deserved reputation in the present times. I must not, however, pass over in silence the name of Condillac, who has certainly contributed, more than any other individual, to the prevalence of the logical errors now under consideration. "I know well," says he on one occasion, "that it is customary to distinguish different kinds of analysis; the logical analysis, the metaphysical, and the mathematical; but there is, in fact, only one analysis; and it is the same in all the sciences." (La Logique, Seconde Partie, chap. vii.) On another occasion, after quoting from the logic of Port Royal a passage in which it is said, is said, "That analysis and synthesis differ from each other only, as the road we follow in ascending from the valley to the mountain differs from the road by which we descend from the mountain into the valley," Condillac proceeds thus: "From this comparison, all I learn is, that the two methods are contrary to one another, and consequently, that if the one be good, the other must be bad. In truth, we cannot proceed otherwise than from the known to the unknown. Now, if the thing unknown be upon the mountain, it will never be found by descending into the valley; and if it be in the valley, it will not be found by ascending the mountain. There cannot, therefore, be two contrary roads by which it is to be reached. Such opinjons," Condillac adds, "do not deserve a more serious criticism." (Ibid. chap. vi.)

To this very extraordinary argument it is unnecessary to offer any reply, after the observations already made on the analysis and synthesis of the Greek geometers. In the application of these two opposite methods to their respective functions, the theoretical reasoning of Condillac is contradicted by the universal experience of mathematicians, both ancient and modern; and is indeed so palpably absurd, as to carry along with it its own refutation, to the conviction of every person capable of comprehending the terms of the question.-Nor would it be found more conclusive or more intelligible, if applied to the analysis and synthesis of natural philosophers; or indeed to these words, in any of the various acceptations in which they have ever hitherto been understood. As it is affirmed, however, by Condillac, that "there neither is, nor can be, more than one analysis," a refutation of his reasoning, drawn from any particular science, is, upon his own principle, not less conclusive, than if founded on a detailed examination of the whole circle of human knowledge. I shall content myself, therefore, on the present occasion, with a reference to the mathematical illustrations contained in the former part of this section.

With regard to the notion annexed to this word by Condillac himself, I am not certain if, after all that he has written in explanation of it, I have perfectly seized his meaning. "To analyze, (he tells us, in the beginning of his Logic,) is nothing more than to observe in a successive order, the qualities of an object, with the view of giving them in the mind that simultaneous order in which

they co-exist." (La Logique, Première Partie, chap. ii.) In illustration of this definition, he proceeds to remark, that "although with a single glance of the eye, a person may discover a multitude of objects in an open champaign which he has previously 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 decomposing, by successive steps, the co-existent parts of a landscape.-It is necessary for me, in other words, to analyze my thoughts."* (Ibid. chap. ii.)

The same author afterwards endeavors 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." (Ibid. chap. iii.)

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 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 decomposition and recomposition of the thing to be analyzed. That a man may be able to execute both of these manual operations on a machine, without acquiring

* 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.

Ce qu'on nomme méthode d'invention, n'est autre chose que l'analyse. C'est elle qui a fait toutes les découvertes; c'est par elle que nous retrouverons tout ce qui a été trouvé.-La Logique, chap. iii.

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 admit of. Instead of allowing his eye to wander at large over the perplexing mazes of such a labarynth, 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.†

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 unwarantable 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

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

That this circumstance of retrogradation or inversion, figured more than 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 :— Την τοιαύτην έφοδον αναλυσιν καλούμεν, οιον αναπαλιν λυσιν. Το 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 Pap pus,αναλύσαι, και συνθεῖναι, και διορίζεσθαι κατα πτωσιν.

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 now been 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. This phraseology, although it has been more than once 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 conplained of it more than fifty years ago; remarking on 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 alegebraical 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 were surely better, however, that mathematicians should cease to give it the sanction of their authority, as it has an obvious tendency.besides 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.t

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

↑ Histoire des Mathématiques, par Montucla, tome premier, pp. 175, 176. In the ingenious and profound work of M. De Gerando, 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 geome

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 manner in which our external senses are struck with that resemblance between different individuals which give 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 discriminating 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.*

ters. (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.

* 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 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 resemblance. Mais l'usage l'applique à une ressemblance éloignée d'ou vient que les conclusions analogiques sont souveut hasardées, et ont besoin d'êtres 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 resemblance prochaine est celle qui fonde la première généralisation, celle qu'on nomme l'espèce. On nomme éloignée la resemblance qui fonde les généralisations superieures, c'est-à-dire, le genre et ses divers degrès. Mais cette definition n'est pars rigoureusement suivie.

"Quoiqu'il en soit, on conçoit des cas, entre lesquels la ressemblance est si parfaite, qu'il ne s'y trouve aucune difference sensible, si ce n'est celle du tems et du lieu. Et il est des cas dans lesquels on apperçoit beaucoup de resemblance, mais