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NOTES AND ILLUSTRATIONS.

NOTES AND ILLUSTRATIONS.

NOTE A. p. 18.

To the logical reader, the object of the whole discussion in this section may be explained in a word; induction (in its physical sense) is the process of collecting the evidence for the truth of the premises of the syllogism into which logic analyzes the reasoning. Our present question refers more especially to that which is at once the most difficult and important part, the evidence for the major.-See ARCHBISHOP WHATELY's Logic, pp. 207 and 228.

The mistake of some writers in supposing that in the enthymematic form, the suppressed premiss is the minor, seems to me not improbably traced to the view they appear to adopt, that the perfect case of induction would be that in which every individual was examined ; the less accurate when only a few. Yet as we have observed above, the last are the only cases in which any reasoning takes place.

Logic being nothing else than the theory of conclusiveness, includes in its analysis the reasoning which takes place in induction as well as in all other cases. It is from a total misconception, therefore, that the dialectic and inductive are often represented as two rival methods on the one hand, or expected to be auxiliaries on the other.

It may, perhaps, be necessary here to remark that the word “ analogy,” which so frequently occurs in this discussion, is invariably used by me in the simple sense of a parallelism or correspondence between two sets of things or events, which may have no similarity or resemblance whatever; analogy is a similarity of relation merely, not of qualities. Those readers to whom the distinction may not be familiar, are referred for a full and luminous exposition of the whole case to the notes on BISHOP COPLESTON's Inquiry into the Doctrines of Necessity, &c., p. 122; or to ARCHBISHOP WHATELY's Logic, p. 168.

The reader will find an excellent brief summary of the nature of induction in the Introduction to Dr. HAMPDEN'S Bampton Lectures, 1837, p. 29.

The view here taken of induction and physical analogy is admirably illustrated in the following masterly passage of Laplace :

“ L'induction, l'analogie, des hypotheses fondées sur les fait et rectifiées sans cesse par de nouvelles observations, un tact heureux donné par la nature et fortifié par des comparaisons nombreuses de ses indications avec l'experience; tels sont les principaux moyens de parvenir à la vérité.

“Si l'on considère avec attention, la serie des objets de même nature; on aperçoit entre eux et dans leurs changemens, des rapports et des lois qui se manifestent de plus en plus, à mesure que la série se prolonge, et qui, en s'étendant et se généralisant sans cesse, conduisent enfin au principe dont ils dependent. Mais souvent ces lois et ces rapports sont enveloppés de tant de circonstances étrangères, qu'il faut une grand sagacité pour les démêler, et pour remonter à ce principe; c'est en cela que consiste le veritable génie des sciences. L'analyse et la philosophie naturelle doivent leurs plus importantes découvertes, à ce moyen fécond que l'on nomme induction. Newton lui a été redevable de son théoréme du binome, et du principe de la gravitation universelle. Il est difficile d'apprécier la probabilité de ses résultats. Elle se fonde sur ce que les rapports et les lois les plus simples, sont les plus communs; c'est se qui se vérifie dans les formules de l'analyse, et ce que l'on retrouve dans les phénomenes naturels, dans la cristallisation, et dans les combinaisons chimiques. Cette simplicité de lois, et de rapports ne paraîtra point étonnante, si l'on considère que tous les effets de la nature, ne sont que les résultats mathématiques d'un petit nombre de lois immuables.”

“ L'analogie est fondée sur la probabilité que les choses semblables ont des causes du même genre, et produisent les mêmes effets. Plus la similitude est parfaite, plus grande est cette probabilité.”—LAPLACE, Essai Philosophique sur les Probabilités, pp. 168–172.

With regard to the importance of analogical considerations, as the guides of inductive research (above spoken of), we shall, perhaps, be reminded (as has been often said,) that the most important philosophical discoveries have been made by chance. It was, however, the observation of D'Alembert, “ Ces hazards ne sont que pour ceux qui jouent bien.” And it seems to me a still more just view of the matter that the chances happen to all alike, though a few only know how to make use of them: viz., those who are thoroughly possessed with just views of natural analogies.

Note B. p. 62.

To expose the various and most preposterous perversions of geological evidence which have acquired popularity, would be an endless task. I will merely observe with respect to the authors of such misrepresentations, that, in common fairness, there is one requisition, the propriety of which

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