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The Terms of Service (http://stackexchange.com/legal) currently prevents posting answers only containing a hint: Section four states that:

Under no circumstances will Subscriber use the Network or the Service to [...] (d) knowingly post any false, inaccurate or incomplete material

A hint is technically incomplete material, so a lot of users (including myself) are in violation with the Terms of Service. I think that this should be fixed in the ToS.

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    $\begingroup$ This reading of the TOS is absurd. $\endgroup$ – quid Mar 28 '16 at 19:10
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    $\begingroup$ @quid As in, you don't think that hints are incomplete material? $\endgroup$ – wythagoras Mar 28 '16 at 19:11
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    $\begingroup$ Indeed, I do not think that hints are incomplete material, in any case not in the sense intended there. (And I say this as somebody that has a serious dislike for HINTS: and would be quite happy to eradicate them.) $\endgroup$ – quid Mar 28 '16 at 19:15
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    $\begingroup$ @quid This raises the question of what kind of incomplete material is actually meant to be prohibited by the ToS. $\endgroup$ – user147263 Mar 28 '16 at 19:16
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    $\begingroup$ @404 first and foremost, the intent is to safeguard against malice. What is forbidden is to spread misinformation via omission. $\endgroup$ – quid Mar 28 '16 at 19:24
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    $\begingroup$ I postulate that anything less than a computer verifiable proof written in Coq or another establish proof assistant is incomplete!!!!!! The entire website is outlawed!!!!! $\endgroup$ – Asaf Karagila Mar 28 '16 at 20:48
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    $\begingroup$ @Asaf this is close to "official policy" :-) $\endgroup$ – quid Mar 28 '16 at 20:55
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    $\begingroup$ @quid: I had a professor in undergrad, that if time would have permitted, he would require all the answers to his exams to begin by stating the axioms of logic and axioms of set theory and deriving more or less everything. $\endgroup$ – Asaf Karagila Mar 28 '16 at 21:00
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    $\begingroup$ Why your emphasis on answers? I find many of the questions on this site to be seriously incomplete. $\endgroup$ – bof Mar 31 '16 at 20:57
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    $\begingroup$ @bof I agree with you that many of the questions on this site are incomplete, but my problem is that Hint answers are currently forbidden by the ToS, while good hints are encouraged and used by most people. $\endgroup$ – wythagoras Apr 1 '16 at 16:25
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    $\begingroup$ @wythagoras Where do you ( where do the ToS) draw the line between "Hint: use induction" and omitting the most trivial step? $\endgroup$ – bof Apr 1 '16 at 21:08
  • $\begingroup$ @quid, Should I not give answers that say Hints? $\endgroup$ – S.C.B. Apr 4 '16 at 7:16
  • $\begingroup$ @MXYMXY No, you should not, in my opinion. This has nothing to do with the ToS though. Instead, of hints you can give a terse answer or even only a sketch of an answer. The difference is that a "terse/sketch of an answer" comes with the implicit promise that it works, while a "hint" does not commit to anything. Moreover, stylistically it is not a good choice. $\endgroup$ – quid Apr 4 '16 at 10:12
  • $\begingroup$ @quid: Regarding Hint: usage, I do this sometimes (usually as a comment, but every now and then as an answer)---even with the boldface and a colon aspects, which leads me to wonder if I started this particular style in which boldface and colon are used (although to be honest, I don't know if I've seen it outside of my own responses). For what it's worth, I was simply copying the style I used on LaTeX prepared tests and quizzes from the mid 1990s to the mid 2000s, when I thought a certain question might be too difficult and decided to gave a hint. $\endgroup$ – Dave L. Renfro Apr 7 '16 at 18:23
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    $\begingroup$ @DaveL.Renfro Such hint notation has been used since the dawn of the site, e.g. you can find it frequently in my posts. $\endgroup$ – Bill Dubuque Apr 9 '16 at 19:49
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Lie of omission or lying by omission are established notions, which also have legal meanings. The intent, I am pretty certain, is to cover this, from Wikipedia page on Lie:

Lying by omission

Also known as a continuing misrepresentation, a lie by omission occurs when an important fact is left out in order to foster a misconception. Lying by omission includes failures to correct pre-existing misconceptions. For example, when the seller of a car declares it has been serviced regularly but does not tell that a fault was reported at the last service, the seller lies by omission. It can be compared to dissimulation.

Specifically, a hint marked as such can never be an issue as it is explicitly disclosed the information is not detailed. An intentionally misleading hint might be a violation, but I do not see a problem with this.

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    $\begingroup$ The ToS avoids the words "lie", "lying", "mislead", "honest/dishonest" for a reason. The terms that are there (false, inaccurate, incomplete) are intended to form a more objective test that applies only to the text posted and not to its author's intentions. I also suspect that the language in ToS on incomplete posts is about more than just lying by omission, and is there to ban all intentional or accidental postings for which omission places them into an enumerated banned category. $\endgroup$ – zyx Mar 28 '16 at 21:13
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    $\begingroup$ "The terms that are there (false, inaccurate, incomplete) are intended to form a more objective test that applies only to the text posted and not to its author's intentions" What about the "knowingly"? $\endgroup$ – quid Mar 28 '16 at 21:15
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    $\begingroup$ Probably for determining consequences such as banning users from the site or not. The material would be deleted or edited independent of what the user intended. $\endgroup$ – zyx Mar 28 '16 at 21:18
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    $\begingroup$ (So "knowingly" is not part of the definition of banned content, but of banned conduct.) $\endgroup$ – zyx Mar 28 '16 at 21:24
  • $\begingroup$ Well, and the big difference as well is that some posters might omit information in their answer not out of malice but out of laziness. For instance, one might solve part of an answer and then say "and you can solve the rest yourself". The difference between that and a hint is that the 'hint' usually describes the entire process of solving questions along with a few pointers. It does not attempt to solve the answer. It attempts to enable the questioner to solve it themselves. Omitting the end of solution is different as you basically just get up and walk away in the middle of solving it. $\endgroup$ – The Great Duck Apr 11 '16 at 18:25
  • $\begingroup$ @TheGreatDuck "[...] the 'hint' usually describes the entire process of solving questions along with a few pointers" this is not true in general, rather often a "hint" just gives, or hints at, a main idea. $\endgroup$ – quid Apr 11 '16 at 23:16
  • $\begingroup$ Well, that's my interpretation of a hint. In general though, a hint isn't omitting information. Rather, it is giving a different set of information. A lack of information would be to solve half a problem and then just walk away for no reason. I'm sure while the definition of hint is vague everyone can agree that getting up and walking away halfway through a calculation is NOT a hint. Hence, it's meant to defend against incompleteness due to laziness rather than incompleteness due to a different manner of answering (AKA the hint). $\endgroup$ – The Great Duck Apr 12 '16 at 0:58
  • $\begingroup$ @TheGreatDuck my remark is based on observation not interpretation. $\endgroup$ – quid Apr 12 '16 at 6:25
  • $\begingroup$ That's fair, but I guess my meaning of "omitting information" is different than yours. A hint omits information, sure, but in a completely different sense. It's not omitting info from their answer. It's omitting information relevant to the question. Whereas an incomplete answer also omits information, but omits information relevant to their own answer.... By just getting up and walking away halfway through. It's in this sense that I say that the TOS isn't purely guarding against lie by omission. It's also gaurding against unfinished answers with regards to the actual work being done in answer. $\endgroup$ – The Great Duck Apr 12 '16 at 17:57
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Funny discovery.

I presume that the intention, though not the wording, was to prevent postings that fall into other forbidden categories (such as "false, inaccurate" in the quotation, or illegal) because of what they omit rather than what they contain.

In that reading, incomplete is not itself a forbidden category of material.

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The key word here is material. The ToS statement proscribes not incomplete answers but (knowingly) incomplete material. Just what might sensibly be construed as constituting the latter, in the context of answers to questions on MSE, is open to interpretation. However, an answer that provides a clear guide to tackling the problem posed by the OP, which omits only details that the OP can be expected to supply, can arguably be considered complete, as a guide or hint, albeit incomplete as an answer. An interpretation of "incomplete material" overriding enough to deem incomplete such complete hints would probably also consign almost any reasonably compact answer to the "incomplete" sin bin. Consequently, such an interpretation (whether or not intended) will not be respected.

One might add that explicit proscription of deliberate obviously-bad behaviour on MSE, even when framed accurately enough to not preclude good behaviour, is pointless because (1) few users will read it for a start, (2) it cannot be enforced (except retrospectively, which will happen in any case), and (3) the handful of people who deliberately behave badly will ignore it anyway (in their short-lived presence on the site).

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