Editing Plural quantification (section)

=== Multigrade (variably polyadic) predicates and relations ===
Sentences like
: Alice and Bob cooperate.
: Alice, Bob and Carol cooperate.
are said to involve a ''multigrade'' (also known as ''variably polyadic'', also ''anadic'') predicate or relation ("cooperate" in this example), meaning that they stand for the same concept even though they don't have a fixed [[arity]] (cf. Linnebo & Nicolas 2008). The notion of multigrade relation/predicate has appeared as early as the 1940s and has been notably used by [[Willard Van Orman Quine|Quine]] (cf.  Morton 1975). Plural quantification deals with formalizing the quantification over the variable-length arguments of such predicates, e.g. "''xx'' cooperate" where ''xx'' is a plural variable. Note that in this example it makes no sense, semantically, to instantiate ''xx'' with the name of a single person.