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As advised by @TRomano in my previous question concerning the use of Either in a negative sentence I ask about the word both in the same role. Here are the examples:

  1. Both this and that fruit are not tasty.
  2. Both cars are not for sale.
  3. Both students will not be restricted.
  4. Both of the lakes are not polluted.
  5. Both paths have not been taken.

Do those sentences sound unnatural? May be even ungrammatical? Or maybe just slightly off?

As I mentioned in my other question, I do not need any help rephrasing those statements using neither. That's an obvious way and a good one too.

My particular concern here is the word both being used for subject in a negation.

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All of those statements do not sound good.
Or, more normally, None of those statements sound good.

Generally, a phrase or sentence has a particular polarity: either positive or negative. In English, there are only a few negative-polarity markers: not, no, never, nowhere, nothing, nobody. When you use one of these markers in a phrase, you "gain license" to use certain words, and "lose license" for others. (I keep being tempted to call these "negative-concord" words, but that is a different (though related) concept.)
In particular, in a negative context, both becomes neither (which also changes plurality: "both are for sale" -> "Neither is for sale"). See the "determination of licensing contexts" section of the wikipedia article on Polarity Items for more details.

Thus, both is not allowed in any of your sentences; Neither is the correct word in all of them.

  • I agree. Does it change if we say Both of these cars are not for sale? – Tᴚoɯɐuo Jan 30 '17 at 20:09
  • @Tromano, I took a more emphatic position and added some references and details. To answer your question, no; you still can't use both there, because both is only licensed in a positive statement, and the presence of not makes your statement negative. – Hellion Jan 30 '17 at 20:37
  • @Hellion Nevertheless, composition "both are not" is definitely above zero on ngram: goo.gl/yb2fK8 – Zverev Evgeniy Jan 31 '17 at 13:24
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Both of them are not to my taste. Both doesn't work well here.

Both is not used in any of these examples. Both could be used like this:

Both cars are mine.

Both of my children go to school here.

I like both of them.

Both lakes are clean and unpolluted.

Both is usually used in a positive way.

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