XVI.

LECT. its part and on the other, looking from the parts to their whole, to say,-What makes up all the parts constitutes the whole; and what does not make up all the parts does not constitute the whole. Now, these two applications of the principles of Identity and Contradiction, as we look from one term of the relation of whole and part, or from the other, determine two different kinds of reasoning. For if we reason downwards, from a containing whole to a contained part, we shall have one sort of reasoning which is called the Deductive; whereas, if we reason upwards, from the constituent parts to a constituted whole, we shall have another sort of reasoning, which is called the Inductive. This I shall briefly express in the following paragraph.

Par. LVIII. Categorical Syllogisms divided into Deductive and Inductive.

I. Deductive Cate

gorical Syllogisms.

¶ LVIII. Categorical Syllogisms are Deductive, if, on the principles of Identity and Contradiction, we reason downwards, from a containing whole to a contained part; they are Inductive, if, on these principles, we reason upwards, from the constituent parts to a constituted whole.

This is sufficient at present to afford you a general conception of the difference of Deductive and Inductive Categoricals. The difference of these two kinds of reasoning will be properly explained, when, after having expounded the nature of the former, we proceed to consider the nature of the latter. We shall now, therefore, consider the character of the deductive cess, the process which has been principally and certainly most successfully analysed by logicians; for though their treatment of deductive reasoning has been one-sided and imperfect, it is not positively

pro

XVI.

erroneous; whereas their analysis of the inductive LECT. process is at once meagre and incorrect. And, first, of the proximate canons by which Deductive Categoricals are regulated.

uni- Par. LIX.

Deductive

take Categorisyllo- canons."

LIX. In Deductive Categoricals the
versal laws of Identity and Contradiction
two modified forms, according as these
gisms proceed in the quantity of Comprehen-
sion, or in that of Extension. The peculiar
canon by which Intensive Syllogisms of this
class are regulated, is,-What belongs to the
predicate belongs also to the subject; what is
repugnant to the predicate is repugnant also to the
subject. The peculiar canon by which Extensive
Syllogisms of this class are regulated, is,—What
belongs to the genus belongs to the species and
individual; what is repugnant to the genus is
repugnant to the species and individual. Or,
more briefly, What pertains to the higher class,
pertains also to the lower.

cals, their

tion.

Both these laws are enounced by Aristotle," and Explicaboth, from him, have passed into the writings of subsequent logicians. The former, as usually expressed, is,-Prædicatum prædicati est etiam prædicatum subjecti; or, Nota notæ est etiam nota rei ipsius. The latter is correspondent to what is called the Dicta de Omni et de Nullo; the Dictum de Omni, when least ambiguously expressed, being,-Quicquid de omni valet, valet etiam de quibusdam et singulis; and the Dictum de Nullo being,-Quicquid de nullo valet, nec de quibusdam nec de singulis valet. But as

a Categ., c. 3. Anal. Prior., i. 1.—ED.

XVI.

LECT. logicians have altogether overlooked the reasoning in Comprehension, they have, consequently, not perceived the proper application of the former canon; which, therefore, remained in their systems either a mere hors d'œuvre, or else was only forced into an unnatural connection with the principle of the syllogism of extension.

Connection of the pro

positions

and terms

gorical Syl

trated by sensible symbols.

Before stating to you how the preceding canons are again, in their proximate application to categorical of the Cate- syllogisms, for convenience sake, still more explicitly fogism illus- enounced in certain special rules, it will be proper to show you the method of marking the connection of the propositions and terms of a categorical syllogism by sensible symbols. Of these there are various kinds, but, as I formerly noticed, the best upon the whole, because the simplest, is that by circles." According to this method, syllogisms with affirmative and negative conclusions would be thus represented :—

Categorical

You are now prepared for the statement and illus- Proximate tration of the various proximate rules by which all Rules of categorical syllogisms are regulated. And, first, in Syllogisms. regard to these rules in relation to the reasoning of sive. Extension.

Aldrich," says Dr Whately, "has given twelve rules, which I find might be more conveniently reduced to six. No syllogism can be faulty which

a

violates none of these rules." This reduction of the syllogistic rules to six is not original to Dr Whately; but had he looked a little closer into the matter, he might have seen that the six which he and other logicians enumerate, may, without any sacrifice of precision, and with even an increase of perspicuity, be reduced to three. I shall state these in a paragraph, and then illustrate them in detail.

1. Exten

Par. LX.

¶ LX. An Extensive Categorical Syllogism, if regularly and fully expressed, is governed by The Three the three following rules :

Rules of the
Extensive
Categorical

I. It must have three, and only three, Terms, Syllogism. constituting three, and only three, Propositions.

a Elements of Logic, B. ii. c. iii. § 2, p. 85, 8th edit.-ED. VOL. I.

U

LECT.
XVI.

Illustration.
First Rule.

II. Of the premises, the Sumption must in quantity be Definite (i.e. universal or singular), and the Subsumption in quality Affirmative.

III. The Conclusion must correspond in Quantity with the Subsumption, and in Quality with the Sumption."

These three simple laws comprise all the rules which logicians lay down with so confusing a minuteness. The first is -A categorical syllogism, if regular and perfect, must have three, and only three, propositions, made up of three, and only three, terms. "The necessity of this rule is manifest from the very notion of a categorical syllogism. In a categorical syllogism the relation of two notions to each other is determined through their relation to a third; and, consequently, each must be compared once with the intermediate notion, and once with each other. It is thus manifest that there must be three, and cannot possibly be more than three, terms; and that these three terms must, in their threefold comparison, constitute three, What is pro- and only three, propositions. It is, however, to be regarded as observed, that it may often happen as if, in a valid

perly to be

a logical

term.

syllogism, there were more than three principal notions, --three terms. But, in that case, the terms or notions are only complex, and expressed by a plurality of words. Hence it is, that each several notion extant in a syllogism, and denoted by a separate word, is not on that account to be viewed as a logical term or

a Krug, Logik, § 80.-ED. [Cf. Alexander Aphrodisiensis, In An. Prior., L. I., f. 17, Ald. Derodon, Logica Restituta, p. 639 et seq. Hoffbauer, Anfangsgründe der Logik, § 317, p. 164. Bachmann, Logik, § 122,

p. 187. Esser, Logik, §§ 88, 89. Schulze, Logik, § 79. Fries, Logik, § 55, p. 224.]

B See Scheibler, Opera Logica, pars. iv., p. 516. Keckermann, Systema Logica Minus, Opera, t. i., p. 239.-ED.