XVIII.

LECT. doctrines are necessary; and these are only necessary inasmuch as their individual applications are necessary; if Logic, therefore, as a whole be not necessary, the necessity of the parts, which constitute, determine, and comprehend that whole, is subverted. In one relation, therefore, reason and consequent are as the whole and a contained part, in another, as all the parts and the constituted or comprised whole. But in both relations, the reason,- the determining notion, is thought as involving in it the existence of the consequent or determined notion. Thus, in one point of view, the genus is the determining notion, or reason, out of which are evolved, as consequents, the species and individual; in another, the individual is the determining notion or reason, out of which, as consequents, are evolved the species and genus." In like manner, if we regard the subject as that in which the attributes inhere, in this view the subject is the reason, that is, the whole, of which the attributes are a part; whereas if we regard the attributes as the modes through which alone the subject can exist, in this view the attributes are the reason, that is, the whole, of which the subject is a part. In a word, whatever we think as conditioned, we think as contained by something else, that is, either as a part, or as a constituted whole; whatever we think as conditioning, we think either as a containing whole, or as a sum of constituting parts. What, therefore, the sumption of an hypothetical syllogism denotes, is simply this:— If A, a notion conceived as conditioning, and, therefore, as involving B, exist, then B also is necessarily conceived to exist, inasmuch as it is conceived as fully

a This is expressly allowed by Aristotle, Metaph., iv. 25, and is

quoted from him by Sir W. Hamilton himself, Discussions, p. 173.—Ed.

XVIII.

conditioned by, or as involved in, A. I am afraid LECT. that what I have now said may not be found to have removed the difficulty; but if it suggest to you a train of reflection which may lead you to a solution of the difficulty by your own effort, it will have done better.

So much for Hypothetico-disjunctive syllogisms, the last of the four classes determined by the internal form of reasoning. In these four syllogisms,-the Categorical, the Disjunctive, the Hypothetical, and the Hypothetico-disjunctive, all that they exhibit is conformable to the necessary laws of thought, and they are each distinguished from the other by their essential nature; for their sumptions, as judgments, present characters fundamentally different, and from the sumption, as a general rule, the validity of syllogisms primarily and principally depends.

LECT.

Syllogisms,

LECTURE XIX.

STOICHEIOLOGY.

SECTION II.—OF THE PRODUCTS OF THOUGHT.

III. DOCTRINE OF REASONINGS.

SYLLOGISMS.-THEIR DIVISIONS ACCORDING TO
EXTERNAL FORM.

A. COMPLEX,- -EPICHEIREMA AND SORITES.

IN our treatment of Syllogisms, we have hitherto XIX. taken note only of the Internal, or Essential Form their Ex. of Reasoning. But besides this internal or essential ternalForm. form there is another, an External or Accidental Form; and as the former was contained in the reciprocal relations of the constituent parts of the syllogism, as determined by the nature of the thinking subject itself, so the latter is contained in the outer expression or enouncement of the same parts, whereby the terms and propositions are variously affected in respect of their number, position, and order of consecution. The varieties of Syllogism arising from their external form may, I think, be conveniently reduced to the three heads expressed in the following paragraph:

Par. LXVIII.
Division of
Syllogisms
according
to External
Form.

¶ LXVIII. Syllogisms, in respect of their External Form, admit of a threefold modification. For while, as pure, they are at once Simple, and Complete, and Regular, so, as qualified, they are

XIX.

either Complex, or Incomplete, or Irregular: LECT.
the two former of these modifications regarding
the number of their parts, as apparently either
too many or too few; the last regarding the in-
verted order in which these parts are enounced.

tion.

I shall consider these several divisions in their order; Explicaand, first, of the syllogisms which vary from the simple A. Complex form of reasoning by their apparent complexity.

Syllogisms.

syllogisms

other.

But before touching on the varieties of syllogism Relation of afforded by their complexity of composition, it may to each be proper to premise a few words in regard to the relation of syllogisms to each other. "Every syllogism may be considered as absolute and independent, inasmuch as it always contains a complete and inclusive series of thought. But a syllogism may also stand to other syllogisms in such a relation that, along with these correlative syllogisms, it makes up a greater or lesser series of thoughts, all holding to each other the dependence of antecedent and consequent. And such a reciprocal dependence of syllogisms becomes necessary, when one or other of the predicates of the principal syllogism is destitute of complete certainty, and when this certainty must be established through one or more correlative syllogisms.' 'A syllogism, viewed Classes and as an isolated and independent whole, is called a of related Monosyllogism (monosyllogismus), that is, a single Monosylloreasoning; whereas, a series of correlative syllogisms, following each other in the reciprocal relation of antecedent and consequent, is called a Polysyllogism Polysyllo(polysyllogismus), that is, a multiplex or composite Chain of reasoning, and may likewise be denominated a Chain of Reasoning (series syllogistica). Such a chain,———

a Esser, Logik, § 104.-ED.

designations

syllogisms.

gism.

gism, or

Reasoning.

LECT.
XIX.

lytic and

Prosyllogism.

gism.

such a series, may, however, have such an order of dependence, that either each successive syllogism is the reason of that which preceded, or the preceding This Ana syllogism is the reason of that which follows. In the Synthetic. former case, we conclude analytically or regressively; in the second, synthetically or progressively. That syllogism in the series which contains the reason of the premise of another, is called a Prosyllogism (prosyllogismus); and that syllogism which contains the Episyllo consequent of another, is called an Episyllogism (episyllogismus). Every Chain of Reasoning must, therefore, be made up both of Prosyllogisms and of Episyllogisms."" When the series is composed of more than two syllogisms, the same syllogism may, in different relations, be at once a prosyllogism and an episyllogism; and that reasoning which contains the primary or highest reason is alone exclusively a prosyllogism, as that reasoning which enounces the last or lowest consequent is alone exclusively an episyllogism. But this concatenation of syllogisms, as antecedents and consequents, may be either manifest, or occult, according as the plurality of syllogisms may either be openly displayed, or as it may appear only as a single syllogism. The polysyllogism is, therefore, likewise either manifest or occult. The occult polysyllogism, with which alone we are at present concerned, consists either of partly complete and partly abbreviated syllogisms, or of syllogisms all' equally abbreviated. In the former case, there emerges the complex syllogism called Epicheirema; in the latter, the complex syllogism called Sorites." Of these in their order.

a Krug, Logik, § 111.-ED.

Reusch, Systema Logicum, § 578, p.

B Esser, Logik, § 104.-ED. [Cf. 664, Ienæ, 1741.]