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Some grammar rules say "All of ... are not" and "Not all of ... are" have the same meaning, yet they are different from "None of ... are". For example:

1) Not all of the books I have are science fiction novels. (PARTIAL Negation: some may be science fiction novels)

2) All of the books I have are not science fiction novels. (PARTIAL Negation: some may be science fiction novels)

3) None of the books I have are science fiction novels. (FULL Negation: not a single one is a science fiction novel)

Is this correct?

I think that 2) and 3) should be FULL negation and have the same meaning that "not a single one is a science fiction novel" whereas 1) is PARTIAL negation　and indicates "Some may be science fiction novels". Am I wrong about this?

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  • "Sentences of the form All X's are not Y may be ambiguous. All of the departments did not file a report may mean that some departments did not file, or that none did. The first meaning can be expressed unambiguously by the sentence Not all of the departments filed a report. The second meaning can be more clearly phrased as None of the departments filed a report or All of the departments failed to file a report." From American Heritage® Dictionary of the English Language, Fifth Edition. (2011)
    – JEL
    Dec 22, 2015 at 7:24

2 Answers 2

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All of the books I have are not science fiction novels. As others have remarked, this sentence structure, and in particular this placement of the negation, is ambiguous. It has been discussed before here; see, for example, this question with its answers, and in particular, the accepted one.

What does not modify in the sentence? If it is intended to modify the complement, and if one can make that apparent, then there is no ambiguity: All of the books I have are non-fiction. This presupposes that there is a sufficiently clearly determined class of books that are labelled non-fiction, and all of the speaker's books belong to it. (Non-fiction is not quite the same as [not fiction], of course, because of the omnipresent grey area between fiction and non-fiction. However, it is often sufficient to express the intended meaning.)

On the other hand, one might shift the reading slightly in favour of what is referred to as partial negation in your question by, e.g., using a contracted form: All of the books I have aren't science fiction novels.

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You are correct: "All of A are not B" means that every single A is not B.

There is another difference as well: "Not all of A are B" carries a heavy implication that at least some of A are B.

However there are some phrases where "all ... not" and "not all ..." are used interchangeably:

"All is not lost" - Logically this means that every single thing ("all") is not lost, i.e. nothing is lost. But it is used to mean that although one or two things may be lost, a lot of other things are.

"All that glitters isn't gold" - Logically this means that every single thing that glitters ("all that glitters") is not gold, i.e. gold doesn't glitter. But it is used to mean that just because it glitters doesn't mean it is gold, i.e. gold glitters but so do many other things.

Both of these phrases are well known, and possibly the fact that people know what they mean results in people not realising that they're not logically correct.

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