It is often in our power to obtain an analogy where we cannot have an induction; in which case reasoning from analogy ought to be admitted; however, with all that uncertainty which properly belongs to it, considered as more or less distant from induction, as built upon more or fewer dependent or independent evidences, &c. Analogy may also, in all cases, be made use of as a guide to the invention. But coincidence in mathematical matters, and induction in others, wherever they can be had, must be sought for as the only certain tests of truth. However, induction seems to be a very sufficient evidence in some mathematical points, affording at least as much evidence there as in natural philosophy; and may be safely relied on in perplexed cases, such as complex series, till satisfactory demonstrations can be had.
The analogous natures of all the things about us are a great assistance in decyphering their properties, powers, laws, &c. inasmuch as what is minute or obscure in one may be explained and illustrated by the analogous particular in another, where it is large and clear. And thus all things become comments on each other in an endless reciprocation.
When there are various arguments for the same thing taken from induction or analogy, they may all be considered as supporting one another in the same manner as independent evidences. Thus, if it could be shewed, that the human understanding is entirely dependent on association, (as is remarked in this and the last section,) the many analogies and connexions between the understanding and affections, as these terms are commonly understood and contradistinguished by writers, would make it very probable, that association presides in the same manner in the generation of the affections; and vice versâ. And the more analogies, and mutual connexions, between the understanding and affections, were produced, so many more independent or concurrent evidences would there be for this prevalence of association in one, admitting it in the other. But, if now it be shewn farther, that the understanding and affections are not really distinct things, but only different names, which we give to the same kind of motions in the nervous system, on account of a difference in degree, and other differences which it would be tedious here to enumerate, but which make no difference in respect of the power of association, then all the arguments from analogy are transformed into one of induction; which, however, is stronger than the united force of them all. For now it may be shewed, that association must prevail in each motion in the brain, by which affection is expounded, from a large induction of particulars, in which it prevails in the generation of ideas, or of the motions by which they are expounded, and which we suppose to be proved to be of the same kind with those that expound the affections. Thus also inductions may be taken from the smell and taste of bread, to prove it wholesome; which would both be transformed into one simple argument stronger
