[409]"For though, in order actually to see that two given lines never meet, it would be necessary to follow them to infinity; yet, without doing so, we may know that if they ever do meet, or if, after diverging from one another, they begin again to approach, this must take place not at an infinite, but at a finite distance. Supposing, therefore, such to be the case, we can transport ourselves thither in imagination, and can frame a mental image of the appearance which one or both of the lines must present at that point, which we may rely on as being precisely similar to the reality. Now, whether we fix our contemplation upon this imaginary picture, or call to mind the generalizations we have had occasion to make from former ocular observation, we learn by the evidence of experience, that a line which, after diverging from another straight line, begins to approach to it, produces the impression on our senses which we describe by the expression 'a bent line,' not by the expression 'a straight line.'"—Mill's "Logic," I. 364.
[410]Mill's "Logic," I. 315.
[411]"We must first observe, that there is a principle implied in the very statement of what Induction is; an assumption with regard to the course of nature and the order of the universe; namely, that there are such things in nature as parallel cases; that what happens once, will, under a sufficient degree of similarity of circumstances, happen again, and not only again, but as often as the same circumstances recur. This, I say, is an assumption, involved in every case of induction. And, if we consult the actual course of nature, we find that the assumption is warranted. The universe, so far as known to us, is so constituted, that whatever is true in any one case, is true in all cases of a certain description; the only difficulty is, to find what description."—Mill's "Logic," I. 337.
[412]Mill's "Logic," I. 351.
[413]Mill's "Logic," I. 359.
[414]Ibid. I. 360.
[415]Ibid. I. 365.
[416]Mill's "Logic," I. 372.
[417]"If we take fifty crucibles of molten matter and let them cool, and fifty solutions and let them evaporate, all will crystallize. Sulphur, sugar, alum, salt—substances, temperatures, circumstances—all are as different as they can be. We find one, and only one, common fact—the change from the liquid to the solid state—and conclude, therefore, that this change is the invariable antecedent of crystallization. Here we have an example of the Method of Agreement. Its canon is:—
"'I. If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon.'"—Ibid. I. 422.