---
tag: J36EHBHF6J
kind: statement
role: proposition
name: Hume's principle
aliases: [hume-principle]
sources:
  - wikipedia: en:314743@r1350988939
    locator: Hume's principle
    note: adopted
    mention: wikipedia://en/314743
    sections: [Statement]
same_as:
  wikidata: Q1553014
  wikipedia: Hume's principle
inventory: [XCJH1RYZQY]
---

## Statement

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