Kant and formalism: Hilbert, Russell and whitehead

A Kantian account of geometry would be couched in terms of spatial intuition-that ‘lazy limbo of mystery’, as Bertrand Russell called it. David Hilbert’s remarks in Foundations of Geometry go beyond a simple neutrality about Immanuel Kant’s philosophy: they suggest that he saw the Foundations as the carrying out of a Kantian project. In 1898, therefore, Russell reacted strongly against Kant about whom he never said another good word. This was …