Quote:

I know perfectly well what an axiom is and I still don't think your "god exists" axiom is useful for anything than stating that "something exists".



You are missing the point then for that is the ONLY thing that axiom is meant to show: that something exists and then use that as a foundation for further investigation as to HOW MANY somethings there are.


Quote:

Ok. I add the axiom A = "for all a,b if a is god and b is god, then a = b". From that it is trivial to derive the theorem "there is only one that is god".[/quopte]

You've proven nothing. Your axiom STARTS with the idea that a is the same god as b. You've derived nothing and merely proved state your axiom as your conclusion.

All the same, a more useful proof would look like:

a = god1
b = god2

[...]

therefore either a=b (and there is one god) or A DNE B (and there are at least two gods). It's the [...] that you skipped over that I'm mostly interested in.

If we find the latter, we would expand thusly

a = god1
b = god2
c = god3

[...]

therefore either a=b DNE c or a=c DNE b or b=c DNE a (and there are only two gods) or a DNE b DNE c (and there are at least 3 gods).

Again, it's the [...] that is interesting to me, whether it be from science or logic.


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