Hume's Principle or HP—the terms were coined by George Boolos—says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence (a bijection) between the Fs and the Gs. HP can be stated formally in systems of second-order logic. Hume's Principle is named for the Scottish philosopher David Hume.
HP plays a central role in Gottlob Frege's philosophy of mathematics. Frege shows that HP and suitable definitions of arithmetical notions entail all axioms of what we now call second-order arithmetic. This result is known as Frege's theorem, which is the foundation for a philosophy of mathematics known as neo-logicism.
Read more about Hume's Principle: Origins, Influence On Set Theory
Famous quotes containing the words hume and/or principle:
“Consciousness never deceives.... We learn the influence of our will from experience alone. And experience only teaches us, how one event constantly follows another; without instructing us in the secret connexion, which binds them together, and renders them inseparable.”
—David Hume (1711–1776)
“There is no teaching until the pupil is brought into the same state or principle in which you are; a transfusion takes place; he is you, and you are he; then is a teaching; and by no unfriendly chance or bad company can he ever lose the benefit.”
—Ralph Waldo Emerson (1803–1882)