64. The predicate of an affirmative proposition, separately considered, is commonly a more general term than the subject.. It is usually a genus, of which the subject is a species. But, when united to the subject, no greater extension is attributed to it than is just sufficient. to enable it to embrace the subject. It is taken in the whole of its comprehension, but in a part only of its extension. [See No. 35.] For example,

Every dog is an animal.

Here it is barely asserted, that the predicate, animal, does extend so far as to include every individual of the subject, dog; but it is neither asserted nor denied, that it is susceptible of a greater extension. Now, though the term, animal, separately considered, is applicable to millions of beings besides dogs, still, in this place, it has no more extension than is expressly given it by the words of the proposition. The predicate of every affirmative proposition being in this way restrained by its subject, universality can never be attributed to it.

65. But in negative propositions, the predi cate, not being restrained by a subject, to which

it is declared inapplicable, is taken in the whole of its extension. Thus,

No animal is a tree.

This proposition implies, that the things, included under tree, are so dissimilar to those, included under animal, that no individual can be found, to which the two terms will apply.

CHAPTER SIXTH.

OPPOSITION AND CONVERSION OF PROPOSITIONS.

66. Opposition in propositions implies a disagreement in respect of quality. Two propositions, which have the same subject and the same predicate, are said to be opposite, when one absolutely denies, in whole or in part, what the other affirms. There are three ways, in which propositions of this sort may be opposed. First, a universal affirmative may be opposed to a particular negative. These are called contradictory. As,

Every defensive war is just.

Some defensive wars are not just.

Secondly, a universal affirmative proposition may oppose a universal negative. These are called contrary. As,

Every disease is contagious.

No disease is contagious.

Thirdly, a particular affirmative may be oppos ed to a particular negative. These are called subcontrary. As,

Some amusements are innocent.

Some amusements are not innocent.

Two contradictory propositions can never be either both true, or both false, at the same time; two contraries may be both false, but they cannot be both true; and two subcontraries may be both true, but they cannot be both false, at the same time.

67. The conversion of a proposition is the transposition of its terms, so that the subject shall take the place of the predicate, and the predicate the place of the subject, with the preservation of truth. When the subject and predicate simply change places, without causing any alteration in the quantity of the propositions, it is called a simple conversion. But if, in the new arrangement, a term of particularity is introduced, to restrain the subject of the derivative proposition within the same extension, which it had as predicate of the original, this is called a particular conversion; by the schoolmen it was

denominated conversio per accidens. Universal affirmative propositions are usually convertible only in the latter mode; but universal negatives and particular affirmatives are convertible in the former.

68. The converse of a universal affirmative proposition must, generally speaking,* be a particular affirmative. It is necessary that both the terms be taken in exactly the same extension, in both arrangements; and since, by the rule stated in No. 63, the predicate of the original proposition must be particular, this same term must be particular in the converse, where it is made the subject, which will therefore render the proposition particular. Thus

Orig. Prop. All swallows are birds.

Converse.

Some birds are swallows.

69. The converse of a universal negative proposition is a universal negative. The subject and predicate, being of equal extent, mutually exclude each other; and as these terms

* This is always the case, except in those propositions, whose predicate is a complete definition of the subject. In such propositions, the subject and predicate are reciprocal terms. As, four times five are twenty; and twenty are four times five. Wine is the juice of

the grape; and the juice of the grape is wine.

are both universal in the first arrangement, [See No. 65,] they must be so in the second. Thus,

Orig. Prop. No deer is an elephant.

70. Particular affirmative propositions are convertible only into the same. In these the terms are both particular; [See No. 61, 63;] and they can never become otherwise by a new arrangement. Thus,

Orig. Prop. Some birds lie dormant during the winter. Converse. Some beings, that lie dormant during the winter, are birds.

71. A particular negative proposition is inconvertible in any mode. Its subject is particular, and by conversion this subject would be made the predicate of a negative proposition, and must therefore be universal, according to No. 65; a whole deduced from a part, which is impossible. For example; from this proposition,

Some birds are not swallows,

we cannot affirm this,

No swallows are birds.

This would be to deduce a whole from a part;