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parts of the universe." "At least, (he adds) I see nothing ❝ of contradiction in all this*." Would Newton have sed himself with equal scepticism concerning the universality of his binomial theorem; or admitted the possibility of a single exception to it, in the indefinite progress of actual involution? In short, did there exist the slightest shade of difference between the degree of his assent to this inductive result, and that extorted from him by a demonstration of Euclid?

Although, therefore, the mathematician, as well as the natu ral philosopher, may, without any blameable latitude of expression, be said to reason by induction, when he draws an inference from the known to the unknown, yet it seems indisputable, that, in all such cases, he rests his conclusions on grounds essentially distinct from those which form the basis of experi mental science.

The word analogy, too, as well as induction, is common to physics, and to pure mathematics. It is thus we speak of the analogy running through the general properties of the different conic sections, with no less propriety than of the analogy running through the anatomical structure of different tribes of animals. In some instances, these mathematical analogies are collected by a species of induction; in others, they are inferred as consequences from more general truths, in which they are included as particular cases. Thus, in the curves which have just been mentioned, while we content ourselves (as many ele

• Query 31.

mentary writers have done)* with deducing their properties from mechanical descriptions on a plane, we rise experimentally from a comparison of the propositions which have been separately demonstrated with respect to each curve, to more comprehensive theorems, applicable to all of them; whereas, when we begin with considering them in their common origin, we have it in our power to trace from the source, both their generic properties, and their specific peculiarities. The satisfaction arising from this last view of the subject can be conceived by those alone who have experienced it; although I am somewhat doubtful whether it be not felt in the greatest degree by such as, after having risen from the contemplation of particular truths to other truths more general, have been at last conducted to some commanding station, where the mutual connections and affinities of the whole system are brought, at once, under the range of the eye. Even, however, before we have reached this vantage-ground, the contemplation of the analogy, considered merely as a fact, is pleasing to the mind; partly, from the mysterious wonder it excites, and partly from the convenient generalization of knowledge it affords. To the experienced mathematician this pleasure is farther enhanced, by the assurance which the analogy conveys, of the existence of yet undiscovered theorems, far more extensive and luminous than those which have led him, by a process so indirect, so tedious, and comparatively so unsatisfactory, to his general conclusions.

L'Hospital, Simson, &c.

In this last respect, the pleasure derived from analogy in mathematics, resolves into the same principle with that which seems to have the chief share in rendering the analogies among the different departments of nature so interesting a subject of speculation. In both cases, a powerful and agreeable stimulus is applied to the curiosity, by the encouragement given to the exercise of the inventive faculties, and by the hope of future discovery, which is awakened and cherished. As the analogous properties (for instance) of the conic sections, point to some general theorems of which they are corollaries; so the analogy between the phenomena of Electricity and those of Galvanism irresistibly suggests a confident, though vague anticipation of some general physical law comprehending the phenomena of both, but differently modified in its sensible results by a diversity of circumstances *. Indeed, it is by no means impossible, that the pleasure we receive even from those analogies which are the foundation of poetical metaphor and simile, may be found resolvable, in part, into the satisfaction connected with the supposed discovery of truth, or the supposed acquisition of knowledge; the faculty of imagination giving to these illusions a momentary ascendant over the sober conclusions of experience; and gratifying the understanding with a flattering consciousness of its own force, or at least with a consolatory forgetfulness of its own weak

ness.

See Note (Y.)

SECTION V.

Of certain misapplications of the words Experience and Induction in the phraseology of Modern Science.-Illustrations from Medicine and from Political Economy.

In the first Section of this Chapter, I endeavoured to point out the characteristical peculiarities by which the Inductive Philosophy of the Newtonians is distinguished from the hypothetical systems of their predecessors; and which entitle us to indulge hopes with respect to the permanent stability of their doctrines, which might be regarded as chimerical, if, in anticipating the future history of science, we were to be guided merely by the analogy of its revolutions in the ages that are past.

In order, however, to do complete justice to this argument, as well as to prevent an undue extension of the foregoing conclusions, it is necessary to guard the reader against a vague application of the appropriate terms of inductive science to inquiries which have not been rigorously conducted, according to the rules of the inductive logic. From a want of attention to this consideration, there is a danger, on the one hand, of lending to sophistry or to ignorance the authority of those illustrious names whose steps they profess to follow; and, on the other, of bringing discredit on that method of investigation, of which the language and other technical arrangements have been thus perverted.

Among the distinguishing features of the new logic, when considered in contrast with that of the schoolmen, the most prominent is the regard which it professes to pay to experience, as the only solid foundation of human knowledge. It may be worth while, therefore, to consider, how far the notion commonly annexed to this word is definite and precise; and whether there may not sometimes be a possibility of its being employed in a sense more general and loose, than the authors who are looked up to as the great models of inductive investigation understood it to convey *.

As the reflections which follow are entirely of a practical nature, I shall express myself (as far as is consistent with a due regard to precision) agreeably to the modes of speaking in common use; without affecting a scrupulous attention to some speculative distinctions, which, however curious and interesting, when considered in connection with the Theory of the Mind, do not lead to any logical conclusions of essential importance in the conduct of the Understanding. In such sciences, for example, as Astronomy, Natural Philosophy, and Chemistry, which rest upon phenomena open to the scrutiny of every inquirer, it would obviously be puerile in the extreme to attempt drawing the line between facts which have been ascertained by our own personal observation, and those which we have implicitly adopted upon our faith in the universal consent of the scientific world. The evidence, in both cases, may be equally irresistible; and sometimes the most cautious reasoners may justly be disposed to consider that of testimony as the least fallible of the two.

By far the greater part, indeed, of what is commonly called experimental knowledge, will be found, when traced to its origin, to resolve entirely into our confidence in the judgment and the veracity of our fellow-creatures; nor (in the sciences already mentioned) has this identification of the evidence of testimony with that of experience, the slightest tendency to affect the legitimacy of our inductive conclusions.

In some other branches of knowledge, (more particularly in those political doctrines which assume as incontrovertible data the details of ancient history) the authority of testimony is, for obvious reasons, much more questionable; and to dignify it, in these, with the imposing character of experience, is to strengthen one of the chief bul

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