the extension of the predicate 'men;' and we may therefore affirm with certainty, that none of the individuals included in the extension of the predicate is found among the individuals included in the extension of the subject,-and consequently, the truth of the converse, viz., No men are angels, necessarily follows. Of Particular Affirmatives. Particular affirmatives are simply convertible, for since the extremes of the convertend are both particular, which is the case in all particular affirmatives, they retain their original quantity when transposed in the converse, e. g.— Some proud men occasionally stoop to acts of the basest servility. may be simply converted thus Some who occasionally stoop to acts of the basest servility, are proud men. The truth of the simple converse of a particular affirmative is proved by Aldrich as follows:-If the particular affir mative-Some blacks are civilised, is true, its contradictory, No blacks are civilised, is false, and so also is the simple converse of the contradictory, No civilised beings are blacks, therefore, the contradictory to this, viz., Some civilised beings are blacks, is true, which is the simple converse of the original proposition, Some blacks are civilised. 2.--Conversion per Accidens. Conversion per accidens, or, as it has been termed, conversion by restriction, or limitation, or particular conversion, is exemplified, when together, with transposing the extremes, of the proposition, the quantity is also changed; in other words, the quantity which is universal in the convertend is changed to particular in the converse, (the affirmation or negation of the original proposition being always, however, retained.) This kind of conversion may probably have been called per accidens,a a inasmuch as it is not a conversion of the universal per se, but rather as containing the particular. The propositions which admit of accidental conversion are universal affirmatives, and universal negatives. When the latter is accidentally converted, it is on the principle of subalternation, for it may be simply converted, as shown above. Universal Affirmatives. This class of propositions may obviously be converted per accidens; for from the truth of a universal affirmative a true subaltern necessarily follows, and as the subaltern is a particular affirmative, it may be converted simply, and when so converted, it will be the accidental converse of the universal affirmative. Thus, if it is true that Every poet is a man of genius, it is also true that Some poets are men of genius; of which the simple converse must also be true, viz., that Some men of genius are poets, which is the accidental converse of the original proposition. For the sake of clearness, the three propositions may be brought together :— ORIGINAL PROPOSITION,...Every poet is a man of genius. a Per accidens, putting in the place of the subject, the quality, whether proprium or accident, which the predicate implies. By the old logicians, the proprium is constantly called 'accidens proprium.'--Moberly, p. 85. The reason why a universal affirmative cannot be converted simply, or into an universal affirmative, is, that in that case the predicate of the convertend would become the subject of the converse; but since the predicates of affirmative propositions are particular, we would be arguing, did we convert such propositions simply, a particulari ad universale. There is a class of universal affirmatives, however, which may be simply converted, viz., reciprocal propositions. In such propositions the predicate is an adequate definition of the subject, as being co-extensive with it, e. g.— Wine is the juice of the grape ; simple converse— The juice of the grape is wine. All triangles are figures bounded by three straight lines; simple converse— All figures bounded by three straight lines are triangles. Cicero was the discoverer of Catiline's conspiracy; simple converse— The discoverer of Catiline's conspiracy was Cicero. The circumstances under which the subject and predicate reciprocate or change places with each other, without a change in signification, have been already explained. Mathematical propositions may be referred to this class, e. g. All equilateral triangles are equiangular; simple converse All equiangular triangles are equilateral. It is not necessary, however, to consider this last example, or its converse, as a universal proposition; for we are not speaking of all triangles, but only of some triangles, viz., those which are equilateral; we may therefore reduce it to a particular affirmative, and convert it simply as such, thus— Some triangles, i. e., all the equilateral, are all the equiangular; simple converse—— Some triangles, i. e., all the equiangular, are all the equilateral. It may be remarked, that the accidental distribution of the predicate in affirmative propositions should not be allowed to affect an argument. An inference drawn from an accidental circumstance of this description would be illogical, for it supposes something to be known which is not made known by the premisses laid down. The inference would be correct in a material but not in a formal point of view. Universal Negatives. Universal negatives can be converted both simply and per accidens. For since the simple converse of a universal negative is true, the subaltern deduced from that simple converse is also true; thus, of the proposition, No larks are web-footed birds, the simple converse is, No web-footed birds are larks; of which simple converse the subaltern is, Some web-footed birds are not larks; and this is the converse per accidens of the original propo sition. Particular negatives cannot be converted either simply or per accidens; for since the subject of a particular negative is not distributed, the converse would require the predicate to be undistributed, which is impossible in negative propositions, whether universal or particular. 3. Conversion by Contraposition or Negation." Particular negatives, it has been said, cannot be converted either simply or per accidens, in the form of particular negatives, yet this class of propositions may be legitimately converted by shifting the sign of negation from the copula to the predicate, and thus rendering a particular negative a particular affirmative, in which form it may be simply converted; e. g., the proposition, Some animals are not rational, becomes affirmative by uniting the negative particle with the predicate, thus—— Some animals are not-rational, or irrational; which may be simply converted into, Some irrational beings are animals. The application of this mode of conversion to particular negatives has the same effect as if the particle of negation were disjoined from the copula and made a part of the predicate, and the proposition then simply converted like an affirmative. This mode of conversion may also be applied to universal affirmatives, in which, after transposing the terms, the negative particle is combined with the new subject, and the proposition made negative by affixing the negative particle a This kind of conversion is not made any use of by Aristotle for logical purposes, although the principle may be gathered from his writings. It was first explained by Boethius. |