« PreviousContinue »
apply the same conception to that mutual action of the internal parts of a body by which they are held together. Newton himself had pointed the way to this attempt.'-Ib. 366-368.
To the first volume, Professor Whewell in (as we think) no very judicious imitation of Bacon, has prefixed a number of 'Aphorisms, which express the substance of the doctrines propounded and illustrated throughout the work. We think they had much better have come at the end of it in the shape of a clear, rapid recapitulation. As they form necessarily a mere outline, as they contain all the technical terms afterwards explained (some of them entirely new, others applications of old words), these aphorisms must necessarily be almost entirely unintelligible to those who have not read the work itself, and will probably exert a most repelling effect upon those who look into them before doing so. Nay, we think it highly probable that many will be deterred altogether from perusing a work which is ushered in by such an ominous introduction. Who will be invited to enter the temple of science, who finds unintelligible hieroglyphics inscribed on the very portals? Or who will enter a house on the very threshold of which he is met by sa harsh a welcome ?
To this set of aphorisms, our author has added another on the * Language of science, or on the history of the formation and growth of scientific terms. These are intelligible enough, and contain a great deal of amusing as well as instructive matter, though we should have been better pleased to see even these in the shape of an appendix rather than in that of a preface. We could wish, moreover, that Professor Whewell" himself had always adhered a little closer to his tenth aphorism; to wit
, that New terms, and changes of terms which are not needed in ' order to express truth, are to be avoided. In his view of the superiority of indigenous over foreign terms of science, where they can be readily had, and of the propriety of freely borrowing from the learned languages whenever the balance of advantages is against our own, we fully accord; we must not, however, omit this opportunity of saying, that the tendency in recent writings is to neglect words derived from the vernacular, and to substitute those of foreign origin, where there is no necessity of so doing, and where the former, on every ground of significance, vividness, and analogy, would be preferable. Many modern works of science are a perfect Babylonish jargon of technicalities, and in reading them one feels somewhat as in reading a work in a foreign language, where, though the words may be understood, they possess no vivacity-make no strong impression. The reading of such works is most laborious--as bad as walking over ploughed land. Let any one compare the vernacular and the foreign terms in the following paragraph, and he will instantly become sensible of our meaning.
** On the other hand, the advantage of indigenous terms is, that so far as the language extends, they are intelligible much more clearly and vividly than those borrowed from any other source, as well as more easily manageable in the construction of sentences. In the descriptive language of botany, for example, in an English work, the terms drooping, nodding, one-sided, twining, straggling, appear better than cernuous, nutant, secund, volubile, divaricate. For though the latter terms may by habit become as intelligible as the former, they cannot become more so to any readers ; and to most English readers they will give far less distinct impressions.
. Since the advantage of indigenous over learned terms or the contrary, depends upon the balance of the capacity of inflexion and composition on the one hand, against a ready and clear significance on the other, it is evident that the employment of scientific terms of the one class or of the other may very properly be extremely different in different languages. The German possesses in a very eminent degree that power of composition and derivation, which in English can hardly be exercised at all, in a formal manner. Hence German scientific writers use native terms to a far greater extent than do our own authors. The descriptive terminology of botany, and even the systematic nomenclature of chemistry, are represented by the Germans by means of German roots and inflexions. Thus the description of Potentilla anserina, in English botanists, is, that it has leaves interruptedly pinnate, serrate, silky, stem creeping, stalks axillar, one-flowered. Here we have words of Saxon and Latin origin mingled pretty equally. But the German description is entirely Teutonic. Die Blume in Achsel ; die Blätter unterbrochen gefiedert, die Blätt. chen scharf gesagt, die Stämme kriechend, die Bluthenstiele einblumig. We could imitate this in our own language, by saying brokenlyfeathered, sharp-sawed; by using threed for ternate, as Germans employ gedreit; by saying finger-feathered, for digitato-pinnate, and the like. But the habit which we have, in common as well as in scientific language, of borrowing words from the Latin for new cases, would make such usages seem very harsh and pedantic.'
-Ib. pp. xcvii., xcviii. We have already remarked that it would have been possible for our author, in various parts of his work, considerably to lighten his style by the occasional substitution of common for more learned and scientific terms. Where no obscurity is the result, there can be no objection, and the reasons on the ground of perspicuity and elegance are manifold.
It may, perhaps, amuse the reader to be reminded of the familiar origin of some of our most formidable terms in the mathematics.
• The earliest sciences offer the earliest examples of technical terms. These are geometry, arithmetic, and astronomy; to which we have
soon after to add harmonics, mechanics, and optics. In those sciences, we may notice the above-mentioned three different modes in which technical terms were formed.
• The simplest and first mode of acquiring technical terms is to take words current in common usage, and, by rigorously defining or other. wise fixing their meaning, to fit them for the expression of scientific truths. In this manner almost all the fundamental technical terms of geometry were formed. A sphere, a cone, a cylinder, had among the Greeks, at first, meanings less precise than those which geometers gave to these words, and besides the mere designation of form, implied some use or application. A sphere (opaiga), was a hand-ball used in games; a cone (rāvos), was a boy's spinning top, or the crest of a helmet; a cylinder (núarvôgos), was a roller ; a cube (xußos), was a die: till these words were adopted by the geometers, and made to signify among them pure modifications of space. So an angle (wva), was only a corner; a point (onjussor), was a signal ; a line (ygodni), was a mark; a straight line (evdeia), was marked by an adjective which at first meant only direct. A plane (ŠTIRÉÒov), is the neuter form of an adjective, which by its derivation means on the ground, and hence flat. In all these cases, the word adopted as a term of science has its sense rigorously fixed ; and where the common use of the term is in any degree vague, its meaning may be modified at the same time that it is thus limited. Thus a rhombus (góußos), by its derivation, might mean any figure which is twisted out of a regular form ; but it is confined by geometers to that figure which has four equal sides, its angles being oblique. In like manner, a trapezium (puslov) originally signifies a table, and thus might denote any form ; but as the tables of the Greeks had one side shorter than the opposite one, such a figure was at first called a trapezium. Afterwards the term was made to signify any figure with four unequal sides; a name being more needful in geometry for this kind of figure than for the original form.'
-Ib. pp. xlix., L. We canot close this article without making one or two remarks on a point in which, in our opinion, Mr. Whewell has not done justice to Dugald Stewart, nor acted with the fairness expected from a candid controvertist. In his Mechanical Euclid, published many years ago, he had combated Mr. Stewart's opinion (founded on that of Locke*), that mathematical truths
* 'Let a man of good parts know all the maxims generally made use of in mathematics never so perfectly, and contemplate their extent and consequences as much as he pleases, he will by their assistance, I suppose, scarce ever come to know that the square of the hypothepuse in a right-angled triangle is equal to the squares of the two other sides.' The knowledge
that the whole is equal to all its parts,' and 'if you take equals from equals the remainders are equal,' helped him not, I presume, to their demonstration: and a man may, I think, pore long enough on those axioms, without ever seeing one jot the more of mathematical truths.'—Locke's Essay, b. iv.
are deduced not, as was commonly said, from 'axioms, but from definitions. Mr. Whewell, on the contrary, affirms that mathematical truths are deduced from axioms' as well as 'de' finitions. To his remarks on this subject, the Edinburgh Review replied in noticing the “Mechanical Euclid,' and in the work now under our notice, Mr. Whewell has published a rejoinder. Into the merits of the controversy between these parties we do not enter. The Edinburgh Reviewer can doubtless take his own part, and in due time we suppose will do so. All we are disposed to do is, to protest against the urfairness with which Mr. Stewart has been treated. It will be observed that Mr. Whewell, in maintaining, against what he is pleased to suppose Stewart's hypothesis, that axioms as well as definitions are the source of mathematical truth, lays the chief stress on the strictly geometrical axioms. Now even if Stewart had said nothing expressly to except these from being included in his remarks, his general observations as well as the notions generally attached to the old phrase, that mathematical science
was built upon self-evident axioms,' ought to have protected him. If any one (before Locke's time) were asked what he meant by the above axioms, he would undoubtedly have referred to the axioms which are really self-evident, and which are not geometrical. In like manner,
if any one were asked now what notion was ordinarily attached to the word axiom, he would reply, a proposition which is self-evident, and would illustrate by some such example as . The whole is equal to all its parts.' Moreover, every body knows how vehemently it has been contended by many mathematicians that the geometrical axioms (so far from having been generally considered truly such) do not properly belong to the class of axioms at all, that they are not at all events self-evident, and that one at least is evidently susceptible of distinct demonstration. But Mr. Stewart, knowing that such propositions are included in the list of Euclid's axioms, and that he might be liable to misconception unless he explained himself, has expressly limited his meaning to the first nine axioms. His words are these-In order to prevent cavil, it may be necessary for me to remark here, that when I speak of mathematical axioms, I have in view only
such as are of the same description with the first nine of those ' which are prefixed to the Elements of Euclid; for in that list,
it is well known, that there are several which belong to a class of propositions altogether different from the others. Can anything be more explicit ?
Upon the supposition that Mr. Whewell had unaccountably overlooked this passage (though in close connexion with Stewart's other observations on the subject) one would have thought that, upon its being pointed out to him, he would at once have
acknowledged that he had done Stewart some injustice, and modified his observations accordingly. But what says he? * If Mr. Stewart afterwards limited himself to showing that
seven (nine] out of twelve of Euclid's axioms are barren tru‘isms, it was no concern of mine to contest this assertion. Mr. Whewell must pardon us for saying that it ought to be the concern of every controvertist, when he disputes the opinions of another, to take care to attach to his words no more than his opponent attaches to them; more especially when he himself has expressly laid down the limitations with which he uses them. Even supposing the tenth, eleventh, and twelfth axioms to be properly such, and properly included in the list, the observations Mr. Stewart had made were explicitly declared not to apply to them, and therefore Mr. Whewell in contesting his views had no right to adduce them as instances of axioms to which Mr. Stewart's reasoning did not apply. It is much as if a man, having asserted that there is no fish but what is capable of that species of locomotion called swimming, should expressly exclude oysters and some other shell-fish as not included in his class of fish. Whereupon some one comes, and without taking any notice of the limitation, affirms that the assertion is false, inasmuch as oysters, &c., do not swim. He might, having stated the limitation, endeavor to show that it was unfounded, or that the definition of 'fish' was altogether unphilosophical. That would have been perfectly fair. In like manner, Mr. Whewell might endeavor to show, that Mr. Stewart's excluded axioms were as truly such as those he had included—that they were selfevident or what not—but candor and fair dealing required that he should not have adduced as instances to which Mr. Stewart's reasoning did not apply-propositions to which Stewart himself expressly asserts he did not intend it to apply. In other words, he had no business to employ as against Mr. Stewart the word • axioms ’ in any other sense than that Mr. Stewart had explicitly attached to it. We are sorry to have been compelled to make these observations, but we do think the conduct on which we have animadverted unworthy of the ingenuousness of true genius and true science.