This article is about induction in philosophy and logic. Inductive reasoning is the counter to deductive reasoning. For other article subjects named induction see induction.

Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the conclusion of an argument is very likely to be true, but not certain, given the premises. It is to ascribe properties or relations to types based on limited observations of particular tokens; or to formulate laws based on limited observations of recurring phenomenal patterns. Induction is used, for example, in using specific propositions such as:

• The ice is cold.
• A billiard ball moves when struck with a cue.

to infer general propositions such as:

• All ice is cold.
• For every action, there is an equal and opposite re-action

Validity

Formal logic as most people learn it is deductive rather than inductive. Some philosophers claim to have created systems of inductive logic, but it is controversial whether a logic of induction is even possible. In contrast to deductive reasoning, conclusions arrived at by inductive reasoning do not necessarily have the same degree of certainty as the initial assumptions. For example, a conclusion that all swans are white is obviously wrong, but may have been thought correct in Europe until the settlement of Australia. Inductive arguments are never binding but they may be cogent. Inductive reasoning is deductively invalid. (An argument in formal logic is valid if and only if it is not possible for the premises of the argument to be true whilst the conclusion is false.)

The classic philosophical treatment of the problem of induction, meaning the search for a justification for inductive reasoning, was by the Scotsman David Hume. Hume highlighted the fact that our everyday reasoning depends on patterns of repeated experience rather than deductively valid arguments. For example we believe that bread will nourish us because it has in the past, but it is at least conceivable that bread in the future will poison us.

Someone who insisted on sound deductive justifications for everything would starve to death, said Hume. Instead of unproductive radical skepticism about everything, he advocated a practical skepticism based on common-sense, where the inevitability of induction is accepted.

20th Century developments have framed the problem of induction differently. Rather than a choice about what predictions to make about the future, it can be seen as a choice of what concepts to fit to observation (see the entry for grue) or of what graphs to fit to a set of observed data points.

Induction is sometimes framed as reasoning about the future from the past, but in its broadest sense it involves reaching conclusions about unobserved things on the basis of what is observed. Inferences about the past from present evidence (e.g. archaeology) count as induction. Induction could also be across space rather than time, e.g. conclusions about the whole universe from what we observe in our galaxy.

Types of inductive reasoning

• argument based on signs
• prediction
• generalization
• causal inference, or simply, inference
• argument from analogy
• argument from authority

Bayesian inference

Of the candidate systems of inductive logic, the most influential is Bayesianism, which uses probability theory as a framework for induction. Bayes theorem is used to calculate how much the strength of one’s belief in a hypothesis should change, given some evidence.

There is debate around what it is that informs the original degree of belief. Objective Bayesians seek an objective value for the degree of probability of a hypothesis being correct, and so do not avoid the philosophical criticisms of objectivism. Subjective Bayesians hold that the prior probabilities represent subjective degrees of belief, but that repeated application of Bayes’ theorem leads to a high degree of agreement on the posterior probability. They therefore fail to provide an objective standard for choosing between conflicting hypotheses. The theorem can be used to rationally justify belief in some hypothesis, but at the expense of rejecting objectivism. Such a scheme cannot be used, for instance, to objectively decide between conflicting scientific paradigms.

Bayesians feel entitled to call their system an inductive logic because of Cox's Theorem, which derives probability from a set of logical constraints on a system of inductive reasoning.

Related topics

• Deductive reasoning
• Explanation
• Logic
• Falsifiability
• Mathematical induction

External link

• Inductive Reasoning