The passages in Condillac to which these criticisms refer, are all selected from his Treatise on Logic, written purposely to establish his favourite doctrine with respect to the influence of language upon thought. The paradoxical conclusions into which he himself has been led by an unwarrantable use of the words Analysis and Synthesis, is one of the most remarkable instances which the history of modern literature furnishes of the truth of his general principle.

Nor does this observation apply merely to the productions of his more advanced years. In early life he distinguished himself by an ingenious work, in which he professed to trace analytically the history of our sensations and perceptions; and yet it has been very justly remarked of late, that all the reasonings contained in it are purely synthetical. A very eminent mathematician of the present times has even gone so far as to mention it "as a model of geometrical synthesis." He would, I apprehend, have expressed his idea more correctly, if, instead of the epithet geometrical, he had employed, on this occasion, logical or metaphysical; in both of which sciences, as was formerly observed, the analytical and synthetical methods bear a much closer analogy to the experimental inductions of chemistry and of physics, than to the abstract and hypothetical investigations of the geometer.

The abuses of language which have been now under our review, will appear the less wonderful, when it is considered that mathematicians themselves do not always speak of Analy

any other in the imagination of Pappus, as the characteristical feature of geometrical analysis, appears indisputably from a clause already quoted from the preface to his 7th book;-Thy Teaútny podov ἀνάλυσιν καλοῦμεν, οἷον ἀνάπαλιν λύσιν. To say, therefore, as many writers have done, that the analysis of a geometrical problem consists in decomposing or resolving it in such a manner as may lead to the discovery of the composition or synthesis-is at once to speak vaguely, and to keep out of view the cardinal principle on which the utility of the

method hinges. There is, indeed, one species of decomposition exemplified in the Greek geometry,-that which has for its object to distinguish all the various cases of a general problem; but this part of the investigation was so far from being included by the ancients in their idea of analysis, that they bestowed upon it an appropriate name of its own ;-the three requisites to a complete solution being (according to Pappus) dváλveai, καὶ συνθεῖναι, καὶ διορίζεσθαι κατὰ πτώσιν.

1 M. Lacroix. See the Introduction to his Elements of Geometry.

sis and Synthesis with their characteristical precision of expression, the former word being frequently employed to denote the modern calculus, and the latter, the pure geometry of the ancients. This phraseology, although it has been repeatedly censured by foreign writers, whose opinions might have been expected to have some weight, still continues to prevail very generally upon the Continent. The learned and judicious author of the History of Mathematics complained of it more than fifty years ago, remarking the impropriety "of calling by the name of the synthetic method, that which employs no algebraical calculus, and which addresses itself to the mind and to the eyes, by means of diagrams, and of reasonings expressed at full length in ordinary language. It would be more exact," he observes farther, "to call it the method of the ancients, which (as is now universally known) virtually supposes, in all its synthetical demonstrations, the previous use of analysis. As to the algebraical calculus, it is only an abridged manner of expressing a process of mathematical reasoning;-which process may, according to circumstances, be either analytical or synthetical. Of the latter, an elementary example occurs in the algebraical demonstrations given by some editors of Euclid, of the propositions in his second book."1

This misapplication of the words analysis and synthesis is not, indeed, attended with any serious inconveniences, similar to the errors occasioned by the loose phraseology of Condillac. It were surely better, however, that mathematicians should cease to give it the sanction of their authority, as it has an obvious tendency-beside the injustice which it involves to the inestimable remains of Greek geometry-to suggest a totally erroneous theory with respect to the real grounds of the unrivalled and transcendent powers possessed by the modern calculus, when applied to the more complicated researches of physics.2

1 Histoire des Mathématiques, par Montucla, Tome Premier, pp. 175, 176. "In the ingenious and profound work of M. Degerando, entitled Des Signes

et de l'Art de Penser, considérés dans leur rapports mutuels, there is a very valuable chapter on the Analysis and Synthesis of metaphysicians and of

SECTION IV.-THE CONSIDERATION OF THE INDUCTIVE LOGIC

RESUMED.

[SUBSECTION] 1.-Additional Remarks on the distinction between Experience and Analogy. Of the grounds afforded by the latter for Scientific Inference and Conjecture.

In the same manner in which our external senses are struck with that resemblance between different individuals which gives rise to a common appellation, our superior faculties of observation and reasoning, enable us to trace those more distant and refined similitudes which lead us to comprehend different species under one common genus. Here, too, the principles of our nature already pointed out, dispose us to extend our conclusions from what is familiar to what is comparatively unknown, and to reason from species to species, as from individual to individual. In both instances, the logical process of thought is nearly, if not exactly, the same, but the common use of language has established a verbal distinction between them, our most correct writers being accustomed (as far as I have been able to observe) to refer the evidence of our conclusions, in the one case to experience, and in the other to analogy. The truth is, that the difference between these two denominations of evidence, when they are accurately analyzed, appears manifestly to be a difference, not in kind but merely in degree; the discriminative peculiarities of individuals invalidating the inference, as far as it rests on experience solely, as much as the characteristical circumstances which draw the line between different species and different genera.1

geometers. (See vol. iv. p. 172.) The view of the subject which I have taken in the foregoing section, has but little in common with that given by this excellent philosopher; but in one or two instances, where we have both touched upon the same points, (particularly in the strictures upon the logic of Condillac,) there is a general coincidence

between our criticisms, which adds much to my confidence in my own conclusions.

1 In these observations on the import of the word analogy, as employed in philosophical discussions, it gives me great pleasure to find that I have struck nearly into the same train of thinking

This difference in point of degree (it must at the same time be remembered) leads, where it is great, to important consequences. In proportion as the resemblance between two cases diminishes in the palpable marks which they exhibit to our senses, our inferences from the one to the other are made with less and less confidence; and, therefore, it is perfectly right that we should reason with more caution from species to species, than from individual to individual of the same kind. In what follows, accordingly, I shall avail myself of the received distinction between the words experience and analogy; a distinction which I have hitherto endeavoured to keep out of view, till I should have an opportunity of explaining the precise notion which I annex to it. It would, in truth, be a distinction of important use in our reasonings, if the common arrangements, instead of originating, as they have often done, in ignorance or caprice, had been really the result of an accurate observation and comparison of particulars. these arrangements, however, a with M. Prévost. I allude more particularly to the following passage in his Essais de Philosophie.

"Le mot Analogie, dans l'origine, n'exprime que la ressemblance. Mais l'usage l'applique à une ressemblance éloignée d'où vient que les conclusions analogiques sont souvent hasardées, et ont besoin d'être déduites avec art. Toutes les fois donc que, dans nos raisonnemens, nous portons des jugemens semblables sur des objets qui n'ont qu'une ressemblance éloignée, nous raisonnons analogiquement. La ressemblance prochaine est celle qui fonde la première généralisation, celle qu'on nomme l'espèce. On nomme éloignée la ressemblance qui fonde les généralisations supérieures, c'est-à-dire, le genre et ses divers degrès. Mais cette définition n'est pas rigoureusement suivie.

"Quoiqu'il en soit, on conçoit des cas, entre lesquels la ressemblance est si parfaite, qu'il ne s'y trouve aucune

With all the imperfections of judicious inquirer will pay so différence sensible, si ce n'est celle du tems et du lieu. Et il est des cas dans lesquels on apperçoit beaucoup de ressemblance, mais où l'on découvre aussi quelques différences indépendantes de la diversité du temps et du lieu. Lorsque nous ferons un jugement général, fondé sur la première espèce de ressemblance, nous dirons que nous usons de la méthode d'induction. Lorsque la seconde espèce de ressemblance autorisera nos raisonnemens, nous dirons que c'est de la méthode d'analogie que nous faisons usage. On dit ordinairement que la méthode d'induction conclut du particulier au général, et que la méthode d'analogie conclut du semblable au semblable. Si l'on analyse ces définitions, on verra que nous n'avons fait autre chose que leur donner de la précision." Essais de Philosophie, tome ii. p. 202.

See also the remarks on Induction and Analogy in the four following articles of M. Prévost's work.

much regard to prevailing habits of thinking, as to distinguish very scrupulously what common language refers to experience from what it refers to analogy, till he has satisfied himself, by a diligent examination, that the distinction has, in the instance before him, no foundation in truth. On the other hand, as mankind are much more disposed to confound things which ought to be distinguished, than to distinguish things which are exactly or nearly similar, he will be doubly cautious in concluding, that all the knowledge which common language ascribes to experience is equally solid; or that all the conjectures which it places to the account of analogy are equally suspicious.

A different idea of the nature of analogy has been given by some writers of note; and it cannot be denied, that, in certain instances, it seems to apply still better than that proposed above. The two accounts, however, if accurately analyzed, would be found to approach much more nearly than they appear to do at first sight; or rather, I am inclined to think, that the one might be resolved into the other, without much straining or over refinement. But this is a question chiefly of speculative curiosity, as the general remarks which I have now to offer will be found to hold with respect to analogy, considered as a ground of philosophical reasoning, in whatever manner the word is defined; provided only it be understood to express some sort of correspondence or affinity between two subjects, which serves, as a principle of association. or of arrangement, to unite them together in the mind.

"a re

According to Dr. Johnson, (to whose definition I allude. more particularly at present,) analogy properly means semblance between things with regard to some circumstances or effects; as when learning is said to enlighten the mind;that is, to be to the mind what light is to the eye; by enabling it to discover that which was hidden before." The statement is expressed with a precision and justness not always to be found in the definitions of this author; and it agrees very nearly with the notion of analogy adopted by Dr. Ferguson,— that "things which have no resemblance to each other may