Definition
Inference is the act of moving from what is known — evidence, premises, observations — to what is not yet known. It is the mechanism by which new knowledge is produced from existing knowledge, making it foundational to logic, science, statistics, law, and artificial intelligence.
The term covers several distinct moves. Deductive inference guarantees its conclusion: if the premises are true, the conclusion cannot be false. Inductive inference generalizes from observed instances to a broader rule; the conclusion is probable but not guaranteed. Abductive inference selects the most parsimonious explanation for a body of evidence — it is the logic of diagnosis, detective work, and scientific hypothesis formation. Each mode is appropriate in different contexts and carries different norms of justification.
What unites all three is the act of going beyond the given data. Inference always involves a commitment to a claim that the available evidence underdetermines. This is why inference can be evaluated for quality: some inferences are well-supported, others are hasty or formally invalid. A central task of epistemology — the study of knowledge and justification — is specifying the conditions under which inference is reliable.
Why it matters
How it works
Deductive, inductive, and abductive modes
Deductive inference works top-down from general rules to particular cases. If all members of a category share a property, and a given entity is in that category, the property applies to it — with certainty. Formal logic and mathematics are built entirely from deductive inference, which is why their conclusions are provable rather than merely probable.
Inductive inference works bottom-up from observed instances to generalizations. Observing that every sampled member of a category shares a property suggests — but does not prove — that all members do. The problem of induction, articulated by Hume, is that no finite number of confirming instances can rule out a future counterexample. Science lives in this gap, managing uncertainty through replication, controls, and probability.
Abductive inference, sometimes called inference to the best explanation, asks: given what we observe, which hypothesis best explains it? A physician triangulating a diagnosis, a detective constructing a theory of the crime, a scientist deciding between competing models — all are engaged in abduction. The inference is defeasible: a better explanation may emerge as evidence accumulates.
Bayesian updating as a formal model
Bayesian inference provides the most general framework for rational belief revision. A prior probability represents how likely a hypothesis is before new evidence arrives. Applying Bayes' theorem updates this prior in proportion to how well the hypothesis predicts the observed evidence, yielding a posterior probability. Repeated updating on incoming evidence produces beliefs that converge on well-calibrated estimates of reality. The framework formalizes what it means to learn from evidence without either ignoring data or over-reacting to it.