4.13

The most striking aspect of Dedkind’s definition is that it determines infinity positively, and subordinates the finite negatively. This is its especially modern accent, something that one almosts always finds in Dedekind. An infinite system has a property of an existential nature: there exists a biunivocal correspondence between it and one of its proper parts. The finite is that for which such a property does not obtain. The finite is simply that which is not infinite, and all the positive simplicity of thought directs itself to the infinite. This intrepid total secularisation of the infinite is a gesture whose virtues we (clumsy disciples of “finitude”, in which our religious dependence still lies) have not yet exhausted.