syllogism, we come next to consider in how many ways three propositions can be constructed out of extremes, that is, out of the minor and major terms which are to form a conclusion when we reach it, and the middle term by which we propose to reach it. Now, disregarding the laws concerning the quality and quantity of propositions, which laws determine what forms are to be accepted as legitimate syllogisms, and what are not, we have no fewer than 256 of these triads of propositions, out of which, only 19, by virtue of the laws referred to, will be legitimate syllogisms; that is, syllogisms, which the dictum of Aristotle, referred to as their axiom, will be found to warrant. To make this understood by our scholar, the technical expedients in the doctrine of the formal syllogism, depending on the quality and quantity of propositions, and the relative situation of the three terms in the premises of a syllogism, must be further explained.

5. Propositions, in the doctrine of formal logic, are of four kinds; 1. Universal affirmative, signified by the letter A ; as, "Every man is mortal;" "Every mare is a horse:" Universal negative, signified by the letter E; as, "No man is sinless;" "No goose is a swan :" Particular affirmative, signified by the letter I; as, "Some men are rogues :" Particular negative, signified by the letter O; as, "Some men are not rogues." These varieties of quality and quantity in the propositions, produce, when the propositions are formed into syllogisms, what are called the different moods of the syllogisms. Now the four symbols, A, E, I, O, and consequently the sorts of propositions that answer to them, can be varied by threes in 64 ways, so that we have 64 triads of propositions without any change of the relative situation of major, minor, and middle terms in each triad; which situation is this, that the middle term is subjected in the major premise, and predicated in the minor one; and, of course, the minor term, by its name, (see the previous section) is the subject of the conclusion, as the major term is its predicate. When, in forming a syllogism, the three terms are thus disposed relatively to each other, the syllogism is said to be in the first figure. There are three other figures. In what is called the second figure, the middle term is predicated in both premises; in what is called the third figure, it is subjected in both premises; in what is called the fourth figure, it is predicated in the major premise, and subjected in

the minor. And as in the first figure, we can have 64 triads of propositions, making up apparent syllogisms of so many different moods, we can, in all the figures, have four times 64, that is, as already stated, 256. But the laws of the syllogism exclude in the first figure all but four moods, A A A; EAE; A II; and EIO: in the second figure all but four, E A E; A EE; EIO; and A O O: in the third figure, all but six, A AI; IAI; AII; E AO; O AO; and EIO: and in the fourth figure, all but five, A A I; AEE; IAI; E A O; and E IO:-thus leaving, as above stated, out of 256, only 19 forms which are legitimate syllogisms; that is, which afford the demonstration proposed by the science.

6. In order that the nineteen legitimate forms of syllogism may be remembered by appropriate names, the symbolic letters of each are formed with consonants into words, otherwise meaningless,* and the words are put together so as to exhibit the following imitation of Latin verse:

Fig. 1. BarbarA, CElArEnt, dArII, fErIoque prioris.
Fig. 2. CESARE, CAMEstres, festino, baroko, secundæ.
Fig. 3.Tertia, darApti, disAmis, datisi, fElapton,

Bokardo, feriso, habet: quarta insuper addit Fig. 4. BrAmAntip, camEnEs, dimaris, fEsapo, frEsIson. Hence, for example, to say of a syllogism that it is in barbara, is to say that it is in the first figure, with a universal affirmative conclusion arising out of universal affirmative premises to say that it is in camestres, is to say that it is in the second figure, with a universal negative conclusion arising out of a universal affirmative major premise, and a universal negative minor premise:‡ to say that it is in fresison, is to say that it is in the fourth figure, with a particular negative conclusion arising out of a universal negative major premise, and a particular affirmative minor premise.§-It is to be

*There is a significant purpose in the added consonants, relating to the conversion of syllogisms; but considering the whole business to be mere trifling, we may be excused from a further detail.

As, "Every man is mortal; every king is a man; therefore every

king," &c.

As, "Every true philosopher is one who counts virtue a good in itself; no advocate of pleasure is one who accounts, &c., therefore, no advocate of pleasure is a true philosopher."

SAs, "No fools are thoughtful; some men are thoughtful; therefore,

some men are not fools."

remarked, before leaving this account of the formal syllogism, that a syllogism in any of the last three figures, can, under the safeguard of certain rules, be converted into a syllogism of the first, which is deemed the only perfect figure. For instance, the syllogism in the fourth figure exemplified in the third note below, can be converted into Ferio; as, "Thoughtful men are not fools: Some men are thoughtful: Therefore, some men are not fools." The fourth figure does not appear in Aristotle, but was added by his followers.

Recapitulation of the Leading Principles in this Manual of Logic; as opposed to the Principles on which (as explained in the foregoing Account) the Syllogism of Formal Logic is

based.

7. In our logic, we presume not to inquire, much less to demonstrate, how or why an intellection takes place. We esteem it a fact, which can no more be accounted for than the fact of a sensation; though we estimate these facts as things in their nature different: we deem, for instance, that a sensation is one thing, and that the knowledge of a sensation, the result of intellection, is another.

8. We deny that, in using words for logical purposes, three operations of the mind are concerned. We affirm that the operation is always the same, however it may be signified outwardly, that is, whether by single terms, or by complex terms, or by propositions, or by propositions united into forms of greater extent and complexity. We affirm, in short, that the difference between terms, and proposition, and syllogism, is a mere grammatical difference, having no foundation in any correspondent original processes of the mind, but being means sometimes convenient in one shape, sometimes in another, for fixing, or for developing the knowledge we have acquired, or for presenting it to another mind. For, in our doctrine, a single term, quite as much as a proposition, and quite as much as a syllogism, is an indication of knowledge arising out of premises. Thus red expresses our knowledge of a colour; which knowledge is the fact of our being aware of one sensation relatively to others of its kind; that is to say, we know what is red, because we know what it is not to be red; nor could we know the one, unless at the same time we knew

the other. That of which we have knowledge, and that by which we know it, are the premises, the consequent knowledge is the conclusion expressed by this term. In a proposition, there is the same fact, with this only difference, that the premises are indicated as well as the resulting knowledge, though not indicated so distinctly as by the syllogism. In this last, the two premises and the conclusion are stated in so many sentences of independent grammatical construction; and the syllogism is therefore the most explicit form in which we can lay down what at any moment we know.

9. But in speaking thus of the syllogism, we do not mean the syllogism which operates by extremes and middle term, under the doctrine of affirmation and negation. With us,

affirmation and negation belong to Grammar, not to Logic. No man, and every man, are equally signs of positive knowledge, in the one case arising out of the premises no and man, in the other out of the premises every and man. The same may be said of the knowledge expressed by is-not: it is positive knowledge, quite as much as that expressed by is. In all cases the resulting expression is one expression with one meaning-Such is the datum of our syllogism, such the related argument. But these are no sooner expressed than the conclusion unites them and makes them one; so that now the whole syllogism is one expression with one meaning,—an expression of the knowledge attained or developed; just as a single term is such an expression; just as a complex term is such an expression; just as a proposition is such an expression.

10. With regard to the Categories, the GENERAL HEADS of all we know, they seem at present to have lost their reputation even with the Aristotelians themselves.* We may indeed fairly ask why they are so many, or why they are not more. As to one of them, RELATION, we affirm this to be included in all the others. A substance, whatever it be, is known, because we are aware of its relation to other substances; so of a quality; so of each of the other heads. We ask also, as to these general heads, or the special heads under them, or the singulars under these,—what is meant by calling them ideas. If by ideas is meant the knowledge which they signify,

"The catalogue certainly is but a very crude one." Whately's Logic, Book IV. ch. II. § 1 (a foot note).

our only objection to the word is, that custom has rendered it, for this meaning, a vague and indistinct expression :-if other is meant than knowledge of the things to which the term can be applied, we object to its application in this way, till it can be shown what it is that words can signify other than things real, things ideal, (both of which come under the common term of things physical,) and things metaphysical: the words in all three cases being immediately significant of knowledge, which, in its nature, is distinct from the things comprehended by it; that is to say, words are, in all cases, immediately significant of what is metaphysical, but can next be applied as names to things real, or to things ideal, or to things which are neither the one nor the other, but are the relations under which those things suggest themselves to the human understanding, which relations we have the power to entertain apart from the things.

11. The science of the formal syllogism proposes a demonstration of its conclusions. Our doctrine is, that we cannot come to a false conclusion in deductive reasoning except by depending on the forms which that syllogism provides, and then neglecting its rules. The science, then, is necessary only to those who use its forms: to propose it for others, is to propose spectacles for people who, without them, cannot but see clearly, or crutches for people who, without them, cannot but walk well. The use of the syllogism in our logic, is, not to test the validity of conclusions, but to spread out our premises, that so we may be induced to consider on what grounds we have assumed them. In a word, our logic leads us always back to what we have acquired, or what we presume we have acquired, in order that, if our knowledge is not sound, we may supply its deficiencies, or set it altogether aside.