distribution the property of standing for every individual designated by a term. The Latin term distributio originated in the twelfth century; it was applied to terms as part of a theory of reference, and it may have simply indicated the property of a term prefixed by a universal quantifier. The term ‘dog’ in ‘Every dog has his day’ is distributed, because it supposedly refers to every dog. In contrast, the same term in ‘A dog bit the mailman’ is not distributed because it refers to only one dog. In time, the idea of distribution came to be used only as a heuristic device for determining the validity of categorical syllogisms: (1) every term that is distributed in a premise must be distributed in the conclusion; (2) the middle term must be distributed at least once.
Most explanations of distribution in logic textbooks are perfunctory; and it is stipulated that the subject terms of universal propositions and the predicate terms of negative propositions are distributed. This is intuitive for A-propositions, e.g., ‘All humans are mortal’; the property of being mortal is distributed over each human. The idea of distribution is not intuitive for, say, the predicate term of O-propositions. According to the doctrine, the sentence ‘Some humans are not selfish’ says in effect that if all the selfish things are compared with some select human (one that is not selfish), the relation of identity does not hold between that human and any of the selfish things. Notice that the idea of distribution is not mentioned in this explanation. The idea of distribution is currently disreputable, mostly because of the criticisms of Geach in Reference and Generality (1968) and its irrelevance to standard semantic theories. The related term ‘distributively’ means ‘in a manner designating every item in a group individually’, and is used in contrast with ‘collectively’. The sentence ‘The rocks weighed 100 pounds’ is ambiguous. If ‘rocks’ is taken distributively, then the sentence means that each rock weighed 100 pounds. If ‘rocks’ is taken collectively, then the sentence means that the total weight of the rocks was 100 pounds. See also SYLLOGIS. A.P.M.