Diagonalization
Diagonalization is a technique first used by George Cantor, a German mathematician. He used it to show that the cardinality of the real numbers is not equal to the cardinality of the natural numbers, thereby demonstrating one infinity is bigger than the other infinity.
This method can be applied to any infinite set to construct an even larger infinite set. The method uses the Axiom of Choice.
Diagonalization and the Existence of God
Some have cited diagonalization as a formal challenge to Saint Anselm's argument for the existence of God. In summary, Anselm argued that there must be a greatest idea and what could be greater than God? Therefore God exists.[1]
However, diagonalization argues that no greatest idea can exist: quite bluntly, God is infinite, therefore He can be diagonalized to produce an even greater infinite.[2] This seeming disproof of the existence of God has cast doubt on the validity of Cantor's diagonalization. In particular, it provides yet another counterintuitive conclusion from the dubious Axiom of Choice.
References
- ↑ http://www.ephilosopher.com/e107_plugins/forum/forum_viewtopic.php?104130
- ↑ Topo-philosophies: Plato's Diagonals, Hegel's Spirals, and Irigaray's Multifolds, Arkady Plotnitsky. In After Poststructuralism: Writing the Intellectual History of Theory Tilottama Rajan, Michael James.