Frege regarded Hume’s Principle as insufficient for a logicist account of arithmetic,
as it does not identify the numbers; it does not tell us which objects the
numbers are. His solution, generally regarded as a failure, was to propose certain
sets as the referents of numerical terms. I suggest instead that numbers are
properties of pluralities, where these properties are treated as objects. Given
this identification, the truth-conditions of the statements of arithmetic can be
Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.