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:
“They relieve and recommend each other, and the sanity of society is a balance of a thousand insanities. She punishes abstractionists, and will only forgive an induction which is rare and casual.”
—Ralph Waldo Emerson (1803–1882)