Infinity

5. Post-Kantian metaphysics of the infinite

Metaphysical thought about the infinite since Kant has continued to be just as deeply involved with human finitude. Existentialists in particular have been greatly exercised by it, especially in its guise of mortality. But they have also for the most part recognized an element of the infinite within us. This too is Kantian. Kant believed that we are free rational agents, and that when our agency is properly exercised, it has an unconditioned autonomy that bears all the hallmarks of the truly infinite. For Kant, this was something which exalts us. But for many of the existentialists, still preoccupied with the fundamental fact of human finitude, it is something which is responsible for the deepest tensions within us, and thus for the absurdity of human existence (see Existentialism §2).

Hegel agreed with Kant that the truly infinite is to be found in the free exercise of reason (see Hegel, G.W.F. §8). But he took this further than Kant. He argued that reason is the infinite ground of everything. Everything that happens, on Hegel’s view, can be understood as the activity of a kind of world-spirit, and this spirit is reason.

This led Hegel to a very non-Aristotelian conception of the infinite. For Hegel, the infinite was the complete, the whole, the unified. Aristotle’s conception of the infinite as the never-ending was in Hegel’s view quite wrong. He explained this conception as arising from our finite attempts to assimilate the truly infinite. And he described Aristotelian infinity as a ‘spurious’, or ‘bad’, infinity – a mere succession of finite elements, each bounded by the next, but never complete and never properly held together in unity. Such ‘infinitude’ seemed to Hegel at turns nightmarish, then bizarre, then simply tedious, but always a pale, inadequate reflection of the truly infinite.