Induktive

Induktive, or inductive, describes reasoning and methods that derive general conclusions from specific observations or data. In epistemology, science, and statistics, induction is often contrasted with deduction, where conclusions follow necessarily from given premises.

Common forms include enumerative induction, where a general rule is inferred from many observed instances (for example, observing many white swans and generalizing that all swans are white). Statistical induction uses probability to infer properties about a population from a sample, while causal induction aims to infer cause-and-effect relationships from patterns of correlation and experiments. Inference by analogy generalizes from similarities between known cases to new ones.

In mathematics and logic, the term induction is also used in a different sense: mathematical induction is a formal, deductive proof technique. It establishes that a statement holds for all natural numbers by proving a base case and an inductive step, then deducing the general result. Despite sharing the word induction, this method is not an inductive inference about empirical facts.

Limitations of induction are central in philosophy. The problem of induction, raised by Hume, notes that past regularities do not guarantee future occurrences. Inductive inferences are defeasible and probabilistic, refined by methods such as Bayesian reasoning, larger or more representative data, and explicit model assumptions.

Applications of inductive reasoning span science, data analysis, and machine learning, where models and hypotheses are built from observed data to generalize beyond the original cases.