Inductive reasoning

How it applies

• What the inference does: Induction moves from particular evidence — observations, measurements, field reports, test runs — to a general claim or to a prediction about the next case. Because the conclusion goes beyond what was observed, the support is a matter of degree: more and more varied cases strengthen it, a single counter-case can destroy it.
• The simplest form: Induction by enumeration generalizes from a list of observed instances to “all Bs are As” or to a proportion in a population. Accounts of inductive logic note that this form is narrow in scope: many empirical hypotheses cannot be reduced to it, and their evidence is not a tally of similar instances, which is why probabilistic and Bayesian treatments were developed.
• Hume's problem: Hume argued that inductive methods assume that unobserved cases resemble observed ones — that nature runs uniformly. That premise cannot be demonstrated deductively, and supporting it by experience uses induction again. Later philosophy debates partial or “logical” answers; there is no settled solution, and the entry should not be read as claiming one.
• Rules of method: John Stuart Mill set out five methods of experimental inquiry in A System of Logic (Book III) — agreement, difference, the joint method, residues and concomitant variations — as a disciplined, eliminative way of inferring causes from observed cases. They remain a readable checklist for anyone narrowing down a defect from field data.
• Which generalizations are projectible: Nelson Goodman's “new riddle of induction” uses the invented predicate grue to show that the same observations support incompatible generalizations, so induction depends on which predicates we are willing to project. In practice this is the question of whether a category you measured (“new users”, “batch 7 devices”) is the category that actually carries the regularity.
• The sceptical counter-position: Karl Popper rejected inductivism as the logic of science and put deductive testing of conjectures in its place; theories are to be exposed to falsification rather than accumulated proof. This remains one position among several in the philosophy of science, not a consensus procedure.
• In documentation work: Usage data, support tickets, reviewer comments and usability sessions are inductive evidence. Record the sample (how many cases, which users, which release) next to the conclusion, so a later editor can see how far the generalization reaches.
• In engineering and AI: Statistical learning generalizes inductively from training data, so distribution shift is a textbook inductive failure: the rule held for the observed cases and not for the new ones. Documenting the data and the limits of the observed range is part of describing what the system can be relied on for.
• Limits you must state: “No failure observed so far” is an inductive conclusion, not evidence of safety. Field experience and test statistics never replace the risk assessment, the required safety information or the verification that an applicable standard or regulation demands, and using inductive evidence well does not by itself make documentation or a product compliant.
• Relation to starting points: Aristotle's Posterior Analytics II.19 describes the grasp of first principles as proceeding from experience by induction (epagōgē) — induction supplies the premises that demonstration then works from, which is also why first principles thinking and the axiomatic method depend on how the starting points were obtained.

Induction vs. deduction

A deductive argument is valid when the conclusion cannot be false while the premises are true: the conclusion contains nothing that was not already in the premises. An inductive argument deliberately exceeds its premises, which is what makes it useful for learning from the world and what makes it fallible. Practically, analysis and synthesis and deductive steps let you work out consequences inside a model, while induction is how the model gets its content — and reasoning by analogy is a third move again, transferring a pattern from one case to another without establishing a rule over all cases. Abductive reasoning, the inference to the best available explanation of a surprising observation, is often separated from induction for the same reason: it selects a hypothesis rather than extending a tally of cases.

External references

• Stanford Encyclopedia of Philosophy: The Problem of Induction
• Stanford Encyclopedia of Philosophy: Inductive Logic
• Stanford Encyclopedia of Philosophy: Nelson Goodman
• Encyclopedia.com: Mill's Methods of Induction
• Wikipedia: A System of Logic