Induction

[gL.edu] This article gathers contributions by Benedikt Küpper, developed within the context of the Conceptual clarification about "Information, Knowledge and Philosophy", under the supervisión of J.M. Díaz Nafría.

This article traces the rise, critique and modern role of inductive reasoning in science and everyday life. It begins chronologically with  Aristotle’s first account through Hume’s skeptical challenge to Popper’s falsificationist remedy, and closes with a brief reflection on induction’s continuing significance.

An introduction to induction

Finding true statements and universal laws is fundamental to all scientific disciplines. Induction is a way to facilitate this leap from particular observations to true statements. The ability to make this leap is critical for science as a whole. Consider how, after witnessing the sun rise each morning, we confidently predict it will rise tomorrow, how sampling a handful of sweet apples leads us to assume that all apples of that variety share the same flavor. Despite the undeniable utility of induction, every inference produced this way hinges on the assumption that past patterns will continue, a premise that no finite collection of samples can ensure. This inherent logical gap has historically provoked doubt by a number of famous philosophers. This article will explore this history.

Aristotle and the roots of Induction

The logic put forth by Aristotle, especially the theory of the syllogism did not always hold this influential position in western logic. His six works of logic  (Categories, On Interpretation, Prior Analytic, Posterior Analytics, Topics and On Sophistical Refutations) are commonly combined under the title Organon (Greek for Instrument). In the Organon Aristotle coined the term epagōgē (ἐπαγωγή) to describe the process by which the mind ascends from particular observations to universal principles. In the Analytica Priora he distinguishes induction from Deduction: whereas a syllogism proceeds from two universals to a particular conclusion, induction moves from repeated instances (“Socrates is mortal; Plato is mortal”) to a universal judgment (“All men are mortal”). Although Aristotle characterizes both deduction and induction, he treats them with markedly different emphasis. Induction only becomes a focus of Aristotle in his work Posterior Analytics in the theory of scientific knowledge.

Hume and the problem of Induction

In the mid-eighteenth century, natural philosophers placed their full confidence in induction, believing that every pattern revealed by experiment would continue without fail. In 1748, David Hume challenged this faith in his Enquiry Concerning Human Understanding. He pointed out that even after observing the sun rise on thousands of mornings, there is no logical guarantee that it will rise again tomorrow. Our expectation that future events will mirror past ones, he argued, depends not on reasoned proof but on a deeply ingrained mental habit. According to Hume, each time we witness a repeated phenomenon, we strengthen a kind of psychological momentum rather than establish a philosophical certainty. This recognition undermines the idea that empirical science can rest on unshakable foundations, since all its generalizations hinge on assumptions that lie beyond rational justification. At the same time, Hume acknowledged that induction is unavoidable: we rely on it to navigate daily life, to build machinery, and to plan for the future. His paradox forced later thinkers to rethink the nature of scientific knowledge: Immanuel Kant sought to explain how the mind’s own structures shape experience, while Karl Popper recast the scientific enterprise as a series of daring guesses meant to be tested and potentially refuted. In this way, Hume’s critique remains a turning point in our understanding of how we know anything about the world.

Popper's Falsificationism

Karl Popper, in his work The logic of scientific discovery,  radically reframed the debate over induction by arguing that no finite series of observations, no matter how exhaustive, can logically establish a universal law. He illustrates this with the classic white-swan example: watching thousands of white swans cannot prove that “all swans are white,” since a single black swan would immediately overturn the rule. Instead of seeking verification through induction, Popper proposed falsifiability as the hallmark of genuine science: a theory must be constructed so that it can, in principle, be contradicted by empirical tests. This shifts our focus away from piling up confirming instances to actively trying to prove our ideas wrong. Under Popper’s view, scientific progress depends on bold conjectures and rigorous trials; a hypothesis remains standing only because it has survived the toughest challenges, not because it has been proven true. When a prediction fails, the theory is definitively refuted, whereas successful predictions merely leave it unrefuted. Popper also cautions against inventing ad hoc tweaks to rescue a theory from disproof, since these maneuvers rob it of genuine testability.

Yet even Popper acknowledged that induction has a role to play once a hypothesis is on the table. As Díaz-Nafría explains, after we generate a bold hypothesis, induction steps in to complete its provisional validation by checking whether the expected “natural messages” actually turn up. In other words, induction never guarantees truth, but it does provide the practical check that helps a surviving conjecture earn its place in scientific discourse. By recasting the demarcation criterion from verifiability to falsifiability, and recognizing that induction serves as the follow-up test, Popper resolves Hume’s problem of induction: empirical laws are adopted tentatively and remain open to future rejection. Science, in this framework, advances not by gathering more confirming examples but by eliminating errors, holding on to theories that keep passing the hardest tests and discarding those that do not. Popper’s falsificationism remains a cornerstone of modern philosophy of science, highlighting the perpetual, self-correcting journey of knowledge.

Conclusion

Tracing the path from Aristotle’s original concept of epagōgē through Hume’s rigorous critique and Popper’s development of falsification reveals both the power and the provisional nature of inductive reasoning. Aristotle showed us how the mind ascends from repeated observations to general principles, laying the groundwork for systematic inquiry. Hume then exposed the logical gap at the heart of induction by demonstrating that experience alone cannot prove that future events will follow past patterns. Popper’s response reframed science as an enterprise of conjectures and tests rather than one of accumulating confirmations; by insisting that theories must be falsifiable, he offered a clear demarcation between empirical science and unfalsifiable speculation. In our data-rich age, accepting induction as always open to revision encourages scientists and laypeople alike to remain humble, to welcome unexpected findings, and to view knowledge not as a final product but as a continuous, self-correcting process.