Finitistic induction is a limited form of mathematical induction in which it can be shown that the inductive process concludes its extension in a finite number of steps.
An extreme form of the constructivist stance in the philosophy of mathematics, finitism proposes that a mathematical object (i.e. a well defined abstract entity capable of possessing properties and bearing relations) does not exist unless it can be "constructed" by a formal procedure from the natural numbers in a finite number of steps. (In contrast, most constructivists allow for the existence of objects constructed in a countably infinite number of steps.)
Kurt Gödel's first incompleteness theorem related to the limits of systems restricted to finitistic inductive means.
Famous quotes containing the word induction:
“One might get the impression that I recommend a new methodology which replaces induction by counterinduction and uses a multiplicity of theories, metaphysical views, fairy tales, instead of the customary pair theory/observation. This impression would certainly be mistaken. My intention is not to replace one set of general rules by another such set: my intention is rather to convince the reader that all methodologies, even the most obvious ones, have their limits.”
—Paul Feyerabend (1924–1994)