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Does all imply that there is one or more of something?

  • Does the statement "all of the books are red" imply there is at least one red book?
  • Could there be zero books and the statement still be factually correct?
  • Is it inherently ambiguous?

Not sure if this is an English question or more of a math or logic question.

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3 Answers 3

up vote 4 down vote accepted

It certainly implies that there are at least two books (because it's plural), although logically and semantically speaking, it is possible for there to be no books at all (or just one).

It's not ambiguous, unless either:

  • the person making the statement has already made it clear, or makes it clear immediately afterwards, that he/she doesn't know if there are any books, but if there were, they would be red, or
  • it is deliberately said in a "can you figure out the trick in this problem?" or similar method in an attempt to confuse someone.
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2  
+1, although technically you use the plural also with zero... "There are zero red books". :) –  nico May 5 '11 at 5:14
    
@nico: cough None of our aircraft is missing cough –  user1579 May 27 '11 at 12:58
    
@nico, technically you use i.e. the plural is applied to the set; "red books" is plural - the cardinality does not matter. –  Unreason May 27 '11 at 13:07
    
@Rhodri: none takes the singular, zero the plural. It just works like that... :). @Unreason: cardinality matters, as 1 is used with the singular, the other numbers with the plural. –  nico May 27 '11 at 16:59
    
@Unreason: sure, red books is plural, but how do you choose to use the plural rather then the singular? By looking at cardinality. –  nico May 28 '11 at 17:45

Depending on context, I could say "I want you to hand over all your books" without knowing whether there were zero, one or more books. But It wouldn't make sense to say "all the books were red" if no books where handed over :-)

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It would depend on the context.

A logician or computer programmer would probably not infer that there are a non-zero number of books. A computer programmer would probably want to know if there can be zero or one books (and accept any of the possible answers as sensible).

In normal speech, it tends to imply that there are at least two books - it would be surprising if there were fewer than two, but you couldn't complain that the statement was strictly inaccurate.

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