Full Idea
What is now known as Hume's Principle says the number of Fs is identical with the number of Gs if and only if the Fs and the Gs are one-to-one correlated with one another.
Gist of Idea
Fs and Gs are identical in number if they one-to-one correlate with one another
Source
E.J. Lowe (The Possibility of Metaphysics [1998], 10.3)
Book Reference
Lowe,E.J.: 'The Possibility of Metaphysics' [OUP 2001], p.214
A Reaction
This seems popular as a tool in attempts to get the concept of number off the ground. Although correlations don't seem to require numbers ('find yourself a partner'), at some point you have to count the correlations. Sets come first, to identify the Fs.