Volume 41, 2008
Philosophy of Mathematics
Numbers, Quantities and Hume’s Principle
This paper argues against neo-Fregeans that Frege was right to conclude that we cannot obtain the concept of number from Hume's Principle. Neo-Fregeans have claimed that Hume's Principle is analytic since it can be viewed as an implicit definition of the concept of cardinal number. But it will be shown that if taken as an implicit definition, Hume's Principle is satisfied not just by the concept of number but also by the concept of discrete quantity, and hence it cannot be viewed as an implicit definition of the concept of cardinal number as distinct from the concept of discrete quantity.