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The minds of the ancient philosophers teemed with speculative schemes of nature before any study of facts had furnished them with substantial materials. Hum- boldt has well observed, that " long before the dis- covery of the New World it was thought land could be seen in the west from the Canaries and the Azores. They were phantasms not produced by any extraordinary refraction of the rays of light, but merely by a longing for the distant, for that which lies beyond the present. The natural philosophy of the Greeks, and the physics of the middle ages and even of much later centuries, presented swarms of such fantastic forms to the imagination. The mental eye still essays to pass the horizon of limited know- 12 INDUCTIVE PRINCIPLE. Something But, from considering tlfe nature of our gene- more than tion gina " ralisations, it is argued, that we must necessarily obtain ideas from some other source than sense, or that the mind possesses a peculiar power or faculty of acquiring a higher degree of certainty from within than experience can give from without. When we analyse the process logically, it is Logical analysis of manifest that, in induction, what is superadded to induction. In the first place, I think it will be allowed, on Mental pro- cesses car- reflection, that general conceptions of this kind, ried on uncon- however apparently abstract in their nature, may sciousiy. Assumption The primary assumption involved in all in- of the uni- formity of duction is the presumed uniformity of phenomena, nature.

Idea of It 18, then, perfectly true that no inductive pro- generalisa- tion derived cess can advance without the assumption of this from gra- dual buy a custom research paper expe- generalising principle, which is, nevertheless, ante- ricnce. Proneness It is true that there exists in the human mind a to hasty generaiisa- strong natural propensity to draw hasty inferences, tion. By trial of theoretical suggestions in succession, and only after repeated failure, we learn their erro- neous nature.

But thus by acquiring more caution and confidence and adopting better conjectures, we revise and amend cheapest paper writing service our attempts, and learn to proceed on more sound principles, until we gain a habit of generalisation worthy the name of inductive power. Again, the tendency to make the primary induc- tive assumption, and the extent to which it reaches, admit of many degrees. It is found in its higher perfection in buy a custom research paper those comprehensive views which con- stitute the discoveries of the greatest philosophers, and in varied inferior degrees in other instances. In the order of time, also, it is always evinced with far less effect in the earlier stages of scientific ESSAY I. But as the cultivation of inquiry advances, the Gains strength by inductive process by habitual exercise derives force advance of experience. And in any case even of the most limited indue- And from absence of tion, there is one argument on which, more than any contradic- tory cases.

The wow-occurrence of such an exception against a sup- posed law is a far stronger argument than the occurrence of hundreds of instances in its favour : and this consideration probably operates far more strongly with most minds than any abstract prin- ciple of conviction. NO intui- If there be any force in what has been advanced, tive percep- tion of ex- then, instead of any primary or inherent principle, ternal truth. It arises in the first instance out of the power of abstraction, acting with unconscious force and power- ful rapidity, by whose aid the mind creates what are indeed new conceptions, yet formed only out of materials already furnished, and this not by addition, but by subtraction of properties and particulars.

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Mainly Above all, the process derives its whole force from aided by perception the discovery and acceptance of sound and well- of analogy. The application of a higher reasoning to the mere Application buy a custom research paper of mathe- facts of observation which essentially constitutes maticai reasoning. Thus the two systems react on each other, and we are often en- abled to carry on our views, and predict results to which no mere extension of observation could have conducted us. The process of inductive generalisation indeed C 2 20 INDUCTIVE PKINCIPLE. Corre- spondence of mathe- matical and physical truths. Asserted a priori evi- dence of physical truths, ex- amined in several in- stances. The application of mathematical formulas, if found to apply to the subject, not only leads with greater readiness to general laws, but carries with it a powerful presumption in many cases that it is really the exponent of some actual and higher natural analogy which we could never have collected from any mere observation of facts.

But this assertion of a priori evidence is some- times made with reference to the primary princi- ples of all natural philosophy the laws of motion and of equilibrium whether in solids or fluids. Now, in the first place, I would observe, that the very notions of a body in uniform rectilinear motion, or of forces acting on it, are essentially ideas of experience, and certainly could have no application without reference to the real existence of matter and force. But such perplexity would be removed if we only put the c 3 22 INDUCTIVE PRINCIPLE. Equili- Again, it has been sometimes asserted, that the brium. When some such principles have been adopted, we can then, and then only, by strict deductive reasoning from them, arrive at the theorem of the lever, which we find confirmed by buy a custom research paper experiment. Undoubtedly the mind can infer deductively this great law of fluids, as a necessary consequence from certain other assumptions, that is, when certain, yet more elementary properties of fluids are known, and taken as the basis of the science, but not other- wise.

Abstract It is, indeed, quite conceivable that a reasoning theory may be con- being, who had never seen a fluid, might imagine ceived. Example of This is no imaginary case : it actually occurs in the undula- tory theory, the speculations pursued by so many philosophers on an imagined sethereal medium.

When, however, by the aid of the eye, the pheno- Unapplied till optical mena of optics present themselves, we find a vast facts are introduced. Nevertheless, such applications of mathematics confer the highest pre- sumption, little or at all short of certainty, for generalising conclusions actually observed to be true only in one or two instances.

To take, perhaps, the strongest instance which inverse square of has been adduced. The law of force or intensity the dis- tance, varying as the inverse square of the distances, it is alleged, and doubtless with truth, is a conception of pure reason (so far as any mathematical conception is so) from abstract geometrical considerations, which 26 INDUCTIVE PRINCIPLE.

But though these geometrical ideas throughout may be pure creations of the mind, yet the idea of any such emanation of actual force, however abs- tract, must have been derived from some ideas of experience, and certainly can apply to nothing in nature without reference to such sensible ideas.

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