Deduction / Induction — Two fundamental modes of inference, distinguished by the relation between premises and conclusion. In deduction, the conclusion follows necessarily from the premises: if they are true and the form of the argument is valid, the conclusion cannot be false. Such reasoning adds no new information but makes explicit what is already contained in the premises, guaranteeing the transmission of truth. Its classic model is the syllogism, whose theory Aristotle elaborated in the Prior Analytics; one example is modus ponens: “If it rains, the street gets wet; it rains; therefore the street gets wet.” Euclidean geometry and formal logic are typically deductive domains. Induction, by contrast, moves from the observation of particular cases to merely probable generalizations — from “all observed swans are white” one concludes, with no logical necessity, that “all swans are white.” Francis Bacon, in the Novum Organum (1620), championed methodical induction as the instrument of a new science of nature, opposed to the scholastic syllogism. David Hume, however, formulated the celebrated problem of induction: no amount of past observation logically justifies a universal conclusion about the future, for this presupposes that nature remains uniform — something that cannot be proved without circularity. In the twentieth century, Karl Popper replied by proposing falsificationism: science does not confirm theories by induction but advances by eliminating those refuted by experience. A third form, abduction (Peirce), infers the best explanation for an observed phenomenon.
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