sin HAMILTON AND MR. 5I r.'

TrusWithin a comparatively recent period the study of logic was not only entirely pretermitted, even by the generality of reflective

Men,- but had fallen into positive disesteem with the large ma- jority of' echieated persons. Probably the most popular notion of logic was that it was a roundabout way of proving, or rather at- tempting to prove, what every one knew already by the light of nature. Sothetimes, perhaps, it would be identified with the pseudo-syllogistic assertion oisome outrageous fallacy; such as a mouse is a syllable ; a mouse"eats cheese;: therefore a syllable eats cheese ; or a eat has one tail more'than no cat ; but no eat has two tails ; therefore a' cat has three tails ; or else it would be con- founded with the sophism of counter-questioning, with the Dile/lima, the Achilles' the Electra, the Crocodilinus, or the Cornutus, in which last form of the fallacy, it is asked—" Have vou cast your • horns? If you answer I have, it is rejoined, Then you' have had horns ; if you answer I have not, it is re- joined,- Then you have them' still."

If we cannot say, "" nous avons •change tout eels," we have at least lived to see the commencement of a decided change for the better in the growing respect with which the science of logic is regarded by the more cultivated minds of our own time.

In England the restoration of this study to the rank from which it had fallen is ascribed by Mr. J. S. Mill to Archbishop Whately, in whose Elementi 'Of Logic, he says,' the whole of the common doctrine of the syllogism is "stated with philosophical precision and -explained with remarkable perspicuity,' and to which he,re- fere us for a most satisfactory treatment of the so-called " Fah lacies of Ratiocinetion." To Archbishop Whately, also, it would appear, must be assigned the merit in our own times and in'our own country of havine.b helped to reinvest logic with its ancient and legitimate rights, by defining it to be the science as well ai the art of reasoning. This profounder view of logic neglected by later logicians, will, we believe, be found implicitly at least in the old " Aldrich" of 1804 and 1771, as well as in Sanderson's writings, where logic is Said to be conversant with second in- tentions, 'that is the forms which the intellect assumes on operating ; informatkn for which we were originally indebted to the MM. of an Oxford friend.

Sir William Hamilton while acknowledging that Whately's

book is the best accessible' work on the subject, seems to be of opinion that bad is the best. He sharply criticizes the opening sentences in the EleniCnts. He declares that Dr. Whately is wrong in affirming that logic -has, in general, been regarded merely as an art ; in discriminating, as he does, between art and scienee, and in limiting the object-matter of logic to that part of the discursive faeulty which is especially denominated reasoning. Now, inasmuch as logic does furnish rules for conducting the Firocess of reasoning, we think it may fairly be considered as an art; and, inasmuch as it institutes an analysis of the intellec- tual process which takes place when we reason—an analysis from which the rules are derived—we regard it as unquestionably and preeminently a science. If, as we suppose is the case, logic in Dr. Whately's view, be convertible with syllogistic, then we agree With Sir William, that the definition is incompetent. We shoiild also agree with him, as against Whately, in condemning the dictum that "logic is wholly concerned with the use of lan- guage." We can scarcely, however, join with his critic in stigmatizing the definition as delusive as well as incompetent ; nor can we see that it neeessarily eonfounds logic with Psychology and Metaphysics. It is with reasoning as reasoning, we imagine, that Whately maintains logic to be concerned ; not with reasoning in its psychological or metaphysical nature. If this distinction is not explicitly made, it is at least presumed by Dr. Whately. Sir William Hamilton's definition of logic is that it is the science of the necessary form of thought, considered not as the operation of thinking but as its product ; it does not treat, he says, of con- ception, judgment, and reasoning, but of concepts, judgments, and reasonings. Logic he divides into-1. Objective and sub- jectire, or systematic and habitual; and 2. General and special, or abstract and concrete. It is general logic only, " as alone a branch of philosophy," that he proposes to make the object of his investigation. This general or abstract logic he divides into two parts-1. Pure ; and 2. Modified logic. Pure logic is, in its turn, divided into two parts--1. The doctrine of elements; and 2. The doctrine of method. The doctrine of elements treats first of "the fundamental laws of thinking or the conditions of the thinkable ;" secondly, " of the laws of thinking, as governing the special func- tions, faculties or products of thought, in its three gradations of conception, judgment and reasoning. The doctrine of method is divided into three parts-1. The method of clear thinking, or the doctrine of illustration or definition ; 2. The method of dis- tinct thinking, or the doctrine of division; 3. The method of connected thinking, or the doctrine of proof. Such is the distri- bution. of pure logic. Modffled logic falls naturally into three parts. The first part

treats of the nature of truth and error, and of the highest laws for their discrimination ; the second, of the impediments to think- ing, whether mental, bodily, or external, with the means of their removal; and the third part of the aids or subsidiaries of think-

• Lectures on Logic. By Sir 'Prilliam 'Hamilton, Bart. Edited by the Reverend

H. L. Mensal, B.D., LL.D., &c., and John Veiteh, M.A., &c. In two volumes. Published by William Blackwood and Sons.

ing, whether through the acquisition or through the communica- tion of knowledge. Such is the distribution of modified logic.

A distinctive feature in Sir William Hamilton's system is the introduction into logic of the so-called fundamental laws of thought, the first division -of his doctrine of elements. These laws have, indeed, a historical derivation, but owe their new dog- matic importance, if we do not, mistake, entirely to the Scotch

"As commonly received," he tells us, the fundamental

laws of thought or conditions of the thinkable, are four. 1. The law of identity. 2. The law of contradiction. 3. The law of ex- clusion or of excluded middle; and, 4. The law of reason and con- sequent, or of sufficient reason. On the first of these laws we shall here offer no special remark; and as in his "Discussions" our author himself subsequently excluded from logic the principle of sufficient reason, we omit all consideration of the last law. The two remaining laws, those of contradiction and excluded middle, have already given us some trouble, and are likely to give us a great deal more; converted, as they are, into controversial weapons and handled with extraordinary skill and power, in a theological fencing-school, temporarily set up at Oxford. The law of contradiction asserts that two contradictory propositions cannot both be true ; the law of exclusion, that two contradictory propositions cannot both be false. Now, notwithstanding Sir William Hamilton's avowal that man is incompetent to a cogni- tion of the absolute, he declares these axioms, says Mr. Mill, to be true even of noumens. (supersensuous realities). They are, to re- sume the quotation, " The chinks through which, as he represents, one ray of light finds its way to us from behind the curtain which veils from us the mysterious world of things in themselves." The question then occurs : Is the axiom of contradiction a law _of thought ? May it not be an identical proposition or even a_gene- ralization from experience ? Going part of the way with the No- minalists, Mr. Mill, (whose judgment will at least be respected even by those who hold the more German-like view of this subject) after expressing the opinion that the principle of contradiction should put off the ambitious phraseology which gives it the air of a fundamental antithesis pervading nature, and should be enunciated in the simpler form that the same pro- position cannot at the same time be false and true ; "- he proceeds to say that he does not regard the statement as a merely verbal proposition, but as like other axioms, one of our first and most familiar generalizations from experience ; the meaning of which, he takes to be " that belief and disbelief are two different mental states excluding one another' as light ex- cludes darkness; sound, silence; motion, quiescence,"&c. " In like manner," he continues, for we cannot do better than transfer to our pages the remaining paragraph of his luminous exposition—" In like manner as the principle of contradiction (that one of two con- tradictories must be false) means that an assertion cannot be both true and false, so the principle of excluded middle, or that one of twd contradictories must be true, means that an assertion must be either true or false ; either the affirmative is true, or otherwise the negative is true, which means that the affirmative is false. I cannot help thinking this principle a surprising specimen of a so- called necessity of thought, since it is not even true, unless with a large qualification." A proposition must be either true or false, provided that the predicate be one which can in any intelligible sense be attributed to the subject (and as this is always assumed. to be the case in treatises on logic, the axiom is always laid down there as of absolute truth). " Abracadabra is a second.intention ; is neither true nor false." Between the true and the false there is a third possibility, the unmeaning ; and this alternative is fatal to Sir William Hamilton's extension of the maxim to noumena. That matter must either have a minimum of divisibility or be in- finitely divisible is more than we can ever know. For, in the first place, matter in any other than the phenomenal sense of the terra' may not exist ; and it will scarcely be said that a nonentity must be either infinitely or finitely divisible. In the second place, though matter, considered as the, occult cause of our sensa- tions, does really exist, yet what we call divisibility may be am at- tribute only of our sensations of sight and touch, and not of their uncognizable cause. Divisibility may not be predicable at all in any intelligible sense of things in themselves, nor therefore of mat- ter in itself ; and the assumed necessity of being either infinitely or finitely divisible may be an.inapplicable alternative."

We shall leave it to the inauirer to pursue the subject further. We shall leave it to him to determine whether the three Hamil- tonian laws of thought—the law of identity, of contradiction, and exclusion—are forms of our thinking faculty, or whether they are not general statements, the origin of which it is not difficult to ascertain.

To return. The fundamental forms of thought necessarily re-

appear in Sir William Hamilton's philosophical construction: in fact, to deny the universal application of the four laws is, in his view, to subvert the reality of thought. They overrule the whole operation of thinking. They do not, indeed, affect the first division of syllogisms into extensive and comprehensive ; but they deter- mine their second grand division into the three classes of cate- gorical, disjunctive, and hypothetical ; to which may be added, as a fourth class, the hypothetical disjunctive syllogism. This account, however, requires a correction. We have seen that Sir William excluded from logic the law of sufficient reason. Ac- cordingly, "this classification of syllogisms," as we read in an editorial note, " cannot be regarded as expressing the author's final view, which, " in a note by Sir William Hamilton appended to Mr. I3aynes's essay on the New Analytic of Logical Forms,"'

is thus expressed : " All mediate inference is one—that incorrectly called categorical ; for the conjunctive and disjunctive forms of hypothetical reasoning are reducible to immediate inferences." If from Sir William Hamilton's definition of logic we turn to Mr. Mill's criticism on it, we shall find that in the judgment of the latter gentleman it requires, "in order to be tenable, limita- tion in one direction as well as extension in another." By limit- ing the word thought to " reasoning and to the intellectual ope- rations auxiliary to reasoning, in so far as they are auxiliary ; and interpreting "laws of thought" to mean the immediate and not the ultimate law, to imply a sufficient though not a complete analysis of " all the processes which the mind goes through when it proves a proposition or judges correctly of proof," Mr. Mill pro- nounces that Sir W. Hamilton's definition might be made to agree with his own. In point of fact, however, it by no means agrees with his own. Mill holds that the province of logic is coextensive with proof ; the Hamiltonian school confine it to " one species of proof, namely, that in which the conclusion follows from the mere form of the expression." Mill accords the name of logic to the

theory and rules which concern the formation of new generaliza- tions; the Hamiltonian school confine it to the theory and rules

of the interpretation of old generalizations. How far Sir Wil- liam's own opinion, as expressed in his recently-published lectures on Logic, is represented by that of his school, may be inferred from the work before us. In his Pure Logic, we find him stating that all probation is syllogistic ; in his Modijied Logic, he tells us that "applied induction rests on the constancy, the uniformity of nature, and on the instinctive (?) expectation we have of this stability." " This constitutes," he goes on, what has been called the principle of logical presumption, though, perhaps, it might with greater propriety be called the principle of philosophical presumption." Some of the remarks which follow this statement are sound and discriminating ; but the subject is not satisfactorily handled. The conclusion is, that by the process of induction we are unable to attain absolute certainty, since the principle which lies at the root of the process implies neither a necessary law of thought, nor a necessary law of nature. From this cursory examination of the Lectures on Logic, we conclude that the system of Sir William Hamilton and that of Mr. Mill are irreconcileable. If we may venture to express an opinion, we should say that the metaphysical spirit pervades the whole of Sir William Hamilton's logical construction ; while that of his antagonist is conceived in a positive or scientific spirit. An ab- solutely abstract logic—logic applied to no order of phenomena— seems to us an extremely futile thing. It is true, indeed, as Mill explains, that logic is not concerned with intuitive truths, but only with inferences. Still, as "by far the greatest portion of our knowledge, whether of general truths or of particular facts, is' avowedly matter of inference, nearly the whole not only of science but of human conduct is amenable to the authority of logic." It is the province of logic not to discover evidence, but to test and judge it when found. Thus, logic is defined by Mr. Millie be "the science of the operations of the understanding which are subservient to the estimation of evidence ; both the process itself of proceeding from known truths to unknown, and all other intellectual operations, in so far as auxiliar to this " ; as naming, definition, classification. Logic extends even to observation, for, while it does not tell us " how or what to observe," it considers " under what conditions observation is to be relied on."

Laying it down as a cardinal error in the philosophy of logic, that ' the investigation of truth consists in contemplating and handling our ideas or conception of things instead of things them- selves," Mr. Mill distributes all propositions or assertions, all affirmations or denials which can possibly be made, except those which are merely verbal, into five different classes ; asserting "five different kinds of matters of fact—namely, existence order in place, order in time, causation and resemblance—reducible, how- ever, to four, by regarding causation as a special case of order in time. It is the business of logic to examine all the propositions, affirmative or negative, that have to do with these five sorts of realities. Logic is the science of inference. "All inference, con- sequently all proof, and all discovery of truth, not self-evident, consists of inductions and the interpretation of inductions." It is then of paramount importance to determine what induction is. Mr. Mill defines if to be the operation of discovering and proving general propositions." Moreover, " the principles and rules of induction, as directed to this end, are the principles and rules of all induction' and the logic of science is the universal logic, ap- plicable to all inquiries in which man can engage."

Induction is a process of inference : proceeding from the known to the unknown, it arrives at a conclusion " wider than the pre- mises from which it is drawn." It infers something unobserved from something observed. It requires, therefore, a test of proof : inductive logic provides that test. Induction, as Mr. Mill understands it, may " be summarily de- fined as generalization from experience." "Certain individuals have a given attribute ; an individual or individuals resemble the former in certain other attributes ; therefore, they resemble them also in the given attribute." We have here the elements which, when combined, constitute a universal type of the reasoning pro- cess. Induction, not syllogism, is the mode of reasoning. Of the relation of induction to deduction, both constituent parts of the same general operation, we can say nothing here. That what happens once will happen again, in all cases 'of a certain kind,—in other words, that the course of nature is uniform, —

is the fundamental prinoiple of induction, itself a generalization from experience founded on prior generalizations. Every in- ference from the known to the unknown, however simple, implies uniformity. Uniformities exist thrOughout nature, some weaker, some stronger ; some, which for any human purpose, may be con- sidered "quite certain and quite universal." We find this ri- gorous universality in the laws of number, and those of extension. We find a law equally certain and equally universal, in the law of causation ; " a law which is universal also in another sense ; it is coextensive with the entire field of successive phenomena, all instances whatever of succession being examples of it." " The truth, that every fact which has a beginning has a cause, is co- extensive with human experience." Thus the notion of cause is the root of the whole theory of induction.

Mr. Mill holds a logic of induction of science, business, and life, to be possible because there are certain and universal induc- tions. The law of universal causation is the strongest of all in- ductions, and the criterion of the strength of all other inductions. Metaphysical certainty it does not give us ; "but, for all practical purposes, it is absolute."

We have now very briefly, and inadequately characterized the two systems of logic, constructed severally by Sir 'William Hamilton and Mr. J. S. Mill. Far from considering the ques- tion unimportant, we regard few questions as more important than that which is suggested by the juxtaposition of these two antagonist constructions. Are these formal laws of thought, or is all our knowledge generalized experience ? We invite men, abler and more expert than ourselves, carefully to study Sir William Hamilton's two volumes, concurrently with Mr. Mill's, aild record their judgment in some form easily intelligible to plain thinking persons.

We have said nothing of the literary merit of these Lectures on Logic. Unfortunately, they do not form a systematic treatise. They constitute the " second and concluding portion of the bien- nial course on metaphysics and logic, which was commenced by Sir William Hamilton on his election to the professional chair in 1836, and repeated with but slight alterations till his decease in 1856. There is an appendix, containing papers written, for the most part, during the same period. Among them is that entitled New Analytic of Logical Forms, first published in 1846. Of the profound and subtile thought of Sir William Hamilton ; of his various and massive erudition ; of his contributions to the syllogistic theory ; or the splendid service rendered by his refuta- tion of the ontologists, in an essay which we read many years ago, with signal delight and lasting profit, we need say nothing here. The intellectual stature of the man is too well known for it to be required of us to measure his inches.

In the pages of the work before us will be found some matter of general interest, in the shape of wise comment, segaeious remark, or curious information. A singular bit of learning is that which acquaints us with the history of the latin mnemonics in logic, the cabalistical verses, Barbara, Celarent, &e., as well as of their Greek counterpart.

" They were, as far as they relate to the three first or Aristotelic figures, the invention of Petrus Rispanus, who died in 1277, Pope John xxii. (or as he is reckoned by some the xxi., and by others the xx.). He was a native of Lisbon. It is curious that the corresponding Greek mnemonics were, so far as I can discover, the invention of his contemporary, NicephorusBlemmidas, who was designated Patriarch of Constantinople. Between them, these two logicians, thus divided the two highest places in the Christian hierarchy ; but as the one had hardly begun to reign when he was killed by the down- fall of his palace, so the other never entered on his office by accepting his nomination at all. The several works of the Pope and the Patriarch were for many centuries the great text-books of logic—the one in the schools of the Greek, the other in the schools of the Latin Church:" Occasionally we find in these lectures a page that amuses as well as informs. Take, for instance, with some omissions, the passage on the

" Enthymeme of the third order—(The conclusion understood) "'Every liar is a coward : And Caius is a liar.'

In this last, you see, the suppression of the conclusion is not only not vio- lent, but its expression is even more superfluous than either of the premises. There occurs to me a clever epigram of the Greek mythology, in which there is a syllogism with the conclusion suppressed. I shall not quote the original, but give you a Latin and English imitation, which will serve equally well to illustrate the point in question. The Latin imitation is by the learned printer, Henricus Stephanus, and he applies his epigram to a certain Petrus, who, I make no doubt, was the Franciscan, Petrus a Cor- nibus, whom Buchanan, Beza, Rabelais, and others, have also satirized. It was, as I recollect, thus- " Sunt monachi nequam ; nequam non unus et alter ; Printer Petrum omnes est sed et hic monachus.' "

The English imitation was written by Person upon Gottfried Hermann (when this was written confessedly the prince of Greek scholars), who, when hardly twenty, had attacked Porson's famous, canons in his work, De metris Greccorum et Bomanorum. The merit of the epigram does not certainly lie in its truth- " The Germans in Greek

Are sadly to seek :

Not five in five score,

But ninety-five more. All, save only Hermann, And Hermann's a German.'

"In these epigrams, the conclusion of the syllogism is suppressed, yet its illative force is felt even in spite of the express exception ; nay, in really conquering by implication the apparent disclaimer, consists the whole point and elegance of the epigram."

"There is recorded, likewise, a dying deliverance of the philosopher Hegel, the wit of which depends upon the same ambiguous reasoning. ' Of all my disciples,' he said, one only understands my philosophy; and he does'ne " But we may take this for an admission by the philospher him- self, " that the doctrine of the Absolute transcends human Com- prehension."