### In This Article Expand or collapse the "in this article" sectionInductive Reasoning

• Introduction
• Textbooks and General Overviews
• Inductive Probability
• Logical Probability
• Frequencies and Propensities
• Testing Statistical Hypotheses
• Induction as Practical Reason
• Formal Learning Theory
• Inference to the Best Explanation

# Inductive ReasoningbyJohn M. VickersLAST REVIEWED: 24 July 2018LAST MODIFIED: 30 September 2013DOI: 10.1093/obo/9780195396577-0171

## Introduction

Well into the 20th century, inductive reasoning and the concomitant problem of its justification concerned what is now known as universal inference—inference from instances (a is black and a raven, b is black and a raven . . .) to a universal generalization (all ravens are black). A slightly weaker form concluded from the same premises just that the next raven to be observed would be black. Since then, however, the forms of inductive reasoning have burgeoned and ramified, so much as to outrun useful categorization. Some thinkers go so far as to count all synthetic reasoning as inductive. Many, indeed most (but with important exceptions), contemporary accounts of induction are probabilistic; they seek canons of reasoning to augment the laws of probability. Among philosophers the most widely favored accounts of induction today are varieties of Bayesianism, which takes its name and its inspiration from Sir Thomas Bayes’s 1764 paper (Bayes 1958, cited under Origins and Foundations of Bayesianism); a nice exegesis of this paper is given in the opening chapter of Earman 1992 (cited under Recent Bayesian Developments). Bayesianism takes probability to be strength of belief, suitably constrained, and this invites coupling induction with theories of decision and action. Induction has also traditionally been called to support if not to verify scientific laws, sometimes by straightforward universal inference, in other cases—the reasoning of the great physicists of the classical period is perhaps the most famous example—in more intricate systems of equations.

## Textbooks and General Overviews

Textbooks abound for courses in induction and the philosophy of science. Skyrms 2000 and Hacking 2001 are accessible to the general reader. The former includes also an introduction to deductive logic, while the latter includes many historical and applied examples, both scientific and mundane. These books complement each other nicely. The encyclopedia articles—Fitelson 2006, Huber 2007, and Vickers 2011—present a good survey of the current state of the discipline. Salmon 1998 is a collection of articles, not a few of which are original and significant contributions, and others of which are expositions of difficult material.

• Fitelson, Branden. “Inductive Logic.” In The Philosophy of Science: An Encyclopedia. Vol. 1, A–M. Edited by Sahotra Sarkar and Jessica Pfeifer, 384–394. New York: Routledge, 2006.

A thorough survey of its topic, with quite general application to inductive reasoning. Parts may be a bit technical for the logically naive reader.

• Hacking, Ian. An Introduction to Probability and Inductive Logic. Cambridge, UK: Cambridge University Press, 2001.

A serious and lucid introduction, as rigorous as it is accessible. Includes also an elementary exposition of the principal theories of probability.

• Huber, Franz. “Confirmation and Induction.” In Internet Encyclopedia of Philosophy. Edited by James Fieser and Bradley Dowden. 2007.

A thorough account of its compound topic. Parts may be a bit technical for the novice, but the distinct sections are self-contained.

• Salmon, Wesley C. Causality and Explanation. New York and Oxford: Oxford University Press, 1998.

A collection of related papers, most of which treat some facet or form of inductive reasoning. The questions discussed range from basic to sophisticated, but the style is simple and understated throughout.

• Skyrms, Brian. Choice and Chance: An Introduction to Inductive Logic. 4th ed. Belmont, CA: Wadsworth/Thomson, 2000.

This book serves the novice as well as the expert. A rich, thorough, and completely up-to-date exposition of the main questions and currents in the study of inductive methods. Originally published in 1966 (Belmont, CA: Dickenson).

• Vickers, John. “The Problem of Induction.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2011.

Explains and discusses various prevalent formulations of the problem, and efforts at their resolution.

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