Counting Gods

How many fingers do you need to count gods?  If you are like most people you simply assume the set of gods is enumerable and then you start fighting over which value in the set of positive integers \mathbb{Z}_{\geq0}  or  {0, 1, 2, 3, \ldots, } is correct.  This process is elegantly explained by this flowchart.

I have a simple question. Is the set of gods enumerable?  For all you innumerates out there a set is enumerable if-and-only-if its members can be counted.   It’s a rather astonishing fact that many humdrum sets cannot be counted.  Do you remember line segments  \overline{AB} from school geometry?

The number of points in any nonzero length Euclidean line segment  \overline{AB} cannot be counted.  There are more points in \overline{AB} than there are counting numbers.  If you don’t believe me  check out Cantor’s diagonal argument and savor a classical mathematical treat.

Once you get your head around the idea that some things cannot be counted the notion of counting gods looks ludicrous.  Why do you expect to tally your supreme beings with ordinary counting numbers when they cannot deal with line segments?  Perhaps god counting requires more than positive integers!

Perhaps the bloody disputes between atheists GodCount=0 and deists GodCount > 0 can be resolved with rational numbers \mathbb{Q}.  How about fractional 1/2 gods?  Let’s just split the difference and all get along.  Unfortunately rational numbers will not satisfy ultrapolytheists, believers in more gods than you can count, because you can count rational numbers.  Ultrapolytheists need to get real \mathbb{R} – the numbers  – anyway.

Counting gods is a complex problem.   Electrical engineers cannot deal with the wiring in your fridge without complex numbers  \mathbb{C}. Maybe a god count of 3 + 7i is the ticket

If this sounds silly, condescending and sarcastic congratulations your bullshit detector is working.  However,  ridiculous as this little diatribe is,  it is as sound as any mainstream religious doctrine. So if you find this absurd and, you have a fixed god count in your little head,  who is really being silly?

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