any other, but points out to what conditions all facts must conform, in order that they may prove other facts. To decide whether any given fact fulfils these conditions, or whether facts can be found which fulfil them in a given case, belongs exclusively to the particular art or science, or to our knowledge of the particular subject.

It is in this sense that logic is, what it was so expressively called by the schoolmen and by Bacon, ars artium; the science of science itself. All science consists of data and conclusions from those data, of proofs and what they prove: now logic points out what relations must subsist between data and whatever can be concluded from them, between proof and everything which it can prove. If there be any such indispensable relations, and if these can be precisely determined, every particular branch of science, as well as every individual in the guidance of his conduct, is bound to conform to those relations, under the penalty of making false inferences-of drawing conclusions which are not grounded in the realities of things. Whatever has at any time been concluded justly, whatever knowledge has been acquired otherwise than by immediate intuition, depended on the observance of the laws which it is the province of logic to investigate. If the conclusions are just, and the knowledge real, those laws, whether known or not, have been observed.

§ 6. We need not, therefore, seek any farther for a solution of the question, so often agitated, respecting the utility of logic. If a science of logic exists, or is capable of existing, it must be useful. If there be rules to which every mind consciously or unconsciously conforms in every instance in which it infers rightly, there seems little necessity for discussing whether a person is more likely to observe those rules, when he knows the rules, than when he is unacquainted with them.

A science may undoubtedly be brought to a certain, not inconsiderable, stage of advancement, without the application of any other logic to it than what all persons, who are said to have a sound understanding, acquire empirically in the course of their studies. Mankind judged of evidence, and often correctly, before logic was a science, or they never could have made it one. And they executed great mechanical works before they understood the laws of mechanics. But there are limits both to what mechanicians can do without principles of mechanics, and to what thinkers can do without principles of logic. A few individuals, by extraordinary genius, or by the accidental acquisition of a good set of intellectual habits, may work without principles in the same way, or nearly the same way, in which they would have worked if they had been in possession of principles. But the bulk of mankind require either to understand the theory of what they are doing, or to have rules laid down for them by those who have understood the theory. In the progress of science from its easiest to its more difficult problems, each great step in advance has usually had either as its precursor, or as its accompaniment and necessary condition, a corresponding improvement in the notions and principles of logic received among the most advanced thinkers. And if several of the more difficult sciences are still in so defective a state; if not only so little is proved, but disputation has not terminated even about the little which seemed to be so; the reason perhaps is, that men's logical notions have not yet acquired the degree of extension, or of accuracy, requisite for the estimation of the evidence proper to those particular departments of knowledge.

§ 7. Logic, then, is the science of the operations of the understanding which are subservient to the estimation of evidence: both the process | itself of advancing from known truths

to unknown, and all other intellectual | like a connected and interdependent operations in so far as auxiliary to chain of proof. If one link of an this. It includes, therefore, the opera- argument breaks, the whole drops to tion of Naming; for language is an the ground; but one step towards an instrument of thought, as well as a analysis holds good and has an indemeans of communicating our thoughts. pendent value, though we should It includes, also, Definition, and never be able to make a second. The Classification. For, the use of these results which have been obtained by operations (putting all other minds analytical chemistry are not the less than one's own out of consideration) valuable, though it should be disis to serve not only for keeping our covered that all which we now call evidences and the conclusions from simple substances are really comthem permanent and readily acces- pounds. All other things are at any sible in the memory, but for so mar- rate compounded of those elements: shalling the facts which we may at whether the elements themselves adany time be engaged in investigat- mit of decomposition, is an important ing, as to enable us to perceive more inquiry, but does not affect the cerclearly what evidence there is, and tainty of the science up to that point. to judge with fewer chances of error I shall, accordingly, attempt to whether it be sufficient. These, there- analyse the process of inference, and fore, are operations specially instru- the processes subordinate to inference, mental to the estimation of evidence, so far only as may be requisite for asand, as such, are within the province certaining the difference between a of Logic. There are other more correct and an incorrect performance elementary processes, concerned in all of those processes. The reason for thinking, such as Conception, Memory, thus limiting our design, is evident. and the like; but of these it is not It has been said by objectors to logic, necessary that Logic should take any that we do not learn to use peculiar cognizance, since they have muscles by studying their anatomy. no special connexion with the problem The fact is not quite fairly stated; of Evidence, further than that, like for if the action of any of our muscles all other problems addressed to the were vitiated by local weakness, or understanding, it presupposes them. other physical defect, a knowledge of Our object, then, will be, to attempt their anatomy might be very necesa correct analysis of the intellectual sary for effecting a cure. But we process called Reasoning or Inference, should be justly liable to the criticism and of such other mental operations involved in this objection, were we, as are intended to facilitate this as in a treatise on logic, to carry the well as, on the foundation of this analysis of the reasoning process beanalysis, and pari passu with it, to yond the point at which any inacbring together or frame a set of rules curacy which may have crept into it or canons for testing the sufficiency must become visible. In learning of any given evidence to prove any bodily exercises (to carry on the same given proposition. illustration) we do, and must, analyse the bodily motions so far as is necessary for distinguishing those which ought to be performed from those which ought not. To a similar extent, and no further, it is necessary that the logician should analyse the mental processes with which logic is concerned. Logic has no interest in carrying the analysis beyond the point at which it becomes apparent whether

With respect to the first part of this undertaking, I do not attempt to decompose the mental operations in question into their ultimate elements. It is enough if the analysis as far as it goes is correct, and if it goes far enough for the practical purposes of logic considered as an art. The separation of a complicated phenomenon into its component parts is not

our

the operations have in any individual doubt, as far as possible, merely by case been rightly or wrongly per- a closer and more attentive interrogaformed in the same manner as the tion of our consciousness, or more science of music teaches us to dis- properly speaking, of our memory; criminate between musical notes, and and so far is not amenable to logic. to know the combinations of which But wherever this method is insuffithey are susceptible, but not what cient to attain the end of its inquiries, number of vibrations in a second cor- it must proceed, like other sciences, respond to each; which, though use- by means of evidence. Now, the ful to be known, is useful for totally moment this science begins to draw different purposes. The extension of inferences from evidence, logic beLogic as a Science is determined by comes the sovereign judge whether its necessities as an Art: whatever it its inferences are well grounded, or does not need for its practical ends, what other inferences would be so. it leaves to the larger science which may be said to correspond, not to any particular art, but to art in general; the science which deals with the constitution of the human faculties; and to which, in the part of our mental nature which concerns Logic, as well as in all other parts, it belongs to decide what are ultimate facts, and what are resolvable into other facts. And I believe it will be found that most of the conclusions arrived at in this work have no necessary connexion with any particular views respecting the ulterior analysis. Logic is common ground on which the partisans of Hartley and of Reid, of Locke and of Kant may meet and join hands. Particular and detached opinions of all these thinkers will no doubt occasionally be controverted, since all of them were logicians as well as metaphysicians; but the field on which their principal battles have been fought, lies beyond the boundaries of our science.

This, however, constitutes no nearer or other relation between logic and metaphysics, than that which exists between logic and every other science. And I can conscientiously affirm, that no one proposition laid down in this work has been adopted for the sake of establishing, or with any reference to its fitness for being employed in establishing, preconceived opinions in any department of knowledge or of inquiry on which the speculative world is still undecided.*

*The view taken in the text, of the definition and purpose of Logic, stands in marked opposition to that of the school of philosophy which, in this country, is represented by the writings of Sir William Hamilton and of his numerous pupils. Logic, as this school conceives it, is "the Science of the Formal Laws of Thought;" a definition framed for the express purpose of excluding, as irrelevant to Logic, whatever relates to Belief and Disbelief, or to the pursuit of truth as such, and restrictof its total province, which has reference ing the science to that very limited portion

to the conditions, not of Truth, but of It cannot, indeed, be pretended Consistency. What I have thought it usethat logical principles can be alto-ful to say in opposition to this limitation of the field of Logic, has been said at some gether irrelevant to those more abstruse discussions; nor is it possible but that the view we are led to take of the problem which logic proposes, must have a tendency favourable to the adoption of some one opinion, on these controverted subjects, rather than another. For metaphysics, in endeavouring to solve its own peculiar problem, must employ means, the validity of which falls under the cognizance of logic. It proceeds, no

length in a separate work, first published in 1865, and entitled An Examination of Sir William Hamilton's Philosophy, and of cussed in his Writings. For the purposes of the Principal Philosophical Questions disthe present Treatise, I am content that the justification of the larger extension which gave to the domain of the science, should rest on the sequel of the Treatise itself. Some remarks on the relation which the Logic of Consistency bears to the Logic of Truth, and on the place which that parit belongs, will be found in the present ticular part occupies in the whole to which volume (Book II. chap. iii. § 9).

I

BOOK I.

OF NAMES AND PROPOSITIONS.

"La scolastique, qui produisit dans la logique, comme dans la morale, et dans une partie de la métaphysique, une subtilité, une précision d'idées, dont l'habitude inconnue aux anciens, a contribué plus qu'on ne croit au progrès de la bonne philosophie."CONDORCET, Vie de Turgot.

"To the schoolmen the vulgar languages are principally indebted for what precision and analytic subtlety they possess."-SIR W. HAMILTON, Discussions in Philosophy.