Roeper, Peter2015-12-100031-8019http://hdl.handle.net/1885/39566Frege 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 obtained from logical principles with the help of definitions, just as the logicist thesis maintains.201510.1093/philmat/nkv0262020-11-02