The second sort of Restriction is called Reduplicative, as it consists in a repetition of the restricted Term. A judge, as judge, ought never to receive presents; that is, he may receive them, like other men, on ordinary occasions, but never in connection with the performance of his official duties. Here, also, the two Judgments into which the Proposition is explicated differ in Quality.

CHAPTER VI.

THE DOCTRINE OF IMMEDIATE INFERENCE.

1. Equipollence or Infinitation. 2. Conversion. 3. Opposition and Integration.

IN

NFERENCE or Reasoning is that act of Pure Thought whereby one Judgment is derived from another, or from two others. The Judgment from which another is deduced is called the Premise; and that which is derived is called the Conclusion. If the Conclusion is drawn directly from one Premise only, without the aid either of an Intuition or another Judgment, it is said to be an Immediate Inference. Thus, from the Premise that No quadruped is rational, I know at once, or by Immediate Inference, that is, by an act of Pure Thought, that Every quadruped is irrational, and that No rational thing is a quadruped. If the Conclusion can be drawn only through the intervention of a third Judgment, in other words, if two Premises are necessary, the result is a Mediate Inference, or Syllogism.

But in either case, the act of Reasoning or Inference, whether Mediate or Immediate, is simple, being one indivisible act of mind. The Premises are considered as given, and their truth is taken for granted; the Inference is the act of deduction, or drawing out the Conclusion from the Premises, and this act is necessarily simple. If it is performed in accordance with the Laws of Pure Thought, it is apodeictic or absolutely certain, as any opposite Conclusion would be Contradictory and absurd. In respect to

their Matter, both the Premises and the Conclusion may be false; and yet the Form of Inference, or the transition from one to the other, may be intuitively true. Thus, the Mediate Inference,

Everything material is mortal;

The Soul is material;

Therefore the Soul is mortal; —

is false in each of its three Judgments. Yet its Conclusion is as correctly drawn, and the Syllogism is therefore just as valid, as in the following instance, where each of the three Judgments is true.

Everything material is divisible;
Gold is material;

Therefore Gold is divisible.

Hence, the material truth of the Conclusion depends upon the material truth of the Premises; its formal validity is the correctness of the process whereby it was deduced from the Premises. Pure Logic has to do only with the latter. Every correct step of Reasoning, considered simply as such, or in reference to its Form, is as indisputable as one of those Primary Axioms of Pure Thought on which it is based, or of which it is an application. The uncertainty or disputable character of much of what is improperly called Reasoning lies altogether in the Premises, and is referable to imperfect observation, to an improper use of words where language has become a substitute for Thought, or to overhasty generalization. But the mere process of Reasoning, irrespective of the data about which we reason, is the same in the moral and physical, as in the purely mathematical, sciences; it is equally demonstrative in all, for it is conditioned by the absolute laws of Pure Thought. The longest chain of argument is but a series or repetition of Inferences, whether Mediate or Immediate, in which the formal validity of each step, taken by itself, is intuitively perceived.

Logic, as Hamilton remarks, "is exclusively conversant about Thought strictly so denominated; and Thought proper, we have seen, is the cognition of one object of thought by another, in or under which it is mentally included; in other words, Thought is the knowledge of a thing through a Concept or General Notion, or of one Notion through another. In Thought, all that we think about is considered either as something containing, or as something contained; in other words, every process of Thought is only a cognition of the necessary relations of our Concepts. This being the case, it need not move our wonder that Logic, within its proper sphere, is of such irrefragable certainty, that, in the midst of all the revolutions of philosophical doctrines, it has stood, not only unshattered, but unshaken. In this respect, Logic and Mathematics stand alone among the sciences, and their peculiar certainty flows from the same source. Both are conversant about the relations of certain a priori forms of intelligence ;- Mathematics about the necessary forms of Imagination; Logic about the necessary forms of Understanding; - Mathematics about the relations of our representations of objects, as out of each other in space and time; Logic about the relations of our Concepts of objects, as in or under each other, that is, as in different relations respectively containing and contained. Both are thus demonstrative, or absolutely certain, sciences, only as each develops what is given,—what is given as necessary, in the mind itself. The laws of Logic are grounded on the mere possibility of a knowledge through the Concepts of the Understanding, and, through these, we know only by comprehending the many under the one. Concerning the nature of the objects delivered by the Subsidiary Faculties to the Elaborative, Logic pronounces nothing, but restricts its consideration to the laws according to which their agreement or disagreement is affirmed."

"It is of itself manifest that every science must obey the laws of Logic. If it does not, such pretended science is not founded on reflection, and is only an irrational absurdity. All Inference, evolution, concatenation, is conducted on logical principles, - principles which are ever valid, ever imperative, ever the same. But an extension of any science through Logic is absolutely impossible; for by conforming to logical canons, we acquire no knowledge, receive nothing new, but are only enabled to render what is already obtained more intelligible, by analysis and arrangement. Logic is only the negative condition of truth. To attempt by a mere logical knowledge to amplify a science, is an absurdity as great as if we should attempt, by a knowledge of the grammatical laws of a language, to discover what is written in this language, without a perusal of the several writings themselves. But though Logic cannot extend, cannot amplify, a science by the discovery of new facts, it is not to be supposed that it does not contribute to the progress of science. The progress of the sciences consists not merely in the accumulation of new matter, but likewise in the detection of the relations subsisting among the materials accumulated; and the reflective abstraction by which this is effected must not only follow the laws of Logic, but is most powerfully cultivated by the habits of logical study."

Aristotle has defined Inference as "a thought or proposition in which, from something laid down and admitted, something distinct from what we have laid down follows of necessity." But this definition, though it describes the Syllogism accurately, seems at first to be inapplicable to Immediate Inference, in which, as there is only one premise, and as the act of Pure Thought through which we reason cannot add any new Matter (that is, any new Intuition or Concept), it would appear that the Conclusion cannot contain anything distinct from what has already been laid down.