these phænomena, so that the law of their production must be very complex; if a new hypothesis be required to account for every new combination of these phænomena; or, at least, one that differs considerably from itself; the best hypothesis which we can form, i.e. the hypothesis which is most conformable to all the phænomena, will amount to no more than an uncertain conjecture; and yet still it ought to be preferred to all others, as being the best that we can form.
That instantaneous and necessary coalescence of ideas, which makes intuitive evidence, may be considered as the highest kind of induction, and as amounting to a perfect coincidence of the effect concluded with those from which it is concluded. This takes place only in mathematics. Thus we infer, that 2 and 2 make 4, only from prior instances of having actually perceived this, and from the necessary coincidence of all these instances with all other possible ones of 2 and 2. Mathematical demonstrations are made up of a number of these, as was observed above.
Where the instances from whence the induction is made are alike, as far as we know, to that under consideration, at least in all things that affect the present inquiry, it affords the highest probability, and may be termed induction, in the proper sense of the word. Thus we infer, that the bread before us is nutritive and wholesome, because its smell, taste, ingredients, manner of composition, &c. are the same as those of other bread, which has often before been experienced to be so.
But, if the instance under consideration be in some respects like the foregoing ones, in others not, this kind of proof is generally termed one taken from analogy. Thus, if we argue from the use and action of the stomach in one animal to those in another, supposed to be unknown, there will be a probable hazard of being mistaken, proportional in general to the known difference of the two animals, as well as a probable evidence for the truth of part, at least, of what is advanced, proportional to the general resemblance of the two animals. But if, upon examination, the stomach, way of feeding, &c. of the second animal should be found, to sense, the same as in the first, the analogy might be considered as an induction properly so called, at least as approaching to it; for precise limits cannot be fixed here. If the second animal be of the same species, also of the same age, sex, &c. with the first, the induction becomes perpetually of a higher and a higher order, approaching more and more to the coincidence, which obtains in mathematical evidences, and yet never being able entirely to arrive at it. But then the difference, being only an infinitesimal fraction, as it were, becomes nothing to all practical purposes whatsoever. And if a man considers farther, that it would be hard to find a demonstration, that he does not mistake the plainest truths; this lessens the difference theoretically also.
