David Warren, staunch man of the 13th century, might be termed an opponent of the notion of infinity:
The term “infinity” was an invention of the Devil. This, gentle reader will understand, is my humble opinion. Or if the Devil didn’t invent it, he “evolved” it, from the more innocent usages that conveyed “unlimited,” or “countless,” or “unknowably” large or small. What is finite has an ending, can be finished, finis. What is infinite cannot be; it is open-ended. There is, where we look for an end, nothing there.
Portrait of Georg Cantor
Photographer unknown, via Wikimedia Commons.Nothing is quite the opposite of something. Perhaps this is a fact no longer taught in our schools: that “nothing” can do nothing for you. Whereas, “something” might. For in its modern usage, “infinity” has become a thing. It has become “virtually” an agent, a kind of god, demanding to be worshipped. The very Christian idea of Alpha and Omega — from the first to the last letter of the (Greek) alphabet, from beginning to end — is subtly replaced in our minds with the progressive idea, “from one to infinity.”
Which is where the human mind checks out. “So what is infinity plus one?” one asks. There can be no answer. Today we are hanging on a cross of “infinity.”
The mathematician Georg Cantor (1845–1918), in his lucid moments (when out of insane asylums), invented set theory. It may be found, lodged in the heart of post-modern reasoning. My hero Wittgenstein, among others, explained how pernicious it was. Scholastic theologians had already spotted the fly in the “infinite” ointment. It is pantheist, and in Cantor’s “final” posit of an infinity of infinities, it is a direct challenge to the unity or uniqueness of the revealed God. Cantor himself was under the impression that God existed, in the sense that God had communicated set theory to Cantor of all people. I, at least, am sceptical of those who claim direct communication with God, especially those who spend a lot of time in bat houses, and wonder with whom they were really chatting. (I don’t doubt that the mad can be brilliant, however.)
