viously surveyed with attention, yet that the prospect is never more distinct, than when it is circumscribed within narrow bounds, and only a small number of objects is taken in at once. We always discern with accuracy

but a part of what we see."

"The case," he continues, "is similar with the intellectual eye. I have, at the same moment, present to it, a great number of the familiar objects of my knowledge. I see the whole group, but am unable to mark the discriminating qualities of individuals. To comprehend with distinctness all that offers itself simultaneously to my view, it is necessary that I should, in the first place, decompose the mass;-in a manner analogous to that in which a curious observer would proceed in decom- · posing, by successive steps, the co-existent parts of a landscape. It is necessary for me, in other words, to analyze my thoughts."

The same author afterwards endeavours still farther to unfold his notion of analysis, by comparing it to the natural procedure of the mind in the examination of a machine. "If I wish," says he, "to understand a machine, I decompose it, in order to study separately each of its parts. As soon as I have an exact idea of them all, and am in a condition to replace them as they were formerly, I have a perfect conception of the machine, having both decomposed and recomposed it." †

In all this, I must confess, there seems to me to be much, both of vagueness and of confusion. In the two first quotations, the word analysis is employed to denote nothing more than that separation into parts, which is necessary to bring a very extensive or a very complicated subject within the grasp of our faculties ;-a description, certainly, which conveys but a very partial and imperfect conception of that analysis which is represented as the great organ of invention in all the sciences and arts. In the example of the machine, Condillac's

Ibid. In this last paragraph, I have introduced one or two additional clauses which seemed to me necessary for conveying clearly the author's idea. Those who take the trouble to compare it with the original, will be satisfied, that, in venturing on these slight interpolations, I had no wish to misrepresent his opinion.

† Ibid. Chap. iii.

"Ce qu'on nomme méthode d'invention, n'est autre chose que l'analyse. C'est

language is somewhat more precise and unequivocal; but when examined with attention, will be found to present an illustration equally foreign to his purpose. This is the more surprising, as the instance here appealed to might have been expected to suggest a juster idea of the method in question, than that which resolves into a literal de-composition and re-composition of the thing to be analyzed. That a man may be able to execute both of these manual operations on a machine, without acquiring any clear comprehension of the manner in which it performs its work, must appear manifest on the slightest reflection; nor is it less indisputable, that another person, without disengaging a single wheel, may gain by a process purely intellectual, a complete knowledge of the whole contrivance. Indeed, I apprehend, that it is in this way alone that the theory of any complicated machine can be studied; for it is not the parts, separately considered, but the due combination of these parts, which constitutes the mechanism.* An observer, accordingly, of common sagacity, is here guided by the logic of nature, to a species of analysis, bearing as much resemblance to those of mathematicians and of natural philosophers, as the very different nature of the cases admits of. Instead of allowing his eye to wander at large over the perplexing mazes of such a labyrinth, he begins by remarking the ultimate effect; and thence proceeds to trace backwards, step by step, the series of intermediate movements by which it is connected with the vis motrix. In doing so, there is undoubtedly a sort of mental decomposition of the machine, inasmuch as all its parts are successively considered in detail; but it is not this decomposition which constitutes the analysis. It is the methodical retrogradation from the mechanical effect to the mechanical power.†

elle qui a fait toutes les découvertes; c'est par elle que nous retrouverons tout ce qui a été trouvé." Ibid.

ry.

*If on any occasion, a literal decomposition of a machine should be found necessaonly be to obtain a view of some of its parts, which in their combined state from observation.

ircumstance of retrogradation or inversion, figured more than any magination of Pappus, as the characteristical feature of geometrical es indisputably from a clause already quoted from the preface to his ὴν τοιαύτην ἔφοδον ἀνάλυσιν καλοῦμεν, οἷον ἀνάπαλιν λύσιν. Το say, there

The passages in Condillac to which these criticisms refer, are all selected from his treatise on Logic, written purposely to establish his favorite 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 analysis 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.

fore, 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) ávaλõoxı, xaì curbiīvaı, καὶ διορίζεσθαι κατὰ πτῶσιν.

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

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."*

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 was 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 transcendant powers possessed by the modern calculus, when applied to the more complicated researches of physics.†

SECTION IV.

THE CONSIDERATION OF THE INDUCTIVE LOGIC RESUMED.

I.

Additional Remarks on the distinction between Experience and Analogy. Of the grounds afforded by the latter for Scientific Inference and Conjecture.

IN the same mannner 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 specie and different genera.*

erine, n'exprime que la ressemblance. Mais l'usage ignée: d'où vient que les conclusions analogiques in d'être déduites avec art. Toutes les fois donc,