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The current and approved modes of reasoning on these subjects are still of the same vicious description against which Bacon protested; the method almost exclusively employed by those professing to treat such matters inductively, is the very inductio per enumerationem simplicem which he condemns; and the experience which we hear so confidently appealed to by all sects, parties, and interests, is still, in his own emphatic words, mera palpatio.
This assertion is in open opposition to first appearances; all terrestrial objects, when in motion, gradually abate their velocity, and at last stop; which accordingly the ancients, with their inductio per enumerationem simplicem, imagined to be the law.
The inveterate logical errors to which physicians have always been subject are chiefly these: The mode of inference per enumerationem simplicem, in scholastic phrase; that is, counting only their favorable cases. This is the old trick illustrated in Lord Bacon's story of the gifts of the shipwrecked people, hung up in the temple.
The directly inductive truths of Mathematics are few: being, first, certain propositions about existence, tacitly involved in the so-called definitions; and secondly, the axioms, to which latter, though resting only on induction, per simplicem enumerationem, there could never have been even any apparent exceptions.
The current and approved modes of reasoning on these subjects are still of the same vicious description against which Bacon protested; the method almost exclusively employed by those professing to treat such matters inductively, is the very inductio per enumerationem simplicem which he condemns; and the experience which we hear so confidently appealed to by all sects, parties, and interests, is still, in his own emphatic words, mera palpatio.
As, however, all rigorous processes of induction presuppose the general uniformity, our knowledge of the particular uniformities from which it was first inferred was not, of course, derived from rigorous induction, but from the loose and uncertain mode of induction per enumerationem simplicem; and the law of universal causation, being collected from results so obtained, can not itself rest on any better foundation.
But though the course of nature is uniform, it is also infinitely various. Hence there is no certainty in the induction in use with the ancients, and all non-scientific men, and which Bacon attacked, viz. 'Inductio per enumerationem simplicem, ubi non reperitur instantia contradictoria' unless, as in a few cases, we must have known of the contradictory instances if existing.
Our only substitute for an universal law of coexistence is the ancients' induction per enumerationem simplicem ubi non reperitur instantia contradictoria, that is, the improbability that an exception, if any existed, could have hitherto remained unobserved. But the certainty thus arrived at can be only that of an empirical law, true within the limits of the observations.
It would seem, therefore, that induction per enumerationem simplicem not only is not necessarily an illicit logical process, but is in reality the only kind of induction possible; since the more elaborate process depends for its validity on a law, itself obtained in that inartificial mode.
The inveterate logical errors to which physicians have always been subject are chiefly these: The mode of inference per enumerationem simplicem, in scholastic phrase; that is, counting only their favorable cases. This is the old trick illustrated in Lord Bacon's story of the gifts of the shipwrecked people, hung up in the temple.
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