Following the fun of the recent evolution v designed designer discussion we knocked some ideas about infinity around in the office starting with the above question.
Clearly the answer is no but is it? Does infinite then presuppose an infinite universe to contain the infinite oranges and boxes but then how can you have two infinite sets in the same space? Now this is possible if you contain each orange in a box (make the oranges a set within the box - literally!) and there are theoretical infinite sets that contain each other but are clearly an impossible reality (infinite number of prime numbers contained within the infinite number of natural numbers). Does infinity describe the impossible rather than the real? - is there in fact anything 'infinite' that exists outside of abstract concepts (i.e. could you have infinite oranges ? You can have infinite numbers but only because they themselves don't actually exist they are an abstraction of reality)
Why do I care? Well its because in my theology we are left with the infinite regression of designers. With an infinity of designers shouldn't the universe be filled with designers so much so that there wouldn't be any room for us? Could you have an infinite regression of designers if time is on a loop and each designer is actually finite? Is it possible to have a designer who themselves exist forever with no beginning or end (certainly not according to LDS theology which postulates a beginning.) Is it possible to have the Daoist 'uncarved block' realise its potentiality at some point and spontaneously create intelligence - sounds suspiciously like abiogenesis coupled with the spontaneous generation of the building blocks of matter.
Sooo - is it in fact possible to have anything within the bounded universe that is in actuality infinite? Do we force God outside the universe (would 'outside' not therefore become bounded by the containment of this universe and one infinite God?) Can you have infinity in the future but not in the past (i.e. have a start but no end?)
Answers on a postcard.