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from the singular, warranted either by the general analogies of nature, or by special presumptions afforded by the object matter of any real science ;—3. A formal illation of the universal from the individual, as legitimated solely by the laws of thought, and abstracted from the conditions of any particular matter.
"That the first of these, an inventive process, is beyond the sphere of a critical science, is manifest; nor has Induction, in this abusive application of the term, been ever arrogated to Logic. By logicians, however, the second and third have been confounded into one, and, under every phasis of misconception, treated as a simple and purely logical operation. Yet nothing can be clearer than that these constitute two separate acts, and that the second is not properly a logical process at all. In logic, all inference is determined ratione forma, the conclusion being necessarily implied in the very conception of the premises. In this second Induction, on the contrary, the illation is effected vi materia, on grounds not involved in the notion of its antecedent. To take, for example, Dr. Whately’s instance: The naturalist who, from the proposition-ox, sheep, deer, goat, (i. e. some) horned animals, ruminate,' infers the conclusion—all horned animals ruminate,' may be warranted in this procedure by the material probabilities of his science; but his illation is logically vi
as the parts constituting, and, therefore, necessitating the determined notion, conceived as their constituted whole. Considered, indeed, absolutely and in themselves, the whole and all the parts are identical. Relatively, however, to us, they are not; for in the order of thought, (and logic is only conversant with the laws of thought,) the whole may be conceived first, and then by mental analysis separated into its parts; or the parts may be conceived first, and then by mental synthesis collected into a whole. Logical inference is thus of two, and only of two, kinds :-it must proceed either from the whole to the parts, or from the parts to the whole; and it is only under the character of a constituted or containing whole, or of a constituting or contained part, that anything can become the term of a logical argumentation.
Before proceeding, we must, however, allude to the nature of the whole and part, about which logic is conversant. These are not real or essential existences, but creations of the mind itself, in secondary operation on the primary objects of its knowledge. Things may be conceived the same, inasmuch as they are conceived the subjects of the same attribute, or collection of attributes, (i. e. of the same nature :) inasmuch as they are conceived the same, they must be conceived as the parts constituent of, and contained under, a whole : and a
they are conceived the same, only as they are conceived to be the subjects of the same nature, this common nature must be convertible with that whole. A logical or universal whole is called a genus when its parts are also containing wholes or species; a species when its parts are only contained parts or individuals.
'Such being the nature and relations of a logical whole and parts, it is manifest what must be the conditions under which the two kinds of logical inference are possible. The one of these, the process from the whole to the parts, is Deductive reasoning, (or Syllogism proper;) the other, the process from the parts to the whole, is Inductive reasoning. The former is governed by the rule—What belongs (or does not belong) to the containing whole, belongs (or does not belong) to each and all of the contained parts. The latter by the rule—What belongs (or does not belong) to all the constituent parts, belongs (or does not belong) to the constituted whole. These rules exclusively determine all formal inference; whatever transcends or violates them, transcends or violates logic. Both are equally absolute. It would be not less illegal to infer by the Deductive syllogism an attribute, belonging to the whole, of something it was not conceived to contain as a part; than by the Inductive, to conclude of the whole, what is not conceived as a predicate of all its
constituent parts. In either case, the consequent is not thought as determined by the antecedent;—the premises do not involve the conclusion.
• The Deductive and Inductive processes are elements of logic equally essential. Each requires the other. The former is only possible through the latter; and the latter is only valuable as realizing the possibility of the former. As our knowledge commences with the apprehension of singulars, every universal whole is consequently only a knowledge at second-hand. Deductive reasoning is thus not an original and independent pro.
The universal major proposition, out of which it developes the conclusion, is itself necessarily the conclusion of a foregone Induction, and, mediately or immediately, an inference-a collection, from individual objects of perception, and consciousness. Logic therefore, as a definite and self-sufficient science, must equally vindicate the formal purity of the synthetic illation, by which it ascends to its wholes, as the analytic illation by which it re-descends to their parts.
· Not only is the Deductive thus, in a general way, dependent for its possibility on the Inductive syllogism; the former is, what has not been observed, in principle and detail, in whole and in part, in end and in means, in perfection and imperfection, precisely an inverted counterpart of the latter. The attempts that have been made by almost every logician, except (perhaps?) Aristotle, to assimilate and even identify the two processes, by reducing the Inductive syllogism to the schematic proprieties of the Deductive-proceeding as they do on a total misconception of their analogy and differences, have contributed to involve the doctrine of Logical Induction in a cloud of error and confusion. The Inductive inference is equally independent, and, though far less complex, equally worthy of analysis, as the Deductive; it is governed by its own laws; and, if judged aright, must be estimated by its own standard. The correlation of the two processes is best exemplified by employing the same symbols in our ascent though an Inductive, and our re-descent through a Deductive syllogism.