But in the history of the subject, the traditional usage has been to confine AEquipollence to cases of equivalence between positive and negative forms of expression. "Not all are," is equivalent to "Some are not": "Not none is," to "Some are". In Pre-Aldrichian text-books, AEquipollence corresponds mainly to what it is now customary to call (_e.g._, Fowler, pt. iii. c. ii., Keynes, pt. ii. c. vii.) Immediate Inference based on Opposition. The denial of any proposition involves the admission of its contradictory. Thus, if the negative particle "Not" is placed before the sign of Quantity, All or Some, in a proposition, the resulting proposition is equivalent to the Contradictory of the original. Not all S is P = Some S is not P. Not any S is P = No S is P. The mediaeval logicians tabulated these equivalents, and also the forms resulting from placing the negative particle after, or both before and after, the sign of Quantity. Under the title of AEquipollence, in fact, they considered the interpretation of the negative particle generally. If the negative is placed after the universal sign, it results in the Contrary: if both before and after, in the Subaltern. The statement of these equivalents is a puzzling exercise which no doubt accounts for the prominence given it by Aristotle and the Schoolmen. The latter helped the student with the following Mnemonic line: _Prae Contradic., post Contrar., prae postque Subaltern._[3] To AEquipollence belonged also the manipulation of the forms known after the _Summulae_ as _Exponibiles_, notably _Exclusive_ and _Exceptive propositions_, such as None but barristers are eligible, The virtuous alone are happy. The introduction of a negative particle into these already negative forms makes a very trying problem in interpretation. The aequipollence of the Exponibiles was dropped from text-books long before Aldrich, and it is the custom to laugh at them as extreme examples of frivolous scholastic subtlety: but most modern text-books deal with part of the doctrine of the _Exponibiles_ in casual exercises. Curiously enough, a form left unnamed by the scholastic logicians because too simple and useless, has the name AEquipollent appropriated to it, and to it alone, by Ueberweg, and has been adopted under various names into all recent treatises. Bain calls it the FORMAL OBVERSE,[4] and the title of OBVERSION (which has the advantage of rhyming with CONVERSION) has been adopted by Keynes, Miss Johnson, and others. Fowler (following Karslake) calls it PERMUTATION. The title is not a happy one, having neither rhyme nor reason in its favour, but it is also extensively used. This immediate inference is a very simple affair to have been honoured with such a choice of terminology. "This road is long: therefore, it is not short," is an easy inference: the second proposition is the Obverse, or Permutation, or AEquipollent, or (in Jevons's title) the Immediate Inference by Privative Conception, of the first.