"Birds are not quadrupeds :" in this instance the connexion is impossible, and therefore the subject is distributed; that is, it asserts that "no bird is a quadruped." In contingent matter, where the terms may or may not agree, an indefinite proposition is understood as a particular; thus, "Food is necessary to life," that is, some food; "Birds sing," that is, some birds sing; "Animals are not quadrupeds," that is, all animals are not, or some are not quadrupeds. "Plato 7. Another class of propositions consists of those denominated singular propositions. Those whose subject is either a proper name, or a common term with a singular sign, are thus called; and they are considered universals, because in them we speak of the whole of the subject. When we say, was a philosopher," we mean the whole of Plato. If any qualifying term is inserted to indicate that the whole of the subject is not to be included, the proposition may be viewed as particular; thus, "This man is not wholly a philosopher;" "Cæsar was not altogether a tyrant;" "I shall not wholly die." Singular propositions, however, are most naturally accounted universals;-it is only when modified as above that they can be contradicted. Of all these divisions the most important are those which class propositions into affirmative or negative, universal or particular; because, considered as to their quality and quantity, every pure categorical proposition must be included in these four divisions. Every proposition is either affirmative or negative; and must either be universal or particular; they are, therefore, ranged under four great classes-viz., Universal Affirmatives, and Universal Negatives; Particular Affirmatives, and Particular Negatives. These are denoted, for the sake of brevity, by the symbols, A, E, I, O: thus, A, denotes a universal affirmative; E, a universal negative; I, a particular affirmative; and O, a particular negative. To aid the memory, the following couplet is usually given, embodying the above symbols: Asserit A, negat E, verum generaliter ambo: It must be particularly remembered that in every universal proposition, the subject is distributed, that is, is taken in the whole of its extension; but never in a particular proposition. But the distribution, or non-distribution of the predicate, does not depend on the quantity, but on the quality of the proposition. If any part of the predicate agrees with the subject, it must be affirmed of it, and cannot be denied of it. In an affirmative proposition, then, it is sufficient that some part of the predicate agrees with the subject; but in a negative proposition, it is necessary that the whole of the predicate should disagree with the subject; thus, it is true that "to study Logic is useful," although the whole of the predicate "useful" does not agree with the subject; for many things are useful besides the study of Logic. On the other hand, "No vice is useful" would be false, if any part of the predicate "useful" agreed with the term vice; that is, if there were any one thing really useful which was a vice. The rules to be observed, then, respecting distribution are these : 1. All universal, but no particular propositions, distribute the subject. 2. All negative, but no affirmative propositions, distribute the predicate. 3. Whatever is universally affirmed or denied respecting any term distributed, may be equally affirmed or denied respecting everything contained under that term: thus, if anything is affirmed or denied universally respecting "animal," it may be equally affirmed or denied of any animal; of "man," "brute,” "Alexander," "Bucephalus." This rule is generally expressed thus, "Dictum de omni et de nullo." The converse of a proposition is made by interchanging the subject and the predicate. In an affirmative proposition, the predicate enters partially; in a negative proposition, it enters wholly. Hence the converse of a true proposition is not necessarily true. For instance, it is true that "all horses are animals;" but it is not true that "all animals are horses." The first proposition here is affirmative, in which we spoke of "all horses," but not of "all animals." Hence in the converse, we are not entitled to speak of "all animals," but only of 66 some animals." The assertion that "all horses are animals," does not imply that all, but only some animals are horses. These remarks on propositions may be illustrated by diagrams. Take the example, "Every horse is an animal." If we suppose all horses enclosed in a triangle, and all animals in a circle, then the preceding assertion, if true, would require that the whole triangle be contained in the circle. Thus : Here the whole of the horses are spoken of; hence the whole of the triangle is within the circle. But there may be other animals besides horses; therefore the triangle does not occupy the whole of the circle. If we convert the original proposition, in which we did not speak of all "animals," but only of a part of them, we must limit the term "animals" by prefixing the word some;" and we see in the diagram that some of the circle coincides with the triangle, whilst all the triangle coincides with a part of the circle. If we Take the proposition, "Some islands are fertile." enclose all the islands in a triangle, and all places that are fertile in a circle, a portion only of the triangle is asserted to be within the circle. Thus : On the right margin, and on the left, the triangle is within the circle; or the whole is contained in it. As the predicate "fertile" is not taken in its whole extent, we must prefix the word "some" if we would convert the proposition. If " some islands are fertile," then "some fertile places are islands." If some of the triangle coincides with the circle, then some of the circle coincides with the triangle. Take the proposition, "No tyrants are happy." If you enclose all tyrants in a triangle, and all the men who are happy in a circle, the triangle will be wholly outside of the circle. Thus : Here the whole of the happy are referred to, as well as the whole of the tyrants. It is a negative pro О position, which may be converted without limiting the terms. If "no tyrants are happy," we are not merely entitled to say, "Some happy men are not tyrants," but "No happy men are tyrants." None of the triangle coincides with the circle, and therefore none of the circle coincides with the triangle. Lastly, Take the proposition, "Some islands are not fertile." Enclose the islands in a triangle, and the fertile places in a circle; then, at least a portion of the triangle must be outside the circle. Thus : But the proposition does not declare what proportion of the islands is unfertile, and what the reverse; nor does 66 some men are not winged animals," we must place not only part, but the whole of the triangle comprising the human race, outside of the circle enclosing winged animals; for we know, not from this proposition, but from other sources of knowledge, that no men are winged creatures. CHAPTER III. OF THE AFFECTIONS OF PROPOSITIONS. We now proceed to consider the Affections, or relations of propositions, which is that property by which they undergo various mutual changes. It must be remembered that a proposition is either universal or particular according to its quantity; and affirmative or negative according to its quality; and that these are denoted, A, universal affirmative; E, universal negative; I, particular affirmative; and O, particular negative. These four classes may be exemplified thus :— A, Every vine is a tree; E, No vine is a tree. O, Some vine is not a tree. Any given subject and predicate may thus form four dis tinct propositions; and these may undergo various changes by which one proposition may be substituted for another. A knowledge of these changes is of considerable importance in all kinds of argumentation. Of these the following are to be noticed-Subalternation, Conversion, and Opposition. SECTION I. Of Subalternation. Subalternation is the substituting a particular proposition for a universal, when they agree in quality; thus, A, All men are mortal; Or thus, I, Some men are mortal. O, Some tyrants are not happy. In subalternation the universal proposition is called the subalternans; and the particular, which is substituted for it, is called the subalterna. In this case the propositions differ in quantity alone: and the maxims laid down in reference to propositions affected in this manner are :— 1. That the truth of the particular proposition is contained in the truth of the universal. 2. The falsity of the universal in the falsity of the par ticular. 3. Whether universal or particular, they may be either both true or both false, or the one true and the other false. SECTION II. Of Conversion. Conversion of propositions is the transposing of their terms, so that the subject is made the predicate, and the predicate the subject thus, Samson was the strongest man ; |