A statement in English such as “all squared nonzero real numbers are positive” is called a distributive plural.  This means that the statement “the square of x is positive” is true for every nonzero real number.  It can be translated directly into symbolic notation:  

Not all statements involving plurals in English are distributive plurals.  The statement “The agents are surrounding the building” does not imply that Agent James is surrounding the building.  This type of statement is called a collective plural. Such a statement cannot be translated directly into a statement involving a universal quantifier.  More about this here.  This discussion on Wordwizard suggests that there may be a difference between British and American usage.

The word “distributive” as used here is analogous to the distributive law of arithmetic.  If the set of things referred to is finite, for example the set {-2, -1, 1, 3} then one can say  that “” is equivalent to “”.

I once found a report on the internet that a Quaker Oats box contained this exhortation: “Eating a good-sized bowl of Quaker Oatmeal for 30 days will actually help remove cholesterol from your body.”  This undoubtedly exhibits a confusion between distributive plurals and the other kind of plural, but I don’t understand the connection well enough to explain it.

I can no longer find the report on the internet.  This may mean the Quaker Oats box with that label never existed.

Send to Kindle