2 Thessalonians 3, Paul is speaking about two different kinds of disorder. In verse 6, he is speaking of the disorder that comes from not following what has been taught previously: the παράδοσις - translated somewhat grudgingly by some as "tradition" (from the Latinization of the Greek word; traditio comes from trans/over + do/give):
Now we command you, brethren, in the name of our Lord Jesus Christ, that ye withdraw yourselves from every brother that walketh disorderly, and not after the tradition which he received of us.
In verse 11 he is speaking of another type of disorder that comes from a lack of personal discipline:
For we hear that there are some which walk among you disorderly, working not at all, but are busybodies.
John Cassian (ca 360-435), explains the passage:
For we have heard that some among you walk disorderly, working not at all, but curiously meddling. He is nowhere satisfied to speak of those who will not give themselves up to work, as if they were victims of but a single malady. [At first] he speaks of them as disorderly, and not walking according to the traditions which they had received from him: and he also asserts that they were restless, and ate their bread for nought. Again he says here [v.11], We have heard that there are some among you who walk disorderly. And at once he subjoins a second weakness, which is the root of this restlessness, and says, working not at all; a third malady as well he adds, which springs from this last like some shoot: but curiously meddling.2
"Idle" is perhaps not the best literal translation of ἀτάκτως, but it fits the second sense in 2 Thessalonians. One of the definitions of the English word "idle" is "having no purpose or basis"3, which seems to accord more or less with the classical usage of ἀτάκτως, but "disorderly" is probably a better fit in my opinion.
1. The Histories, VI.93
2. Institutes, X.XIII
3. Concise Oxford English Dictionary (11th ed.)