Editing Hume's principle (section)

{{Short description|Logical principle}}
{{more footnotes|date=May 2020}}

'''Hume's principle''' or '''HP''' says that, given two collections of objects <math>\mathcal F</math> and <math>\mathcal G </math> with properties <math>F</math> and <math>G</math> respectively, the number of objects with property <math>F</math> is equal to the number of objects with property <math>G</math> if and only if there is a [[one-to-one correspondence]] (a bijection) between <math>\mathcal F</math> and <math>\mathcal G</math>. In other words, that bijections are the "correct" way of measuring size.

'''HP''' can be stated formally in systems of [[second-order logic]]. It is named for the Scottish philosopher [[David Hume]] and was coined by [[George Boolos]]. The principle plays a central role in [[Gottlob Frege]]'s philosophy of mathematics. Frege shows that HP and suitable definitions of arithmetical notions [[logical consequence|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 [[Logicism#Neo-logicism|neo-logicism]].