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Well, obviously there are two negatives in the sentence. But, at least I am of the opinion that it can't be contracted into a positive- "Not X is Not Required" means a very different thing to "X is Not Required", but I would like to know what grammatical mechanisms are in play here!

(I was actually sent here after a disagreement with somebody on this topic led them to sarcastically say "go ahead and bring it to english.stackexchange" - seemed like a good suggestion though!

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    In the unlikely event there was a sign in the bar saying Not smoking is not required, nobody would assume this implied Smoking is required. On the other hand, I think we can safely assume that another sign in the same bar, saying Not paying for your drink is not allowed would indeed mean You must pay for your drinks! :)
    – FumbleFingers
    Commented Jan 19, 2021 at 16:36
  • Does this answer your question? Isn’t this sentence a case of double negative? It's not the same example, but the principles involved are the same. Professor Lawler has written somewhere I can't locate at the moment (paraphrasing) 'Double negation is a complex issue, and people using the term 'double negative' as a taboo have usually not considered the overarching concept of negation in English adequately (modals and quantifiers needing consideration).'
    – Edwin Ashworth
    Commented Jan 19, 2021 at 17:12
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    If you're asking about acceptability, "Not smoking is not required" is grammatical but bordering on the unacceptable according to the Gricean maxim addressing the avoidance of unnecessarily cumbersome phrasings (the maxim of manner). //// Ah, JohnLawler's response on 'double negatives'.
    – Edwin Ashworth
    Commented Jan 19, 2021 at 17:14
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    Does this answer your question? Isn’t this sentence a case of double negative?
    – KillingTime
    Commented Jan 20, 2021 at 6:19

2 Answers 2

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It is true that there are two negations here and that it is possible to eliminate both of them (and so get a clearer, more natural formulation), but they do not simply cancel out. To see what this sentence actually means, consider first that

Not X is not required.

is equivalent to

It is not required to not X.

A more natural way of saying to not X (where X is some action) is to abstain from X. We thus get

It is not required to abstain from X.

Now, to be required to abstain from something is to be prohibited from doing it. The sentence can therefore be transformed into

It is not prohibited to X.

What is it to not be prohibited to do something? It is, of course, to be permitted to do it. So we get

It is permitted to X.

which is a simple, clear reformulation of the sentence we have started from.

The formal, symbolic apparatus of deontic logic makes such equivalences more obvious than they are in a natural language, such as English.

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This has little to do with language and lots to do with logic. There are four, and only four, logical possibilities. I use R to represent Required and {} to represent Not:

X R ; X{R} ; {X}R ; {X}{R}

Each is different from the others.

Your opinion is therefore correct that "Not X is Not Required" is very different to "X is Not Required".

Or, more formally: {X}{R} ≠ X{R}

This is just one example of the differences between the four possibilities.

I add that it is also clear from this logic that (X not required) does not imply (X Required); that would be to ignore the other two logical possibilities.

Your question title asks if {X}{R} is a double negative; it contains two negatives so is a double negative, but this seems a trivial point compared to the above.

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  • DV please explain. Something wrong with the logic or do you feel it inappropriate to answer such a question? Please help the questioner by explaining yourself.
    – Anton
    Commented Jan 21, 2021 at 18:27

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