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Updated: June 2, 2025
But as we can never be quite certain of this, the evidence derived from the Method of Residues is not complete unless we can obtain C artificially and try it separately, or unless its agency, when once suggested, can be accounted for, and proved deductively, from known laws. Even with these reservations, the Method of Residues is one of the most important among our instruments of discovery.
Lewes's 'History of Philosophy, and presumably, therefore, expressing the sentiments of both writers, Comte is described as pronouncing inappropriate to the Science of Society, the method universally admitted to be proper to all other sciences that, namely, of obtaining by induction the laws of the elementary phenomena, then, from these laws thinking out deductively those of the complex phenomena, and, finally, of verifying by specific observation the laws obtained by deduction.
It may be affirmed as a general principle, that all inductions, whether strong or weak, which can be connected by a ratiocination, are confirmatory of one another: while any which lead deductively to consequences that are incompatible, become mutually each other’s test, showing that one or other must be given up, or at least, more guardedly expressed.
The conclusion which we have thus reached deductively from a consideration of the fundamental ideas of magic and religion is confirmed inductively by the observation that among the aborigines of Australia, the rudest savages as to whom we possess accurate information, magic is universally practised, whereas religion in the sense of a propitiation or conciliation of the higher powers seems to be nearly unknown.
It needs scarcely be observed, that,—if direct observation and collation of instances have furnished us with any empirical laws of the effect, whether true in all observed cases or only true for the most part,—the most effectual verification of which the theory could be susceptible would be, that it led deductively to those empirical laws; that the uniformities, whether complete or incomplete, which were observed to exist among the phenomena, were accounted for by the laws of the causes—were such as could not but exist if those be really the causes by which the phenomena are produced.
"The conditions" to use a phrase of Emerson's "are hard but equal": and at their best, the realist, working inductively, and the romantic, working deductively, are equally able to present the truth of fiction. We have now considered the subject-matter of fiction and also the contrasted attitudes of mind of the two great schools of fiction-writers toward setting forth that subject-matter.
From observations like these we can obtain certain principles from which we can argue deductively to facts of a like nature, but the process is limited, and we are suspicious of all reasoning in that direction applied to the processes of healthy and diseased life. We are continually appealing to special facts.
Few gamblers but would stare if they were told that the falling of a die on a particular face is as much the effect of a definite cause as the fact of its falling; it is a proverb that "the wind bloweth where it listeth;" and even thoughtful men usually receive with surprise the suggestion, that the form of the crest of every wave that breaks, wind-driven, on the sea-shore, and the direction of every particle of foam that flies before the gale, are the exact effects of definite causes; and, as such, must be capable of being determined, deductively, from the laws of motion and the properties of air and water.
Pythagoras taught the obliquity of the ecliptic, probably learned in Egypt, and the identity of the morning and evening stars. It is supposed that he maintained that the sun was the centre of the universe, and that the earth revolved around it; but this he did not demonstrate, and his whole system was unscientific, assuming certain arbitrary principles, from which he reasoned deductively.
The conclusions which that yields, when the number of instances compared is small, are of no real value, except as, in the character of suggestions, they may lead either to experiments bringing them to the test of the Method of Difference, or to reasonings which may explain and verify them deductively.
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