chapter  13
23 Pages

Chastened Logicism?

The logicist programme is generally reckoned to have failed. Frege had hoped to found arithmetic on logic, but the intuitive theory of sets-the successors to his Umfänge-turned out to be inconsistent,1 and when we abandoned intuitive set theory, and replaced it by some axiomatized version, it lost its innocent simplicity, and no longer seemed like logic. But once we distinguish transfinite arithmetic, which is much more a mathematical theory than an articulation of logical principles, from arguing with adjectives, which has a good claim to be just logic, the fundamental objection to the logicist programme is removed.