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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, in as much 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 favourite doctrine with respect to the influence of language upon thought. The paradoxical conclusions into which be 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 mathe
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 ;-Thy ToIRUTHY -φιδν αναλυση καλουμεν, οιον αναπαλιν λυσιν. 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) avaλvodi, xal ourθεῖναι, και διοριζεσθαι κατα πτωσιν.
+ M. Lacroix. See the Introduction to his Elements of Geometry.
maticians 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 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 call"ing 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 de"monstrations, 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 cir"cumstances, be either analytical or synthetical. Of the latter, an "elementary example occurs in the algebraical demonstrations 66 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 errours 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.†
THE CONSIDERATION OF THE INDUCTIVE LOGIC RESUMED.
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
*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 geometers. (See Vol. IV. p. 172.) The view of the subject which I have taken in the foreging section, has but little in common
common appellation, our superiour 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.
This difference in point of degree (it must at the same time be remembered) leads, where it is great, to important consequences.
with that given by this excellent philosopher; but in one or two instances, were we have both touched upon the same points, (particularly in the strictures upon the logic of Con dillac) 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 bave 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 ressemblance. Mais l'usage l'applique à une ressemblance éloignée: d'où vient que les conclusions analogiques sont sou vent 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'espéce. On nomme éloignée la ressemblance qui fonde les généralisations superieures, c'est-à-dire, le genre et ses divers degrès. Mais cette definition 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 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 decouvre aussi quelques différences indépendantes de la diversité du temps et du lieu. Lorsque nous ferons un jugement general, fondé sur la première espèce de ressemblance, nous dirons que nous usons de la methode 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 methode d'analogie conclut du semblable au semblable. Si l'on analyse ces definitions, on verra que nous n'avons fait autre chose que leur donner de la précision." (Essais de Philosophie, Tome 11 202.)
See also the remarks on induction and analogy in the four following articles of M. Prévost's works.
t[The word Analogy, in its origin, expresses only resemblance. But custom has applied it to a distant resemblance. Hence Analogical conclusions are often ventured upon, when they ought to be drawn with great care and skill. Always, when in our reasonings we transfer like conclusions to objects which have no other than a distant resemblance, we reason analogically. The nearest resemblance is that which forms the first generalization;
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. With all the imperfections of these arrangements, however, a judicious inquirer will pay so 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 reason. ing, in whatever manner the word is defined; provided only it be, understood to express some sort of correspondence or affinity
this we call the species. We call that resemblance distant, which forms the next superior generalization; that is to say, the Genus and its various degrees. But this definition is not rigorously followed.
However this may be, we can conceive cases between which the resemblance is so perfect, that we discover no other difference but that of time and place. And there are cases in which we perceive much resemblance, but in which we discover also some diversities, independent of those of time and place. When we make a general judgment, founded upon the first species of resemblance, we say that we make use of the method of induction. When the second species of resemblance authorizes our reasonings, we say that it is the method of analogy which we use. We commonly say, that the method of induction con cludes from particular to general, and that the method of analogy concludes from like to like. If we analyse those definitions, we shall find that we have done nothing but given them greater exactness.
between two subjects, which serves, as a principle of association or of arrangement, to unite them together in the mind.
According to Dr. Johnson, (to whose definition I allude more particularly at present) analogy properly means "a resemblance be"tween 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 66 may nevertheless be analogous; analogy consisting in a resem"blance or correspondence of relations."* As an illustration of this, Dr. Ferguson mentions the analogy between the fin of a fish and the wing of a bird; the fin bearing the same relation to the water, which the wing does to the air. This definition is more particularly luminous, when applied to the anologies which are the foundation of the rhetorical figures of metaphor and allusion; and it applies also very happily to those which the fancy delights to trace between the material and the intellectual worlds; and which (as I have repeatedly observed,) are so apt to warp the judgment in speculating concerning the phenomena of the human mind.
The pleasure which the fancy receives from the contemplation of such correspondences, real or supposed, obviously presupposes a certain disparity or contrast in the natures of the two subjects compared; and, therefore, analogy forms an associating principle, specifically different from resemblance, into which Mr. Hume's theory would lead us to resolve it. An additional proof of this is furnished by the following consideration, That a resemblance of objects or events is perceived by sense, and, accordingly, has some effect even on the lower animals; a correspondence (or, as it is frequently called, a resemblance) of relations, is not the object of sense, but of intellect, and consequently, the perception of it implies the exercise of reason.
Notwithstanding, however, the radical distinction between the notions expressed by the words resemblance and analogy, they may often approach very nearly to each other in their meaning; and cases may even be conceived in which they exactly agree. In proof of this, it is sufficient to remark, that in objects, the parts of which respectively exhibit that correspondence which is usually distinguished by the epithet analogous, this correspondence always deviates, less or more, from an exact conformity or identity; in so much, that it sometimes requires a good deal of consideration to trace in detail the parallel circumstances, under the disguises which they borrow from their diversified combinations. An obvious instance of this occurs when we attempt to compare the bones and joints in the leg and foot of a man with those in the leg and foot of a horse. Were the correspondence in all the relations perfectly exact,
* Principles of Moral and Political Science. Vol. I. p. 107.