CANTOR’S PARADISE SHOWS RELIGION IS A PHANTOM CITY

All religion, as theologians — and their opponents — understand the word, is something other than it is assumed to be. Religion is a vehicle. Its expressions, rituals, moral and other teachings are designed to cause certain elevating effects, at a certain time, upon certain communities. Because of the difficulty of maintaining the Science of Man, religion was instituted as a means of approaching truth. The means always became, for the shallow, the end, and the vehicle became the idol. Only the man of wisdom, not the man of faith or intellect, can cause the vehicle to move again. Alauddin Attar (1318–1400) (quoted in Idries Shah, The Sufis)

Let me tell a tale of large cardinals. I’m not referring to overweight Princes of the Catholic Church, but to really, really, really big numbers. What does this have to do with my title? Hang on and all will be clear.

Counting to Infinity

In the third part of Dante’s Divine Comedy, Paradiso, Christ is said to have “opening the golden way from Earth to Heaven.” In a less grandiose but mathematically more doable move, Georg Cantor opened the way to what David Hilbert called “Cantor’s Paradise,” the paradise of infinite sets. In the late nineteenth century, the mathematician Cantor put infinity on a sound footing by developing the theory of infinite sets. Most importantly, he showed that there were different sizes of infinity and that there was an uncountably infinite sequence of larger and larger infinities.