Изображения страниц
PDF
EPUB

If, however, the account given by Mr. Mill of the philosophical genesis of induction be insufficient, it must be added that, as in his reconciliation of the syllogism with induction, so in his account of the different inductive processes, he is unrivalled. But these belong to a more ad

ciation has maintained itself, while the logi- | mind, and some definite mental faculty, becal law of substitution of similars has been yond the mere sensation, to discern these defeated-has found no place for its exer- uniformities. I have endeavoured in the cise. And, in point of fact, if there be no above analysis to assume no mental faculty connection in external nature between A that would not be granted by the most and B, their junction in consciousness, which stringently searching philosopher. was accidentally established, will in time be dissolved. The law of association will have played its part, and will slowly become too feeble to retain a tie unsupported from independent causes. But suppose that between any two phenomena, say A and F, there is a connection in external nature, so that when A happens, F invariably or gene-vanced part of the subject than belongs to rally follows. Then that association in thought between A and F, which was established by their first appearance together or in succession, will be strengthened by every such appearance that takes place afterwards; the expectation of F, which ensues upon the observation of A, will be confirmed, not disappointed. And in this case the logical law of the substitution of similars will be found to hold; we shall be able to predicate of any phenomenon that includes A, that it will also include F.

According to the above theory, the law of association of ideas is a necessary preliminary of the logical law of the substitution of similars; were it not for the psychological law, we should never be able to draw a logical conclusion at all. But, though a necessary condition, it is not the only condition-the other being a certain disposition of external nature. Were it not that nature really contains certain fixed sequences, we should never know that it contained such sequences; but also, we should never know that it contained such sequences were it not for this principle of the association of ideas originally native to our minds. In logic, in the attainment of truth, mind and nature are alike necessary: they each contribute their separate element to certain knowledge.

this article; and it is necessary to hasten to the improvements in the theory of logic effected by the rival school.

In spite of the statement at the commencement of the article, that the two philosophical schools came to closer quarters in logic than in any other portion of mental science, it is even here no easy task to attain a position from which one may do justice to them both. The truth is that the aims of the two schools, though very cognate to each other, so cognate that to a superficial reader they appear the same, are yet different-not widely different, it is true, but so much so that the assumption of entire identity of purpose serves only to mislead and irritate the disputants on either side. The practical mind of Mr. Mill, always looking out for some concrete use to which to apply his science, cannot away with distinctions and definitions which, like those of Hamilton, appear to lead nowhither; nor can we much doubt that Hamilton found Mr. Mill's treatise unphilosophical, and possibly vulgar. The scientific character of Mr. Mill's treatise has been here maintained; the greater abstruseness of the German speculations will make it a harder task to show their exact position; yet this may be done.

The difference, then, between Mr. Mill The above is an endeavour to give a clear and the German school (which was briefly account of the genesis of that law the na- indicated at the outset) is this. Mr. Mill ture of which has been so ably expounded tries to bring the mind of his readers into by Mr. Mill. Mr. Mill's own account of the argumentative posture: Kant and Hamthe genesis of the law can hardly be deemed ilton endeavour to make their reader sursatisfactory. He contents himself with say-vey as from an external point the arguing that we know by experience that the course of nature is uniform; that we have always observed it to be uniform; and so on. But have we always observed the course of nature to be uniform? No one has maintained more strenuously than Mr. Mill that the course of nature possesses not merely uniformity but infinite diversity; the uniformities do but stretch as a shining web over a field of immense variety that expands far beyond our ken. It needs

mentative mind, the mind in the act of reasoning. Mr. Mill looks at the process of reasoning, so to speak, with the naked eye; he looks at it as a calm and sober reasoner who cared only to know the main elements of an argument might look at it. Kant and Hamilton turn a microscope on the reasoning process; the practical matter, whither it will lead them, they care less for; their object is to analyse it speculatively. Those who keep this difference of purpose in view

one.

[ocr errors]

are the most likely to do justice to both | victory, without knowing how he wins it? sides. Yet the object of Kant and the ob- Mr. Mill would say simply that he had colject of Mr. Mill are not wholly alien; lected a great deal of previous experience, though diverse, they are akin to each other; and drew his conclusions from that. But and both belong to the science of logic. it is very plain that the general need not The Germans, and Hamilton with them, consciously remember his previous experiendeavoured to analyse the reasoning mind, ence in order to reap the benefit of it; nay, and to give names to all its operations and in the crisis of a great battle, the probabilattitudes. Thus, while Mr. Mill, on all ity is that he will be far too keenly engaged ordinary occasions, speaks of a proposition, with the present to be able to turn his eyes which is the natural word that an arguer backwards on the past. What happens is would use himself when thinking of that something of this sort. In all his previous which he lays before an opponent, Hamil- battles he has accustomed himself to note ton, on the other hand, speaks of a judg- the kind of combinations that contributed ment, which is the mental attitude of the to success; these combinations, without rearguer when he is propounding anything. membering them in their entirety, without This, however, is a less striking instance giving them any name or appellation, he than some others. Here is a more peculiar has yet symbolized to himself, in some Mr. Mill speaks of classes, which are manner which he himself perhaps hardly material phenomena contemplated by the recognises, but in such a way that the main arguer himself: Hamilton rather avoids the elements of the combinations shall be ready word class, but analyses the mental state of to start within him when need is. Now one who is contemplating a class, and frames this may well and accurately be expressed the word concept to express it. Now there by saying that his mind is stored with conis no word in the Hainiltonian vocabulary ceptions or concepts. For he does not rewhich irritates Mr. Mill so much as this member the whole configuration and picword concept. He cannot deny it a mean- ture of his previous experiences; but the ing; but he thinks it wholly unneeded. law of association of ideas calls back to He thinks it a "misfortune that it was ever him the principal elements of them, which, invented; he calls it a bad and obscure however, in themselves would be but bare expression for the "signification of a class-outlines, though being applied to the conname. All this results from the fact that he has never put himself in the point of view of the Germans; he sympathizes too keenly with the argumentative temper to be able to analyse the argumentative process as an unengaged person; portraying it, he portrays it from the inside, not from the outside. In fact, it is rather the expression "signification of a class-name" that is clumsy; the word concept (Begriff) is one much needed to express a particular, and quite real, mental attitude. As Hamilton well defines it, it is "the cognition or idea of the general character or characters, point or points, in which a plurality of objects. coincide." And this too must be remembered: if, as is surely the case, we can and do reason sometimes, i.e., draw inferences, without the use of language, then the word "judgment" is wider than the word "proposition," the word "concept " wider than the word "signification of a class-name." Let me borrow an example from Mr. Mill. A general, from long experience, knows how to arrange his troops in a battle so as to be secure of the victory; yet he cannot explain to another what his knowledge is, how he comes to make such and such arrangements. By what terms shall we de scribe the mental attitude of the general, the turn of mind which enables him to win a

crete phenomena before him they prove themselves endowed with a power of combining, ordering, and classifying these phe nomena, and furnishing their possessor with valuable contrivances for his present material need. I do not know any English word, except concept or conception (which latter, however, Hamilton uses to express the process of gathering concepts), that at all expresses the mental attitude which I have endeavoured to describe above. Certainly Mr. Mill's proposed substitute, "signification of a class-name," is very inapposite indeed.

of

Let us take another illustration. A person learns to play at chess; in the first game he plays, being unaccustomed to the board, the men, and the different moves the pieces, he has continually to strain his attention to remember what he may do, and see what it is best for him to do. After a dozen games, he finds no difficulty at any rate in the simpler matter. After a hundred games he may be a fair player. What has happened in the interval? This; he has seen the chessboard frequently, and a large number of individual positions, moves, and combinations, to which, moreover, his attention has been more strenuously directed from the fact of his being himself one of the players. Of these positions, moves,

وو

conception from concept, using the former to represent the mental effort, the latter the result of that effort, is not perhaps of any great consequence; but as it has been employed in philosophical works, and may prove useful, there seems no reason for abandoning it.

I have dwelt at some length on the explanation of this word concept, because it is a point in which the difference between the two logical schools comes out very plainly. Mr. Mill, thinking of classes, speaks of classes: Hamilton, thinking of the mind in the act of contemplating a class, speaks of a concept. And as Mr. Mill's phraseology is better calculated to assist a man in arguing himself, Hamilton's is more likely to furnish him with the means for understanding the arguments of another. That is, it will furnish him with a kind of blank forms for the understanding of an argument, just as Mr. Mill's work will supply him with blank forms for arguing himself. It may justly be thought that Mr. Mill illustrates his blank forms a great deal better than Hamilton. Yet there are one or two admirable illustrations in these chapters on concepts; and the whole set of explanations and distinctions contained in them, with hardly an exception, are excellent. The main outline of them had, indeed, been given by Kant; and the greater number of them are taken either from him or some other German logician.

and combinations, some have occurred more | Mr. Mill's proposed substitute for concept, frequently than others, or from other rea-"signification of a class-name," will not insons have been more specially noticed by variably hold. Hamilton's distinction of him; these he will remember most readily; and the very sight of the board and men will, by the law of association, call up some of them before his mind. But this is not all; there will be a generalizing process going on in his mind with respect to those images which the law of association excites. For instance, a particular combination of the bishop and knight occurs to his mind. This combination he can set in any part of the board he pleases; again, he can dispose the other pieces differently in relation to it; he can add a castle to his combination, thereby increasing its complexity, but diminishing the number of subsidiary combinations which, from the capacity of his mind, he is capable of disposing around it; or he can take away the bishop and substitute a pawn, and so on. Now these kind of combinations we do, even in our common talk, call conceptions; Hamilton called them concepts; but whichever word we use, there can be no doubt of the utility of some such word. Mr. Mill would perhaps use the phrase "classes of combinations; but, not to speak of the length of such an expression, there seems reason, where the mental element comes into such prominence as it does here, to employ a word that will bring it out. We might also use the word "combination" simply; but this would, I think, be understood in a less general sense. Thus, to recur to our former example, a general would, on any particular occasion, be said to have made excellent combina- One more point in these chapters is worth tions; but if the whole class and nature of dwelling on. It is this:-The word conhis combinations were being spoken of, it cept has been defined as indicating a general would be said that his conceptions were ex- notion, not an individual thing: can we, cellent. It will be observed that every con- then, correctly speak of the concept of an ception implies a class, and every class im- individual? There is no doubt that in plies a conception; and we should use the common language we could speak of our one word or the other according as we do conception of Socrates; and Hamilton says or do not wish to lay a stress on the mental himself, "If I think of Socrates as son of labour of apprehending the class. Thus we Sophroniscus, as Athenian, as philosopher, should speak of the class of vertebrate ani- as pug-nosed, these are only so many charmals; because the labour of apprehending acters, limitations, or determinations which the notion of a vertebrate animal is incon-I predicate of Socrates, which distinguish siderable. But for a philosopher who wished him from all other men, and together make to lay stress on the mental element of ap-up my notion or concept of him." This, prehension, there would be no inaccuracy even here in speaking of the conception or concept of vertebrate animals, And it is observable that, though every conception corresponds to a class, every conception has not a class-name, Thus any particular disposition of the bishop and knight on the chessboard may be made the centre of a class of combinations; but yet such a disposition has no peculiar name. So that

VOL. LI.

N-4

Mr. Mill charges on him as an inconsistency. The case, however, is very simple.. I may have a conception or concept of an individual, without the individual being that conception or concept. No one knows bet-ter than Mr. Mill that reality extends be-.. yond, is greater than, our conceptions; it is a thing always to be remembered, in dealing with realities; having framed our fullest conception, we must allow for some-

thing in nature beyond it. But, for all that, we must frame conceptions of realities. It is true that there appears a contradiction in terms between the definition of a

66

concept as the characters in which a plurality of objects coincide" and an expression which implies that the concept only indicates a single individual; but nothing is more common, as all mathematicians know, than for a limiting case to be apparently not included in the definition of its class. Thus a parabola is the limiting case of an ellipse; if one focus be supposed removed to an infinite distance; and propositions true of an ellipse may, under this condition, be at once applied to the parabola. And yet the definitions of an ellipse (whether taken from the sections of a cone or from the eccentricity) do in terms exclude the parabola. In the same way, our conception (or concept) of an individual (meaning, as it does, the whole sum of the characteristics of the individual that we know) is the limiting case of a concept in respect to the number of individuals contained under it. There is, however, a real error in another passage which Mr. Mill quotes, where Hamilton says, "When the extension of a concept becomes a minimum, that is, when it contains no other notions under it, it is called an individual." Hamilton should have said, "it represents an individual to us," for the individual extends beyond our conception of it. But this is an isolated slip on his part; for the third passage quoted by Mr. Mill as an example of inconsistency is perfectly explicable, though I cannot here stop to explain it. It is to be observed that, when we speak of our conception of Socrates, we mean something quite different from our perception or sight, hearing, etc., of him; and it was the use of conception in this latter sense that Hamilton protested against.

The three great divisions into which the German school divide our thinking, are Concepts, Judgments, and Reasonings. Before proceeding to consider these two latter divisions, it may be remarked that one great excellence of the school is the thoroughness with which they consider, not specially reasonings, but the whole process of thought. The object of reasonings is to obtain Judgments-to know fresh truths; these fresh truths enlarge our conceptions, our knowledge; the conceptions thus enlarged become the groundwork of new reasonings, new judgments, and still more enlarged conceptions, and so on. It is an ever-recurring circle, which no other class of logicians, as far as I know, have described so clearly. The conceptions, in most cases,

are confirmed by having names given to them; but this, as we have seen, does not always take place, even when further progress is made by their means, though of course it must take place if the knowledge thus obtained is to be communicated to others.

66

But it is necessary briefly to consider the main charge which Mr. Mill makes against Hamilton, and which he would no doubt make against the whole German school of logicians, and especially as respects their doctrine of judgments and reasonings; namely, that in it they take no notice of that which he affirms, and rightly affirms, to be the central object of logic, the discernment of truth from falsehood. "A judgment," says Kant (Logik, p. 156), "is the representation of the unity in consciousness of diverse phenomena, or the representation of their mutual relation, in so far as they make up a conception." ("Ein Urtheil ist die Vorstellung der Einheit des Bewusstseyns verschiedener Vorstellungen, oder die Vorstellung des Verhältnisses derselben, so fern sie einen Begriff ausmachen.") "To judge," says Krug, means to think how representations are related to an object which is to be represented by them, and consequently to determine their relation for the unity of consciousness." ("Urtheilen heisst denken, wie sich Vorstellungen in Bezug auf einen dadurch vorzustellenden Gegenstand verhalten, mithin ihr Verhält niss zur Einheit des Bewusstseins bestimmen.") "To judge," says Hamilton, "is to recognise the relation of congruence or of confliction, in which two concepts, two individual things, or a concept and an indi vidual compared together, stand to each other" (Works, iii. 225). Now for the other side. "I give the name of judg ment," says Reid," to every determination of the mind concerning what is true or what is false. This, I think, is what logi cians, from the days of Aristotle, have called judgment." And this," says Mr. Mill, is the very element which Sir W. Hamilton's definition omits from it." The fact is, however, that Hamilton and his fel low logicians were endeavouring to contem plate and describe from the outside the mental attitude of a judgment. Hence they laid the greatest stress, not on the affirmation or negation itself, but on its mental concomitants; but that affirmation and negation of reality were necessary to a judg ment they would not have denied; indeed, it is implicitly contained in their words. The clumsiness of their definitions cannot be denied; though that of Hamilton would have been tolerably clear, had he written

[ocr errors]

(as would have been far better) class instead | tions, already alluded to, of Hegel. And of concept. A cognate, though not quite the same, accusation of Mr. Mill against Hamilton is that his logic has for its object to determine, not truth, but consistency. Yet this, again, is not entirely correct; for, however imperfectly, induction is still recognised by Kant and his followers.

The definitions, however, of these philosophers are the most obscure parts of those chapters of their treatises which relate to judgments. On the whole, the excellence of their analysis of the different kinds of judgments is undeniable; that of Kant is especially full and concise. On the subject of reasonings there is little in them, comparatively, that is original; and their scantiness in this branch may be at once gathered from the fact that they almost entirely neglect induction. On the whole, the chief excellences of the German school of logicians lie, first, in the severity of their conception of the science, and at the same time the clearness of their discernment of its relation to the connected topics of investigation in every point, except (a very important exception) in the case of the physical sciences, which are reached by inductive logic; secondly, in the comprehensiveness of their view in showing the whole connection of thought, and not stopping at mere reasonings; thirdly, in the accuracy of their analysis of conceptions, and, in a less degree, of judgments.

here too must be named a class of problems that remain as yet unsolved-I mean those which lie at the root of mathematics, which relate to measure and number. Each party at present has its pet formula for the solution of these problems. The one side say, Mathematical axioms are known to us by experience, and the science is thence drawn by deduction: the others say, The axioms are known to us a priori, and (Kant at any rate would add) the science is built up from them synthetically. But the problem is considerably too difficult to be disposed of in either of these ways; and, before it is solved, a much more accurate analysis must be made of the genesis of number and measure than has ever yet been done. The third direction in which logical science may progress lies in those subsidiary investigations which concern our practical advance towards truth; and here would come in, not merely intellectual, but moral and even physical considerations.

[blocks in formation]

"THE Title," says Remigius on Donatus, "is the key or porch of the work to In conclusion, what are the inquiries that which it is prefixed. And note,” adds pseuin the present state of the subject lie im- do-Aquinas upon Boethius, after quoting it, mediately before the logician? First, there" that Title is so called from Titan, that is is the extension in the direction of material science; the development of the formulæ for induction, the examination into the topics of testimony, of chance, of analogical reasoning. Doubtless there is much to be discovered on these points. Here too may be mentioned the advantage that would ensue from laying the different sciences side by side, with a view to comparing the evidence by which they are severally supported—a comparison which would probably be of great service to us in those not infrequent cases in which we know the evidence by which a supposed fact has been supported, but hesitate as to its exact value. If, in such a case, we could immediately refer to some known science, and find that in such and such a case less evidence than the present had been deemed satisfactory, or on the other hand greater evidence than the present had not been deemed satisfactory, such a discovery would be no slight help to our judgment. But in the second place, logic may progress in the psychological direction. In this quarter we touch upon the investiga

the Sun. For as the Sun enlighteneth the world, so doth the Title the book." The title of Mr. Browning's new poem is so far from doing this, that he is obliged to set apart a book of the poem to shed light on the title. At first sight it might appear that it referred to the ring or circle of cantos of which the book consists; or that it hinted at the poet's solicitude for proportion, and his care that the architecture of his poem should be as good as its masonry, and that the whole should be symmetrical as a circle. These ideas may be implied; but the author's primary meaning is something far more material and realistic. He presents himself to us with a ring in one hand and a book in the other. The first, he tells us, is Roman work by Castellani; and be explains by what art so delicate a filigree is produced-how, in order to render the thin gold capable of bearing the tools which are to emboss it, it is mixed with alloy, and the composite mass

*The Ring and the Book. By Robert Browning. (London: Smith, Elder, and Co.)

« ПредыдущаяПродолжить »