Inductive logic, generally speaking, takes elements of a set and applies this subset of elements to a broader set. More specifically, the principle of mathematical induction states that if zero has a property, P, and if whenever a number has the property its successor also has the property, then all numbers have the property:
Induction works by enumeration: as support for the conclusion that all p’s are q’s, one could list many examples of p’s that are q’s. It also includes ampliative argument in which the premises, while not entailing the truth of the conclusion, nevertheless purports good reason for accepting it.
Inductive probability in the sciences has been generally successful in the past. It has been used by Galileo, Kepler, and has even resulted in the discovery of Neptune. The English astronomer John Michell exemplified this discuss in a discussion of ‘probable parallax and magnitude of the fixed stars’ published by the Royal Society in 1767. Michell found that the incidence of apparently close pairings of stars was too great for them all to be effects of line of sight, and that next to a certainty such observed pairs of stars must actually be very close together, perhaps moving under mutual gravitation. Michell’s conclusion was not corroborated for forty years until William Herschel’s confirmatory observations.