Why an Actual Infinity Cannot Exist and Therefore We Know that the Universe Had a Beginning


Philosopher William Lane Craig has done more than any other contemporary to popularize and develop the Kalam Cosmological Argument, which is simple to formulate and difficult to refute. The premises of the argument are as follows:

  1. Everything that begins to exist has a cause.
  2. The universe begins to exist.
  3. Therefore, the universe has a cause.

Dr. Craig has used Hilbert’s Infinite Hotel Paradox to show the absurdities of an actual infinity (as opposed to a potential infinity) existing. Maria Papova explains the origin and popularization of Hilbert’s paradox:

To help ordinary humans tussle with this extraordinary concept, German mathematician David Hilbert conceived of what is now known as the Infinite Hotel Paradox — a brilliant and mind-bending specimen of that neat intersection of science and philosophy: the thought experiment. Hilbert came up with the Infinite Hotel Paradox in 1924, but it was popularized only after his death by Russian-American theoretical physicist George Gamow’s 1947 book One Two Three . . . Infinity: Facts and Speculations of Science.

Jeff Dekofsky produced an animation for TED-Ed, which you can watch here:

You can watch below as Dr. Craig explains the concept and applies it to this argument:

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