The central project of Frege’s life was to demonstrate that...

The central project of Frege’s life was to demonstrate that arithmetic is reducible to logic, and in pursuing this he both invented modern quantificational logic, which made the project feasible, and provided analyses of number statements. On his account, a number statement such as ‘Jupiter has four moons’ is analyzed as ‘The concept moon of Jupiter has four instances’ (cf.

1884, §§ 46, 54).[^5] That is, it is viewed not as predicating of Jupiter the property of having four moons, as a simple decompositional analysis might suggest, but as predicating of the (first-level) concept moon of Jupiter the (second-level) property has four instances , which can be logically defined in Frege’s theory. To make clear that number statements can be logically defined, in other words, Frege had to transform the statements to show what was ‘really’ involved. What…