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Updated: May 26, 2025
Of these uses of the method, we shall presently cite some remarkable examples. The canon of the Method of Residues is as follows:— Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.
The examination having led to the rejection of those arguments, we have thought ourselves warranted in concluding that axioms are but a class, the highest class, of inductions from experience; the simplest and easiest cases of generalization from the facts furnished to us by our senses or by our internal consciousness.
But the fundamental fallacy, from which so many thinkers M. Garofalo among them can not free themselves, and to which I myself yielded, before I had penetrated, thanks to the Marxian theory of historic materialism or, more exactly, of economic determinism into the true spirit of socialist sociology, is the tendency to judge the inductions of socialism by the biological, psychological and sociological data of the present society, without thinking of the necessary changes that will be effected by a different economic environment with its inevitable concomitants or consequences, different moral and political environments.
Dr. Whewell’s remark, therefore, is philosophically correct. Successive expressions for the colligation of observed facts, or, in other words, successive descriptions of a phenomenon as a whole, which has been observed only in parts, may, though conflicting, be all correct as far as they go. But it would surely be absurd to assert this of conflicting inductions.
If inductive philosophers have often been opposed to religion and the Bible, it is because they have not carried their inductions far enough to cover the entire world of facts.
Socrates makes his soul move a natural and common motion: a peasant said this; a woman said that; he has never anybody in his mouth but carters, joiners, cobblers, and masons; his are inductions and similitudes drawn from the most common and known actions of men; every one understands him.
There was an instantaneous effect at the closing and breaking of the voltaic circuit; electric inductions appeared when the two wires were moved to and from one another; but these are phenomena of a different class.
The earliest and latest inductions must either coincide or approximate the same end. No links must be broken, no chasms bridged, in the scientific series. There must be a distinct and separate link connecting each preceding and each succeeding one in the chain. The lowest known mammal must be found in immediate relationship with his higher congener or brother, not in any remote cousinship.
Whewell exhorts those who have any difficulty in recognising the distinction held by him between necessary and contingent truths, to study geometry,—a condition which I can assure him I have conscientiously fulfilled,—I, in return, with equal confidence, exhort those who agree with him, to study the elementary laws of association; being convinced that nothing more is requisite than a moderate familiarity with those laws, to dispel the illusion which ascribes a peculiar necessity to our earliest inductions from experience, and measures the possibility of things in themselves, by the human capacity of conceiving them.
It is of this sort of induction that brutes are capable; it is in this shape that uncultivated minds make almost all their inductions, and that we all do so in the cases in which familiar experience forces our conclusions upon us without any active process of inquiry on our part, and in which the belief or expectation follows the suggestion of the evidence with the promptitude and certainty of an instinct.
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