pluralitive logic also called pleonetetic logic, the logic of ‘many’, ‘most’, ‘few’, and similar terms (including ‘four out of five’, ‘over 45 percent’ and so on). Consider (1) ‘Almost all F are G’ (2) ‘Almost all F are not G’ (3) ‘Most F are G’ (4) ‘Most F are not G’ (5) ‘Many F are G’ (6) ‘Many F are not G’ (1) i.e., ‘Few F are not G’ and (6) are contradictory, as are (2) and (5) and (3) and (4). (1) and (2) cannot be true together (i.e., they are contraries), nor can (3) and (4), while (5) and (6) cannot be false together (i.e., they are subcontraries). Moreover, (1) entails (3) which entails (5), and (2) entails (4) which entails (6). Thus (1)–(6) form a generalized ‘square of opposition’ (fitting inside the standard one).
Sometimes (3) is said to be true if more than half the F’s are G, but this makes ‘most’ unnecessarily precise, for ‘most’ does not literally mean ‘more than half’. Although many pluralitive terms are vague, their interrelations are logically precise. Again, one might define ‘many’ as ‘There are at least n’, for some fixed n, at least relative to context. But this not only erodes the vagueness, it also fails to work for arbitrarily large and infinite domains. ‘Few’, ‘most’, and ‘many’ are binary quantifiers, a type of generalized quantifier. A unary quantifier, such as the standard quantifiers ‘some’ and ‘all’, connotes a second-level property, e.g., ‘Something is F’ means ‘F has an instance’, and ‘All F’s are G’ means ‘F and not G has no instance’. A generalized quantifier connotes a second-level relation. ‘Most F’s are G’ connotes a binary relation between F and G, one that cannot be reduced to any property of a truth-functional compound of F and G. In fact, none of the standard pluralitive terms can be defined in first-order logic. See also FORMAL LOGIC, SQUARE OF OPPO- SITION , VAGUENES. S.L.R.