CHAPTER SECOND.

OF REASONING AND OF DEDUCTIVE EVIDENCE.

SECTION I.

Doubts with respect to Locke's Distinction between the Powers of Intuition and of Reasoning.

ALTHOUGH, in treating of this branch of the Philosophy of the Mind, I have followed the example of preceding writers, so far as to speak of intuition and reasoning as two different faculties of the understanding, I am by no means satisfied that there exists between them that radical distinction which is commonly apprehended. Dr. Beattie, in his Essay on Truth, has attempted to show, that, how closely soever they may in general be connected, yet that this connexion is not necessary; insomuch, that a being may be conceived endued with the one, and at the same time destitute of the other.* Something of this kind, he remarks, takes place in dreams and in madness; in both of which states of the system, the power of reasoning appears occasionally to be retained in no inconsiderable degree, while the power of intuition is suspended or lost.

But this doctrine is liable to obvious and to insurmountable objections; and has plainly taken its rise from the vagueness of the phrase common sense, which the author employs through the whole of his argument, as synonymous with the power of intuition. Of the indissoluble connexion between this last power and that of reasoning, no other proof is necessary than the following consideration, that, "In every step which reason makes in demonstrative knowledge, there must be intuitive certainty;" a proposition which Locke has excellently

* Beattie's Essay p. 41, 2d edit.

illustrated, and which, since his time, has been acquiesced in, so far as I know, by philosophers of all descrip tions. From this proposition (which when properly interpreted, appears to me to be perfectly just) it obviously follows, that the power of reasoning presupposes the power of intuition; and, therefore, the only question about which any doubt can be entertained is, Whether the power of intuition (according to Locke's idea of it) does not also imply that of reasoning? My own opinion is decidedly, that it does; at least, when combined with the faculty of memory. In examining those processes of thought which conduct the mind by a series of consequences from premises to a conclusion, I can detect no intellectual act whatever, which the joint operation of intuition and of memory does not sufficiently explain.

Before, however, proceeding farther in this discussion, it is proper for me to observe, by way of comment on the proposition just quoted from Locke, that although, "in a complete demonstration, there must be intuitive evidence at every step," it is not to be supposed, that, in every demonstration, all the various intuitive judgments leading to the conclusion are actually presented to our thoughts. In by far the greater number of instances, we trust entirely to judgments resting on the evidence of memory; by the help of which faculty, we are enabled to connect together the most remote truths, with the very same confidence as if the one were an immediate consequence of the other. Nor does this diminish, in the smallest degree, the satisfaction we feel in following such a train of reasoning. On the contrary, nothing can be more disgusting than a demonstration where even the simplest and most obvious steps are brought forward to view; and where no appeal is made to that stock of previous knowledge which memory has identified with the operations of reason. Still, however, it is true, that it is by a continued chain of intuitive judgments, that the whole science of geometry hangs together; inasmuch as the demonstration of any one proposition virtually includes all the previous demonstrations to which it refers.

Hence it appears, that, in mathematical demonstrations, we have not, at every step, the immediate evidence of intuition, but only the evidence of memory. Every demonstration, however, may be resolved into a series of separate judgments, either formed at the moment, or remembered as the results of judgments formed at some preceding period; and it is in the arrangement and concatenation of these different judgments or media of proof, that the inventive and reasoning powers of the mathematician find so noble a field for their exercise.

With respect to these powers of judgment and of reasoning, as they are here combined, it appears to me that the results of the former may be compared to a collection of separate stones prepared by the chisel for the purposes of the builder; upon each of which stones, while lying on the ground, a person may raise himself, as upon a pedestal, to a small elevation. The same judgments, when combined into a train of reasoning, terminating in a remote conclusion, resemble the formerly unconnected blocks, when converted into the steps of a staircase leading to the summit of a tower, which would be otherwise inaccessible. In the design and execution of this staircase, much skill and invention may be displayed by the architect; but, in order to ascend it, nothing more is necessary than a repetition of the act by which the first step was gained. The fact I conceive to be somewhat analogous, in the relation between the power of judgment, and what logicians call the discursive processes of the understanding.

Mr. Locke's language, in various parts of his Essay, seems to accord with the same opinion. "Every step in reasoning," he observes, "that produces knowledge, has intuitive certainty; which, when the mind perceives, there is no more required but to remember it, to make the agreement or disagreement of the ideas, concerning which we inquire, visible and certain. This. intuitive perception of the agreement or disagreement of the intermediate ideas, in each step and progression of the demonstration, must also be carried exactly in the mind, and a man must be sure that no part is left out; which, in long deductions, and in the use of many proofs, the

memory does not always so readily and exactly retain : therefore it comes to pass, that this is more imperfect than intuitive knowledge, and men embrace often falsehood for demonstrations." *

The same doctrine is stated elsewhere by Mr. Locke, more than once in terms equally explicit; † and yet his language occasionally favors the supposition, that, in its deductive processes, the mind exhibits some modification of reason essentially distinct from intuition. The account, too, which he has given of their respective provinces, affords evidence that his notions concerning them were not sufficiently precise and settled. "When the mind," says he, "perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other, its knowledge may be called intuitive. When it cannot so bring its ideas together, as, by their immediate comparison, and, as it were, juxta-position, or application one to another, to perceive their agreement or disagreement, it is fain, by the intervention of other ideas (one or more as it happens) to discover the agreement or disagreement, which it searches; and this is that which we call reasoning." According to these definitions, supposing the equality of two lines A and B to be perceived immediately in consequence of their coincidence; the judgment of the mind is intuitive : Supposing A to coincide with B, and B with C; the relation between A and C is perceived by reasoning. Nor is this a hasty inference from Locke's accidental language. That it is perfectly agreeable to the foregoing definitions, as understood by their author, appears from the following passage, which occurs afterwards: "The principal act of ratiocination is the finding the agreement or disagreement of two ideas, one with another, by the intervention of a third. As a man, by a yard, finds two houses to be of the same length, which could not be brought together to measure their equality by juxta-position." §

*B. IV. Chap. ii. § 7. See also B. IV. Chap xvii. § 15. † B. IV. Chap. xvii. § 2. B. IV. Chap. xvii. § 4. § 14.

B. IV. Chap. ii. §§ 1 and 2.

§B. IV. Chap. xvii. § 18.

This use of the words intuition and reasoning, is surely somewhat arbitrary. The truth of mathematical axioms has always been supposed to be intuitively obvious; and the first of these, according to Euclid's enumeration, affirms, That if A be equal to B, and B to C, A and C are equal. Admitting, however, Locke's definition to be just, it only tends to confirm what has been already stated with respect to the near affinity, or rather the radical identity, of intuition and of reasoning. When the relation of equality between A and B has once been perceived, A and B are completely identified as the same mathematical quantity; and the two letters may be regarded as synonymous wherever they occur. The faculty, therefore, which perceives the relation between A and C, is the same with the faculty which perceives the relation between A and B, and between B and C.*

In farther confirmation of the same proposition, an appeal might be made to the structure of syllogisms. Is it possible to conceive an understanding so formed as to perceive the truth of the major and of the minor propositions, and yet not to perceive the force of the conclusion? The contrary must appear evident to every person who knows what a syllogism is; or rather, as in this mode of stating an argument, the mind is led from universals to particulars, it must appear evident, that in the very statement of the major proposition, the truth of the conclusion is presupposed; insomuch, that it was not without good reason Dr. Campbell hazarded the epigrammatic, yet unanswerable remark that, "there is always some radical defect in a syllogism, which is not chargeable with that species of sophism known among logicians by the name of petitio principii, or a begging of the question." +

* Dr Reid's notions, as well as those of Mr. Locke, seem to have been somewhat unsettled with respect to the precise line which separates intuition from reasoning. That the axioms of geometry are intuitive truths, he has remarked in numberless passages of his works and yet, in speaking of the application of the syllogistic theory to mathematics, he makes use of the following expression : "The simple reasoning, A is equal to B, and B to C, therefore A is equal to C,' cannot be brought into any syllogism in figure and mode."-See his Analysis of Aristotle's Logic.

† Phil. of Rhet. Vol. I. p. 174.