inductive reasoning
In plain wordsReasoning from particular examples to a general rule or prediction — every swan I have seen is white, so swans are probably white — which is useful but can always turn out wrong.
Inference from observed cases to general conclusions or to predictions about unobserved cases, in which the premises support the conclusion without guaranteeing it. Its main forms are generalization from a sample to a population, prediction, and argument by analogy. David Hume's problem of induction asks what justifies such inference at all; statistics, Bayesian inferenceBayesian inference, n.: Reasoning that treats unknowns as uncertain beliefs and updates them with evidence using Bayes' theorem. The result is not one answer but a range of answers, each with a probability., PAC learningPAC learning, n.: A mathematical definition of what it means to learn from examples: given enough data, a learner should, with high probability, find a rule that is almost always right. and Solomonoff inductionSolomonoff induction, n.: A mathematical recipe for ideal prediction: consider every computer program that could have produced the data so far, trust shorter programs more, and predict what they would output next. give formal answers under different assumptions. Machine learningmachine learning, n.: A way of building software that learns from examples instead of following rules written by a programmer. Shown thousands of labeled photos, for instance, a program can learn to recognize cats. is induction mechanized: a learner generalizes from training examples, and its inductive biasinductive bias, n.: The assumptions built into a learning method that decide how it fills the gaps between the examples it was shown, such as that similar inputs get similar answers. Every learner needs some to cope with new cases. determines which of the many hypotheses consistent with the data it prefers. Inductive logic programminginductive logic programming, n.: A kind of machine learning that discovers general logical rules — such as 'X is a grandparent of Z if X is a parent of a parent of Z' — from examples and background knowledge. and program synthesisprogram synthesis, n.: Getting a computer to write a program automatically from a description of what the program should do — a logical specification, a few input–output examples or a request in plain language. from examples induce symbolic rules or programs, and in-context learning by language modelslarge language model, n.: A computer program trained on enormous amounts of text to predict the words that come next. At vast scale, that simple skill lets it chat, answer questions, translate, summarize and write code. is often described as induction from the examples in a prompt.
Origin
Aristotle discussed epagōgē, rendered in Latin as inductio. Francis Bacon's Novum Organum (1620) made induction the method of natural science, and David Hume posed its central philosophical problem in A Treatise of Human Nature (1739).
Usage note
Not to be confused with mathematical induction, which is a deductive proof technique, or with induction headsinduction head, n.: A pattern-completing mechanism inside language models: having seen 'Harry Potter' once, it spots the next 'Harry' and predicts 'Potter' — a simple trick behind much learning from examples in a prompt., circuits that implement a copying pattern inside transformers.
Related
- deductive reasoningdeductive reasoning, n.: Reasoning in which true starting points guarantee a true conclusion: if every square is a rectangle and this shape is a square, then it must be a rectangle.
- abductive reasoningabductive reasoning, n.: Reasoning from an observation to its most likely explanation — the grass is wet, so it probably rained — the kind of educated guess that doctors and detectives make.
- inductive biasinductive bias, n.: The assumptions built into a learning method that decide how it fills the gaps between the examples it was shown, such as that similar inputs get similar answers. Every learner needs some to cope with new cases.
- inductive logic programminginductive logic programming, n.: A kind of machine learning that discovers general logical rules — such as 'X is a grandparent of Z if X is a parent of a parent of Z' — from examples and background knowledge.
- Solomonoff inductionSolomonoff induction, n.: A mathematical recipe for ideal prediction: consider every computer program that could have produced the data so far, trust shorter programs more, and predict what they would output next.
- machine learningmachine learning, n.: A way of building software that learns from examples instead of following rules written by a programmer. Shown thousands of labeled photos, for instance, a program can learn to recognize cats.
- deductive reasoningdeductive reasoning, n.: Reasoning in which true starting points guarantee a true conclusion: if every square is a rectangle and this shape is a square, then it must be a rectangle.
Sources
- Hume, D. (1739). A Treatise of Human Nature, Book I, Part III.
Mentioned in
abductive reasoningabductive reasoning, n.: Reasoning from an observation to its most likely explanation — the grass is wet, so it probably rained — the kind of educated guess that doctors and detectives make., deductive reasoningdeductive reasoning, n.: Reasoning in which true starting points guarantee a true conclusion: if every square is a rectangle and this shape is a square, then it must be a rectangle.