XVI.

LECT. subsumption, the minor term is compared with the middle; that is, the minor is affirmed as under the middle. In the conclusion, the major term cannot, therefore, be predicated of more things than were affirmed as under the middle term in the subsumption. Is the subsumption, therefore, universal, so likewise must be the conclusion; on the contrary, is the former particular, so likewise must be the latter.""

a Krug, Logik, § 80, p. 250-1.-ED.

SECT. II.-OF THE PRODUCTS OF THOUGHT.

III. DOCTRINE OF REASONINGS.

SYLLOGISMS.-THEIR DIVISIONS ACCORDING TO

INTERNAL FORM.

A. SIMPLE.- -CATEGORICAL-II. DEDUCTIVE IN COMPRE-
HENSION-III. INDUCTIVE IN EXTENSION AND COM-
PREHENSION.-B. CONDITIONAL.-DISJUNCTIVE.

XVII.

tion.

IN my last Lecture, after terminating the considera- LECT. tion of the constituent elements of the Categorical Syllogism in general, whether in the quantity of Com- Recapitulaprehension or of Extension, I stated the subdivision of Categorical Syllogism into Deductive and Inductive,—a division determined by the difference of reasoning from the whole to the parts, or from the parts to the whole. Of these, taking the former,-the Deductive, first into consideration, I was occupied, during the remainder of the Lecture, in giving a view of the laws which, in their higher or lower universality, -in their remoter or more proximate application, govern the legitimacy and regularity of Deductive Categorical Syllogisms. Of these laws, the highest are the axioms of Identity and Contradiction, by which all Categorical Syllogisms are controlled. These, when proximately applied to the two forms of Deductive Categoricals, determined by the two quantities of

XVII.

LECT. Comprehension and Extension, constitute two canons, -the canon of the Intensive Syllogism being,-What belongs to the predicate belongs also to the subject,what is repugnant to the predicate is repugnant also to the subject;—the canon of the Extensive Syllogism being, What belongs to the genus belongs also to the species and individual,—what is repugnant to the genus is repugnant also to the species and individual. Each of these, however, in its more proximate application, is still further developed into a plurality of more explicit rules. In reference to Extensive Syllogism, the general law, or the Dictum de Omni et de Nullo, (as it is technically called), is evolved into a series of rules, which have been multiplied to twelve, are usually recalled to six, but which, throwing out of account irregular and imperfect syllogism, may be conveniently reduced to three. These are, I. An Extensive Categorical Deductive Syllogism must have three, and only three, terms,-constituting three, and only three, propositions. II. The sumption must in quantity be definite, (i.e. universal or singular); the subsumption must in quality be affirmative. III. The conclusion must correspond in quantity with the subsumption, and in quality with the sumption. The Lecture concluded with an explanation of these rules in detail.

2. The In

tensive

Syllogism.

We have now, therefore, next to consider into what Categorical rules the law of Intensive or Comprehensive Syllogism Deductive is developed, in its more proximate application. Now, as the intensive and extensive syllogisms are always the counterparts of each other, the proximate rules of the two forms must, consequently, be either precisely the same, or precisely the converse of each other. Accordingly, taking the three rules of extensive syllogisms, we find that the first law is also, without dif

XVII.

ference, a rule of intensive syllogisms. But the second LECT. and third, to maintain their essential identity, must be externally converted; for to change an extensive syllogism into an intensive, we must transpose the order or subordination of the two premises, and reverse the reciprocal relation of the terms. The three general rules of an Intensive Categorical Deductive Syllogism will, therefore, stand as follows:

Rules of the

¶ LXI. An Intensive Categorical Deductive Par. LXI. Syllogism, that is, one of Depth, if regularly and Intensive fully expressed, is governed by the three follow- Deductive Syllogism. ing rules.

I. It must have three, and only three, terms, -constituting three, and only three, propositions.

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

III. The Conclusion must not exceed the Sumption in Quantity, and in Quality must agree with the Subsumption.

Categorical

tion.

In regard to the first of these rules, the rule which Explicais identical for syllogisms whether extensive or inten- First Rule. sive, it is needless to say anything; for all that I stated in regard to it under the first of these forms, is valid in regard to it under the second.

Rule.

I proceed to the second, which is,-The sumption Second must in quality be affirmative, the subsumption must in quantity be definite, (that is, universal or singular). And, here, we have to answer the question,-Why in an intensive syllogism must the sumption be affirmative in quality, the subsumption definite in quantity? Let us take the following syllogism as explicated:

LECT.
XVII.

the rules

S comprehends M;

M does not comprehend P ;

Therefore, S does not comprehend P.

Prudence comprehends virtue;

But virtue does not comprehend blameworthy;

Therefore, prudence does not comprehend blameworthy.

Here all goes on regularly. We descend from the major term prudence to the middle term virtue, and from the middle term virtue to the minor term blameworthy. But let us reverse the premises. We at once see that though there is still a discoverable meaning, it is not directly given, and that we must rectify and restore in thought what is perverse and preposterous in expression. In the previous example, the sumption is affirmative, the subsumption negative. Now let us take a negative sumption :

S does not comprehend M;

But M comprehends P.

Here there is no conclusion competent, for we can neither say S comprehends P, nor S does not comprehend P. Or to take a concrete example,

Prudence does not comprehend learning;

But learning comprehends praiseworthy.

We can draw, it is evident, no conclusion; for we can neither say, from the relation of the two propositions, that Prudence comprehends praiseworthy, nor that Prudence does not comprehend praiseworthy. Grounds of The reason why an extensive syllogism requires a regarding universal sumption, and an intensive syllogism an affirmative, and why the one requires an affirmative Extensive and the other a definite subsumption, is the following. prehensive The condition common to both syllogisms is that the Syllogisms. sumption should express a rule. But in the extensive syllogism this law is an universal rule, that is, a rule

Sumption and Subsumption in

and Com.