Background perspectives on infinity and God

Abstract

Initially the connection between divinity and infinity was accompanied by an initial notion of infinity in the literal sense of one, another one, and so on – without an end, endless. Via Anaxagoras we reach Aristotle for whom it would be contradictory to hold that God is infinite, because the unlimited nature of infinity cannot be reconciled with the fullness of being of perfect reason. After Origen it was Gregor von Nyssa who positively affirmed that infinity belongs to the essence of God. Augustine was also more explicit in his view of infinity, because, according to him, the set of ‘all finite integers’ could be comprehended at once as an actual-infinite totality. An element of the thinking of Thomas Aquinas acknowledges that God’s infinity could be known, albeit in an inadequate manner. Aquinas continues key elements of the Greek-Medieval tradition, for according to him, in eternity there is no succession, because it exists totally at once. Cusanus took God as the actual infinite to be the coincidentia oppositorum . Descartes defends the view that the infinite, which is God, is known before the finite. Kant aptly introduces the expression ‘successive infinite’ but rejects the idea of an infinite totality. After Kant Maimon distinguishes between the human mind and a divine mind associated with succession and at once respectively. Hegel grasped the distinction between ordinal and cardinal numbers. Bolzano, Weierstrass, Dedekind and Cantor explored the at once infinite mathematically. Finally, what has been explained thus far sheds light on the struggle of theologians with the assumption that infinity is actually a theological notion (God’s infinity) transferred to mathematics.