Inductivism is the traditional and still commonplace philosophy of scientific method to develop scientific theories. Inductivism aims to neutrally observe a domain, infer laws from examined cases—hence, inductive reasoning—and thus objectively discover the sole naturally true theory of the observed.

Inductivism's basis is, in sum, "the idea that theories can be derived from, or established on the basis of, facts". Evolving in phases, inductivism's conceptual reign spanned four centuries and began with Francis Bacon's 1620 proposal in his Novum Organum, itself a reply to the pre-scientific scholastic model of inquiry which prioritized deductive reasoning from sources of belief taken to be authoritative such as religious texts.

In the 19th and 20th centuries, inductivism succumbed to hypotheticodeductivism—sometimes worded deductivism—as scientific method's realistic idealization. Yet scientific theories as such are now widely attributed to occasions of inference to the best explanation, IBE, which, like scientists' actual methods, are diverse and not formally prescribable.

Francis Bacon, articulating inductivism in England, is often falsely stereotyped as a naive inductivist. Crudely explained, the "Baconian model" advises to observe nature, propose a modest law that generalizes an observed pattern, confirm it by many observations, venture a modestly broader law, and confirm that, too, by many more observations, while discarding disconfirmed laws. Growing ever broader, the laws never quite exceed observations. Scientists, freed from preconceptions, thus gradually uncover nature's causal and material structure. Newton's theory of universal gravitation—modeling motion as an effect of a force—resembled inductivism's paramount triumph.

Near 1740, David Hume, in Scotland, identified multiple obstacles to inferring causality from experience. Hume noted the formal illogicality of enumerative induction—unrestricted generalization from particular instances to all instances, and stating a universal law—since humans observe sequences of sensory events, not cause and effect. Perceiving neither logical nor natural necessity or impossibility among events, humans tacitly postulate uniformity of nature, unproved. Later philosophers would select, highlight, and nickname Humean principles—Hume's fork, the problem of induction, and Hume's law—although Hume respected and accepted the empirical sciences as inevitably inductive, after all.

Immanuel Kant, in Germany, alarmed by Hume's seemingly radical empiricism, identified its apparent opposite, rationalism, in Descartes, and sought a middle ground. Kant intuited that necessity exists, indeed, bridging the world in itself to human experience, and that it is the mind, having innate constants that determine space, time, and substance, and thus ensure the empirically correct physical theory's universal truth. Thus shielding Newtonian physics by discarding scientific realism, Kant's view limited science to tracing appearances, mere phenomena, never unveiling external reality, the noumena. Kant's transcendental idealism launched German idealism, a group of speculative metaphysics.

While philosophers widely continued awkward confidence in empirical sciences as inductive, John Stuart Mill, in England, proposed five methods to discern causality, how genuine inductivism purportedly exceeds enumerative induction. In the 1830s, opposing metaphysics, Auguste Comte, in France, explicated positivism, which, unlike Bacon's model, emphasizes predictions, confirming them, and laying scientific laws, irrefutable by theology or metaphysics. Mill, viewing experience as affirming uniformity of nature and thus justifying enumerative induction, endorsed positivism—the first modern philosophy of science—which, also a political philosophy, upheld scientific knowledge as the only genuine knowledge.

Nearing 1840, William Whewell, in England, deemed the inductive sciences not so simple, and argued for recognition of "superinduction", an explanatory scope or principle invented by the mind to unite facts, but not present in the facts. John Stuart Mill rejected Whewell's hypotheticodeductivism as science's method. Whewell believed it to sometimes, upon the evidence, potentially including unlikely signs, including consilience, render scientific theories that are probably true metaphysically. By 1880, C S Peirce, in America, clarified the basis of deductive inference and, although acknowledging induction, proposed a third type of inference. Peirce called it "abduction", now termed inference to the best explanation, IBE.