A History of the Infinite IV: Human Finitude

I begin by looking back at the early modern period in the history of thought about the infinite, the period of enlightenment that began with the work of René Descartes. Descartes was a paradigmatic enlightenment philosopher, who sought to establish what understanding we can have of the infinite using our own finite resources. Descartes’ answer was that our idea of the infinite must have originated in something that was itself infinite; indeed this was one of his basic arguments for the existence of God. But more empirically minded philosophers took issue with this and were prepared to infer from the fact that we had no direct experience of the infinite that we did not really have any idea of it at all; and Immanuel Kant played his quintessential rôle of arbiter. I pass from these historical reflections to broader considerations of our own finitude. I look in particular at the question of whether, if we could, we would want to live for ever. I conclude the lecture by asking where this all leaves us, and what grasp we really have of the infinite. I argue that it is our grasp of our own finitude that is fundamental to whatever grasp we have of the infinite. But there is a final paradox here with which we must reckon: our grasp of our own finitude not only gives us whatever grasp we have of the infinite, but also makes us think that we cannot have any real grasp of the infinite at all. I sketch a way of coming to terms with this paradox.