Enumerative induction

Enumerative induction or, as the basic form of inductive inference, simply induction, reasons from particular instances to all instances, thus an unrestricted generalization. If one observes 100 swans, and all 100 were white, one might infer All swans are white. As this reasoning form's premises, even if true, do not entail the conclusion's truth, this is a form of inductive inference. The conclusion might be true, and might be thought probably true, yet it can be false. Questions regarding the justification and form of enumerative inductions have been central in philosophy of science, as enumerative induction has a pivotal role in the traditional model of the scientific method.

For a move from particular to universal, Aristotle in the 300s BCE used the Greek word epagogé, which Cicero translated into the Latin word inductio. In the 300s CE, Sextus Empiricus maintained that all knowledge derives from sensory experience—concluded in his Outlines of Pyrrhonism that acceptance of universal statements as true cannot be justified by induction.

At 1620, Francis Bacon repudiated mere experience and enumerative induction, and sought to couple those with neutral and minute and many varied observations before to uncover the natural world's structure and causal relations beyond the present scope of experience via his method of inductivism, which nonetheless required enumerative induction as a component.

The supposedly radical empiricist David Hume's 1740 stance found enumerative to have no rational, let alone logical, basis but to be a custom of the mind and an everyday requirement to live, although observations could be coupled with the principle uniformity of nature—another logically invalid conclusion, thus the problem of induction—to seemingly justify enumerative induction and reason toward unobservables, including causality counterfactually, simply that modifying such an aspect prevents or produces such outcome.

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