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am afterwards to make, it will appear, that, without general terms, all our reasonings must necessarily have been limited to particulars; and, consequently, it is owing to the use of these, that the philosopher is enabled to speculate concerning classes of objects, with the same facility with which the favage or the peasant fpeculates concerning the individuals of which they are composed. The technical terms, in the different sciences, render the appropriated language of philosophy a still more convenient inftrument of thought, than those languages which have originated from popular use; and in proportion as these technical terms improve in point of precision and comprehensiveness, they will contribute to render our intellectual progress more certain and more rapid. “While engaged" (says Mr. Lavoisier) “in “ the composition of my elements of Chemistry, I “ perceived, better than I had ever done before, the “ truth of an observation of Condillac, that we think “ only through the medium of words; and that lan
guages are true analytical methods. Algebra, “ which, of all our modes of expression, is the most “ fimple, the most exact, and the best adapted to its
purpose, is, at the same time, a language and an
analytical method. The art of reasoning is noth“ing more than a language well arranged.” The influence which these very enlightened and philosophical views have already had on the doctrines of chemistry, cannot fail to be known to most of my readers.
The foregoing remarks, in so far as they relate to the possibility of assisting our reasoning and inven. tive powers, by new instrumental aids, may perhaps appear to be founded too much upon theory ; but this objection cannot be made to the reasonings I have offered on the importance of the study of method. To the justness of these, the whole history of science bears testimony; but more especially, the
histories of Physics and of pure Geometry ; which afford so remarkable an illustration of the general doctrine, as can scarcely fail to be fatisfactory, even to those who are the moft disposed to doubt the efficacy of art in directing the exertions of genius.
With respect to the former, it is sufficient to mention the wonderful effects which the writings of Lord Bacon have produced, in accelerating its progress. The philosophers, who flourished before his time, were, undoubtedly, not inferior to their lucceffors, either in genius or industry : but their plan of investigation was erroneous ; and their labours have produced only a chaos of fictions and absurdities. The illustrations which his works contain, of the method of induction, general as the terms are, in which they are expressed, have gradually turned the attention of the moderns to the rules of philofophifing ; and have led the way to those important and sublime discoveries in physics, which reflect so much honour on the present age.
The rules of philosophising, however, even in physics, have never yet been laid down with a sufficient degree of precision, minuteness, or method ; nor have they ever been stated and illustrated in so clear and popular a manner, as to render them intelligible to the generality of readers. The truth, perhaps, is ; that the greater part of physical inquirers have derived what knowledge of them they possess, rather from an attention to the excellent models of investigation, which the writings of Newton exhibit, than from any of the speculations of lord Bacon, or his commentators : and, indeed, such is the incapacity of most people for abstract reasoning, that I am inclined to think, even if the rules of inquiry were delivered in a perfectly complete and unexceptiona. ble form, it might still be expedient to teach them to the majority of students, rather by examples, than in the form of general principles. But it does not
therefore follow, that an attempt to illustrate and to methodize these rules, would be useless ; for it must be remembered, that, although an original and inventive genius, like that of Newton, be sufficient to establish a standard for the imitation of his age, yet, that the genius of Newton himself was encouraged and led by the light of Bacon's philosophy.
The use which the ancient Greek geometers made of their analysis, affords an additional illustration of the utility of method in guiding scientific invention. To facilitate the study of this species of investigation, they wrote no less than thirty-three preparatory book ; and they considered an address, in the practice of it, (or, as Marinus calls it a duvapais ávadutixn) as of much more value, than an extensive acquaintance with the principles of the science.* Indeed, it is well known, to every one who is at all conversant with geometrical investigations, that although it may be possible for a person, without the assistance of the method of analysis, to stumble accidentally on a solution, or on a demonstration ; yet it is impossible for him to pofsess a just confidence in his own powers, or to carry on a regular plan of invention and discovery. It is well known, too, that an acquaintance with this method brings geometers much more nearly upon a level with each other, than they would be otherwise : not that it is poslible, by any rules, to supercede, entirely, ingenuity and address; but, because, in consequence of the uniformity of the plan on which the method proceeds, experience communicates a certain dexterity in the use of it; which must in time give to a very ordinary degree of fagacity, a fuperiority, on the whole, to the greatest natural ingenuity, unafsifted by rule.t
Μειζον εςι το δυναμιν αναλυτικης κτησασθαι, του πολλας αποδειξεις των επι μέρους εχειν. .
+ " Mathematica multi sciunt, mathesin pauci. Aliud est enim nosse propositiones aliquot, et nonnullas ex iis obvias elicere, case
To these observations, I believe, I may add, that, after all that was done by the Greek philosophers to facilitate mathematical invention, many rules still remain to be suggested, which might be of important use, even in pure geometry. A variety of such occur to every experienced mathematician, in the course of his inquiries, although, perhaps, he may not be at the trouble to state them to himself in words; and it would plainly have saved him much expence of time and thought, beside enabling him to conduct his researches on a more regular plan, if he had been taught them fyftematically at the commencement of his studies. The more varied, abftrule, and general investigations of the moderns, stand in need, in a much greater degree, of the guidance of philosophical principles ; not only for enabling us to conduct, with skill, our particular researches, but for directing us to the different methods of reasoning, to which we ought to have recourse on different occafions. A collection of such rules would form, what might be called with propriety, the logic of mathe. matics; and would probably conrtibute greatly to the advancement of all those branches of knowledge, to which mathematical learning is fubfervient.
The observations which have been now made, on the importance of method in conducting physical and mathematical researches, particularly those which re. late to the last of these subjects, will not appřy lite: rally to our inquiries in metaphysics, morals, or
potius quam certa aliqua discurrendi norma, aliud scientiæ ipsius naturam ac indolem perspectam habere, in ejus se adyta penetrare, et as universalibus instructum esse præceptis, quibus theoremata ac problemata innumera excogitandi, eademque demonstrandi facilitas comparetur. Ut enim pictorum vulgus prototypon sæpe sæpius exprimendo, quendam pingendi usum, ruliam vero pictoriæ artis quam optica suggerit, scientiam adquirit, ita multi, lectis Euclidis et aliorum geometrarum libris, eorum imitatione fingere propositiones aliquas ac demonstrare solent, ipsam tamen secretissimam difficiliorum theorematam ae problematum solvendimethodum prorsus ignorant.”---Joannis de la Faille Theoremata de Centro Gravitatis, in præfat.-Antwerpæ, 1632.
politics ; because, in these sciences, our reasonings always consist of a comparatively small number of intermediate steps ; and the obstacles which retard our progress, do not, as in mathemnatics, arise from the difficulty of finding media of comparison among our ideas. Not, that these obstacles are less real, or more easily surmounted : on the contrary, it seems to require a still rarer combination of talents to furmount them; for how small is the number of indi. viduals, who are qualified to think juftly on metaphysical, moral, or political subjects ; in comparison of those, who may be trained by practice to follow the longest processes of mathematical reasoning. From what these obstacles arise, I shall not inquire particularly at present. Some of the more important of them may be referred to the imperfections of language ; to the difficulty of annexing precife and steady ideas to our words ; to the difficulty, in some cases, of conceiving the subjects of our reasoning; and, in others, of discovering, and keeping in view, all the various circumstances upon which our judgment ought to proceed; and above all, to the prejudices which early impreßions and affociations create, to warp our opinions.-To illustrate these sources of error, in the different sciences which are liable to be affected by them, and to point out the most effectual means for guarding against them, would form another very interesting article, in a philosophical system of logic.
The method of communicating to others, the principles of the different sciences, has been as much neglected by the writers on logic, as the rule of investigation and discovery; and yet, there is certainly no undertaking whatever, in which their assistance is more indispensibly requisite. The first principles of all the sciences are intimately connected with the