XV.

LECT. rical proposition. The same is, likewise, the case in regard to the conclusion, and, therefore, we can no more look towards the conclusion for a determination of the diversity of syllogism than towards the subsumption. We have thus only to inquire in regard to the various possible kinds of major proposition."

Syllogisms

to be divided

the charac

sumptions

tion between

premises

and conclusion.

Now as all sumptions are judgments, and as we according to have already found that the most general division of ter of their judgments, next to the primary distinction of intenand the law sive and extensive, is into simple and conditional, this regulating the connec division of judgments, which, when developed, affords the classes of categorical, disjunctive, hypothetical, and hypothetico-disjunctive propositions, will furnish us with all the possible differences of major premises. "It is also manifest that in any of these aforesaid propositions, (categorical, disjunctive, hypothetical, and hypothetico-disjunctive,) a decision of the question, —which of two repugnant predicates belongs to a certain subject,-can be obtained according to a universal and necessary law. In a categorical sumption, this is competent through the laws of Identity and Contradiction; for what belongs or does not belong to the superordinate notion, belongs or does not belong to the subordinate. In disjunctive sumptions, this is competent through the law of Excluded Middle; since of all the opposite determinations one alone belongs to the object; so that if one is affirmed the others must be, conjunctively, denied, and if one is denied the others must be, disjunctively at least, affirmed. In hypothetical sumptions, this is competent through the law of Reason and Consequent; for where the reason is, there must be the consequent, and where a Esser, Logik, § 85.-ED.

There LECT.

the consequent is, there must be the reason.
are thus obtained three or four great classes of Syllo-
gisms, whose essential characteristics I shall comprise
in the following paragraph

XV.

Second

the grand divi

sion of Syl

the logisms

according to

gulating the

¶ LVI. Syllogisms are divided into different Par. LVI. classes, according as the connection between premises and conclusion is determined by different fundamental laws, 1o, Of Identity and the law reContradiction; 2°, Of Excluded Middle; 3°, Of inference. Reason and Consequent; these several determinations affording the three classes of Categorical, of Disjunctive, and of Hypothetical Syllogisms. To these may be added a fourth class, the Hypothetico-disjunctive or Dilemmatic Syllogism, which is determined by the two last laws in combination.

of the four

syllogism.

Before proceeding to a consideration of these seve- Examples ral syllogisms in detail, I shall, first of all, give you species of examples of the four species together, in order that you may have, while treating of each, at least a general notion of their differences and similarity.

1.-OF A CATEGORICAL SYLLOGISM.

Sumption..........All matter is created;

Subsumption......But the heavenly bodies are material;
Conclusion........Therefore, the heavenly bodies are created.

a See Esser, Logik, § 86, p. 161. This classification of syllogisms cannot be regarded as expressing the Author's final view; according to which, as before observed, the principle of Reason and Consequent is not admitted as a law of thought. See above, p. 86, note a. In a note by Sir W. Hamilton, appended to Mr Baynes's Essay on the New An

alytic of Logical Forms, the Author's
later view is expressed as follows:
"All Mediate inference is one-
that incorrectly called Categorical;
for the Conjunctive and Disjunctive
forms of Hypothetical reasoning are
reducible to immediate inferences."
Compare Discussions, p. 651 et seq.
-ED.

1. Categorical.

2. OF A DISJUNCTIVE SYLLOGISM.

Sumption......... The hope of immortality is either a rational expectation or an illusion;

Subsumption.....But the hope of immortality is a rational expecta

tion;

LECTURE XVI.

STOICHEIOLOGY.

SECTION II.-OF THE PRODUCTS OF THOUGHT.

XVI.

Recapitula

IN our last Lecture, I entered on the Division of LECT. Syllogisms. I first stated to you the principles on which this division must proceed; I then explained tion. the nature of the first great distribution of Reasonings into those of Intensive and those of Extensive Quantity; and, thereafter, that of the second great distribution of reasonings into Simple and Conditional, the Simple containing a single species,-the Categorical; the Conditional comprising three species, -the Disjunctive, the Hypothetical, and Hypotheticodisjunctive." These four species, I showed you, were severally determined by different fundamental Laws of Thought: the Categorical reposing on the laws of Identity and Contradiction; the Disjunctive on the law of Excluded Middle; the Hypothetical on the law of Reason and Consequent; and the Hypothetico-disjunctive on the laws of Excluded Middle and Reason and Consequent in combination.

a Compare above, p. 236.-ED.

LECT.

XVI.

Syllogism.

The Cate

gorical.

I now go on to the special consideration of the first of these classes of Syllogism-viz. the Syllogism 1. Simple which has been denominated Categorical. And in regard to the meaning and history of the term categorical, it will not be necessary to say anything in addition to what I have already stated in speaking of The term judgments." As used originally by Aristotle, the term categorical meant merely affirmative, and was opposed to negative. By Theophrastus it was employed in the sense of absolute,-simple,-direct, and as opposed to conditional; and in this signification it has continued to be employed by all subsequent logicians, without their having been aware that Aristotle never employed it in the meaning in which alone they used it.

Categorical.

Par. LVII. The Categorical Syllogism,what.

¶ LVII. A Categorical Syllogism is a reasoning whose form is determined by the laws of Identity and Contradiction, and whose sumption is thus a categorical proposition. In a Categorical Syllogism there are three principal notions, holding to each other the relation of whole and part ; and these are so combined together, that they constitute three propositions, in which each principal notion occurs twice. These notions are called Terms (termini, opoi), and according as the notion is the greatest, the greater, or the least, it is called the Major, the Middle, or the Minor Term. The Middle Term is called the Argument (argumentum, λóyos, Tíστis); the Major and

a See above, p. 234 et seq.-Ed.

8 [On principle of name of Major and Minor terms, see Alex. Aphrodisiensis, In An. Prior., L. i. cc. iv. v.; Philoponus, In An. Prior., L. i. f. 23 b; Fonseca, Instit. Dialect., L.

vi. c. xii. p. 343; Hurtado de Mendoza, p. 469.] [Disput. Philosophi ca, t. i.; Disp. Logicæ, d. x. § 50 et seq. Tolosa, 1617. See also Discussions, p. 666 et seq.-ED.]