#
Is it conceivable that something finite can become infinite? Isn't there an inherent conceptual problem in a transition from finiteness to infinity? (My question comes from science, but the scientists don't seem to bother to explain this, such as in the case of gravity within a black hole -- a massive star collapses into a black hole and gravity in it rises to infinity? The more interesting example to me is the notion that the universe may well be infinite, but the main view in cosmology is that it began as finite and even had a definable size early on in its expansion. How could an expanding universe at some point cross over to have infinite dimensions?)

Good question, and a controversial topic! Some philosophers, going back to Aristotle, are happy with the concept of a potential infinite: a series that expands indefinitely. But they are unhappy with the concept of an actual infinite, partly due to the supposition that an actual infinitude could never be attained through any number of succesive events / acts. Start now, and no matter how many events transpire it seems that (just as there is no greatest possible number) you would never reach infinity. There are abundant puzzles, going back to Zeno in the fifth century BCE, about achieving an actual infinite. Here are two brief ones, the first is called Hilbert's hotel. Imagine (for the sake of argument) that you have an infinite number of rooms in a hotel and each person pays you $50 per night. How much money do you bring in per day? An infinite amount. But now imagine guests in rooms divisible by 1,000 all check out (guest in room 1,000 checks out, guest in 2,000 check out...). How much less...

- Log in to post comments