God is so quiet

[pocaracas]

I think the problem many of us have with "abstract objects" is whether they are discovered or invented.
Is mathematics discovered or invented?

Is the concept of the perfect circle a discovery or an invention?
Is the concept of existence a discovery or an invention?

If they are discoveries, then I'd agree with you on there being such a world, or realm, of abstract concepts.
But if they are invented, then they are contingent upon rational minds - minds which, as far as we can tell, are contingent upon working brains, which are contingent upon a whole plethora of biological machinery, which is contingent on chemistry and, ultimately, physics.... the same physics that popped out of the big bang through... who knows?... quantum fluctuations?
So the best guess we have for the only necessary thing is the framework upon which all of existence plays out: space-time.

I agree with your analysis about abstract objects. I for one do not believe they are real objects because I think all those things can be grounded in the mind of God. However, atheists have to wrestle with the question and the consequences of either decision. 

I think you're not working in the right direction...
When trying to establish that a god exists, one can't posit that it already does so and has a mind.

However, why do you say our space-time contains within it an explanation of its existence (the definition of necessary)? Most philosophers consider all concrete objects as contingent.

Space-time is not exactly a "concrete object" is it?
I'd describe it more as a framework upon which concrete objects exist.... a framework that can bring forth concrete objects, it seems.