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 COPLES TON'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 théorème 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

requires to be peculiarly impressed on them, namely, to acquaint themselves, in some moderate degree, with the general nature of the subject, before they adduce detached points of objection as fatal to the whole train of conclusions.

To take, however, an instance of the kind of objection alluded to: one geologist dwells on the uncertainty attending a positive distinction of particular formations from their mineral characters alone, and insists on the attainment of certainty only from their characteristic fossil remains. Another remarks that, in some particular cases, considerable ambiguity attaches to the determination of fossil remains, and that those really belonging to different formations may, in some instances, be confounded together. Hence the objector contends that the argument "halts on both its legs," and triumphs in his inference that there can be no certainty at all in the science! In other words, because either source of evidence alone may be defective, therefore both together cannot be satisfactory. Or again, because, in some instances, there may be confessed ambiguities in the interpretation, therefore in no case can there be any certainty. A passage is sometimes cited from Cuvier's account of his researches on fossil bones, in which he, with all the caution of a true philosopher, carefully insists on all the sources of fallacy by which his inquiries were liable to be affected; and speaks, with becoming modesty, of his conclusions, as often being far removed from the evidence of demonstration. And this is then construed by the sceptic into a confession that the whole science has no solid foundation, and is little more than a system of gratuitous hypotheses!

It would be useless to dwell further on such speculations. I should not, perhaps, have noticed them at all, had they not recently received a certain stamp of respectability from their association with the name of a writer of old repute,

who has thought it necessary, at the present day, to reappear in a field so different from that of moral and religious discussion, in which his former distinction might have given weight to his opinions: I allude to a pamphlet entitled, Considerations on Modern Theories of Geology, &c., by T. GISBORNE, M.A., Prebendary of Durham. London, 1837. This is surely not an age in which dignitaries of the Church should be found arraying themselves in hostility to

science.

NOTE C. p. 87.

LORD BROUGHAM in his Discourse on Natural Theology, in a note on Cause and Effect, after stating the nature, and upholding the soundness (as far as it goes,) of Hume's doctrine of causation, yet contends that something more is necessary to a complete view of the subject. Besides the notion of invariable sequence, he maintains we have also a "belief that the one event occasions the other; that there is between the two a connexion beyond the mere relation of junction and sequence, and that the preceding event exerts an influence, a force, a power, over the other, and produces the other."-p. 228.

And the grounds of this belief, he contends, are to be found in the proofs, 1st, of the invariable sequence; 2nd, of the condition that "not only must the second event always have been found to follow the first, but the second must never have been observed without the first preceding it, or at least without some other preceding it, in which case the causation is predicated alike of both these preceding events."-p. 229.

Or, in fewer words, we must prove "that one event