Inductive Reasoning

Inductive reasoning is the mode of inference that moves from particular observations to general conclusions. Unlike deductive reasoning, which guarantees truth-preservation given true premises, inductive reasoning offers only probabilistic support — its conclusions outrun the evidence and remain perpetually revisable. This gap between evidence and conclusion is called the problem of induction, and no logical solution to it has ever been found.

David Hume established the problem in its sharpest form: past regularities provide no logical guarantee of future ones. Every inductive argument assumes that unobserved cases resemble observed cases — an assumption that cannot itself be inductively justified without circularity. The algorithmic response to Hume — Solomonoff's universal prior — provides the theoretically optimal inductive strategy but does so at the cost of uncomputability.

Inductive reasoning is the engine of empirical science, the foundation of Machine Learning, and the source of systematic cognitive distortions when applied carelessly. That it cannot be logically justified is the most important fact about it.