Are Theists Illogical for Believing in God?

[Ramsin.Kh]

Secondly you should realize that we can construct new logical frameworks that are not compatible with the one we have by starting from other axioma or basic operations. Modular arithmetic is such an example (in modular arithmetic with modulo 3 you will see that 2 + 2 = 1). It is not applicable, in one sense anyway, to our universe: material objects in our universe seem countable as natural numbers and not as finite modular sets. But at the same time we can construct logic that isn't applicable to our universe at all.

All math theorems have been proved by previous theorems and original axioms.
(2+2=1 mod 3) does not exist in math, a correct modular statement is ( 2 + 2 ≡ 1 mod 3).
(≡) is the sign of congruence, not equality. Modular arithmetic is in fact applicable in our universe, the most common thing which involves modular math is the clock.

Certain parts of mathematics we have come up with have no counterpart in our universe as far as we now know. Logic does not necessitate reality. Logic is not necessarily a description of reality, our reality or any other reality that might coexist with ours.

All math theorems are proved by original axioms (ex. of axiom: 1+1=2).
Logic is very necessary for describing the universe, since all classical and modern physics involves logical math.

Well, a startling find with the discovery of quantum mechanics seems to suggest that this indeed is the case. At the quantum level of our very own universe even countability breaks down due to the Heisenberg Uncertainty Principle. In this realm a different logic, quantum logic, is used to describe the phenomena.

I don't see any reason of bringing quantum physics here, it only appears magical to public.
Same math axioms and theorems are used in quantum physics, you can see that in any physics book.
There is no 'our realm' and quantum realm, every macroscopic event can be explained by quantum physics, but the classical physics is used for that because it's simpler and gives a fair approximate answer.

What this shows is that you cannot conclude from logic that it has a counterpart in reality and vice versa that you can't conclude that any possible reality necessarily is a reality that obeys one unified logical framework, let alone the logical framework we might arrive at for our universe.

Logic is not a rule or something to be obeyed. Logic is not something that have properties, because you say quantum logic, different logics...
Logic is simply the study of reasoning. In all universes, you can reason and use your intellect and therefore think and deduce logically.