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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.
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.
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.
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.
In the absence, then, of any universal law of co-existence similar to the universal law of causation which regulates sequence, we are thrown back upon the unscientific induction of the ancients, per enumerationem simplicem, ubi non reperitur instantia contradictoria.
The frequency of the particular event, apart from all surmise respecting its cause, can give rise to no other induction than that per enumerationem simplicem; and the precarious inferences derived from this are superseded, and disappear from the field as soon as the principle of causation makes its appearance there.
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 induction of the ancients has been well described by Bacon, under the name of “Inductio per enumerationem simplicem, ubi non reperitur instantia contradictoria.” It consists in ascribing the character of general truths to all propositions which are true in every instance that we happen to know of.
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.
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