Friday, January 25, 2013

Cantor, Hilbert's Hotel, and the Logic of Infinity

Monroe County

In my MCCC Philosophy of Religion classes I'm now presenting William Lane Craig's Kalam Cosmological Argument for the Existence of God. It's formulated as:










  1. Whatever begins to exist has a cause.
  2. The universe began to exist.
  3. Therefore, the universe has a cause.
We're looking at two reasons to support premise 2. One of those reasons is: the impossibility of an actual infinite.

If premise two is false, then the universe has always existed, which means it has existed for an infinite number of years. But this cannot be true, since infinity applies to nothing actual. Craig uses mathematician David Hilbert and his famous "hotel" example to show this.

Here's an essay from the New York Times - "The Hilbert Hotel" - using Hilbert and mathematician George Cantor to show the non-applicability of infinity to anything actual.