Russell: Logicism

What, if any, problem does the axiom of infinity pose for Russell's logicism?

Key readings

(Russell, 1919, ch. 3,8,17,18)

(Whitehead and Russell, 1927, pp. 1-30)

Putnam (1979) (you may skip the discussion of formalism)

(Sainsbury, 1979, ch. VIII, §§1,2,5)

Further readings

Gödel (1983)

(Sainsbury, 1979, ch. VIII, §§3,4)

Carnap (1983)