XVI. LECT. posed in the expression. You will, hereafter, find that the sumption is not always the proposition which The mere stands first in the enunciation, as the conclusion is not order of does not the sump sumption ing. enunciation always the proposition which stands last. Such transconstitute positions are, however, only external accidents, and tion or sub- the mere order in which the premises and conclusion in a reason of a syllogism are enounced, no more changes their nature and their necessary relation to each other, than does the mere order in which the grammatical parts of a sentence are expressed, alter their essential character and reciprocal dependence. In the phrases vir bonus and bonus vir,—in both, the vir is a substantive and the bonus an adjective. In the sentence variously enounced, -Alexander Darium vicit, - Alexander vicit Darium, Darium Alexander vicit,—Darium vicit Alexander,—Vicit Alexander Darium,—Vicit Darium Alexander :-in these, a difference of order may denote a difference of the interest we feel in the various constituent notions, but no difference of their What truly grammatical or logical relations. It is the same with the sump- syllogisms. The mere order of enunciation does not subsump change a sumption into a subsumption, nor a subreasoning. sumption into a sumption. It is their essential relation and correlation in thought which constitutes the one proposition a major, and the other a minor premise. If the former precede the latter in the expression of the reasoning, the syllogism is technically regular; if the latter precede the former, it is technically irregular or transposed. This, however, as you will hereafter more fully see, has not been attended to by logicians, and in consequence of their looking away from the internal and necessary consecution of the premises to their merely external and accidental arrangement, the science has been deformed and per constitutes tion and tion in a XVI. plexed by the recognition of a multitude of different LECT. forms, as real and distinct, which exist only, and are only distinguished, by certain fortuitous accidents of expression. This being understood, you will not marvel at the rule in regard to the quantity of sumptions in extensive syllogisms, (which, however, I limited to those that were regularly and fully expressed),—that it must be definite. Nor will you marvel at the counter canon in regard to the quality of sumptions in intensive syllogisms, that it must be affirmative." The necessity of the last rule is equally manifest as that of the preceding. It is :-The conclusion must Third Rule. correspond in quantity with the subsumption, and in quality with the sumption. "This rule is otherwise enounced by logicians :-The conclusion must always follow the weaker or worser part, the negative and the particular being held to be weaker or worser in relation to the affirmative and universal. The conclusion, in extensive categoricals (with which we are at present occupied) is made up of the minor term, as subject, and of the major term, as predicate. Now as the relation of these two terms to each other is determined by their relation to the middle term, and as the middle term is compared with the major term in the sumption; it follows that the major term must hold the same relation to the minor in the conclusion which it held to the middle in the sumption. If then the sumption is affirmative, so likewise must be the conclusion; on the other hand, if the sumption be negative, so likewise must be the conclusion. In the subsumption, the minor term is compared with the a [See Bachmann, Logik, § 124, pp. 192, 194, Anm. 3; Drobisch, Logik, § 73, p. 65, §§ 42, 44, pp. 34, 36; Schulze, Logik, § 79, p. 114; Krug, Logik, § 82, p. 249; Cf. § XVI. LECT. 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 a Krug, Logik, § 80, p. 250-51.-ED. LECTURE XVII. STOICHEIOLOGY. SECT. II.-OF THE PRODUCTS OF THOUGHT. III.-DOCTRINE OF REASONINGS. SYLLOGISMS.-THEIR DIVISIONS ACCORDING TO A. SIMPLE.- -CATEGORICAL-II. DEDUCTIVE IN COMPRE- XVII. tion. IN 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 XVII. LECT. proximately applied to the two forms of Deductive Categoricals, determined by the two quantities of 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 Intensive Deductive We have now, therefore, next to consider into what Categorical rules the law of Intensive or Comprehensive Syllogism Syllogism. 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 |