Induction is a basic method of scientific and philosophical inquiry. The work seeks to show against the skeptical tide that the method is secure and reliable. The problem of induction has been a hotly debated issue in modern and contemporary philosophy since David Hume. However, long before the modern era Indian philosophers have addressed this problem for about two thousand years. This work examines some major Indian viewpoints including those of Jayarasi (7th century), Dharmakirti (7th century), Prabhakara (8th century), Udayana (11th century) and Prabhacandra (14th century). It also discusses some influential contemporary positions including those of Russell, Strawson, Popper, Reichenbach, Carnap, Goodman and Quine. The main focus is on the Nyaya view developed by Gangesa (13th century). A substantial part of the work is devoted to annotated translation of selected chapters from Gangesa's work dealing with the problem of induction with copious references to the later Nyaya philosophers including Raghunatha (15th century), Mathuranatha (16th century), Jagadisa (17th century) and Gadadhara (17th century). An annotated translation of selections from Sriharsa (12th century) of the Vedanta school, Prabhacandra of the Jaina school and Dharmakirti of the Buddhist school is also included. A solution is presented to the classical problem of induction and the Grue paradox based on the Nyaya perspective. The solution includes an argument from counterfactual reasoning, arguments in defense of causality, analyses of circularity and logical economy, arguments for objective universals and an argument from belief-behavior contradiction.

Definition is an important scientific and philosophical method. In all kinds of scientific and philosophical inquiries definition is provided to make clear the characteristics of the things under investigation. Definition in this sense, sometimes called real definition, should state the essence of the thing defined, according to Aristotle. In another (currently popular) sense, sometimes called nominal definition, definition explicates the meaning of a term already in use in an ordinary language or the scientific discourse or specifies the meaning of a new term introduced in an ordinary language of the scientific discourse. Definition combines the purposes of both real and nominal definition and is promoted by the Nyaya philosophers of India. Another important method of science and philosophy is induction. In a narrow sense induction is a method of generalization to all cases from the observation of particular cases. In a broad sense induction is a method for reasoning from some observed fact to a different fact not involved in the former. We understand induction in the broad sense though more often we shall actually be concerned with induction in the narrow sense. How can our limited experience of nature provide the rational basis for making knowlege claims about unobserved phenomena?