But if this is just an analogy for something like a referee, then the origin of logic would still need to be explained. — Teaisnice

Logic is an axiomatic system based on 14 speculative beliefs, i.e. axioms. Logic cannot explain its own basic rules. There is simply no motivation for these basic beliefs that can be reached through reason.

Hence, the basic beliefs at the origin of logic -- pretty much like all other basic beliefs -- are supplied by other, unknown mental faculties that are not documented, and that cannot be explained reasonably.

Now look in detail at how reason functions.

Reason accepts three inputs: premises, conclusions, and an argument by which the conclusion necessarily follows from the premises. So, reason is a verification predicate function with three inputs and one yes/no output:

isReasonable(premises,conclusion,argument) = yes/no

Can reason by itself supply the argument? In other words, will reason be able to fill in the missing argument by itself?

isReasonable(premises,conclusion,unknown) = yes/no

No, because in that case we would, after 160 years, already have discovered the proof/argument for the Riemann hypothesis.

It is not because we can see a pattern that we consistently fail to falsify -- for which nobody has been able to discover a counterexample -- and it is not because we also know the premises of number theory -- its nine basic beliefs -- that we can supply the argument that will connect the Riemann conclusion to its premises.

Now the next question. Can reason discover the premises that will explain existing premises? In other words, is the following question solvable?

isReasonable(unknown premises, premises, unknown)

No, because as we can see, if the premises are unknown then the proof/argument is also unknown, and as argued in the previous case, reason by itself cannot discover the proof/argument.

Therefore, it is absolutely not possible that it would be reason that supplies the basic beliefs.

It cannot do that.

Therefore, "reasoning" about the validity of basic beliefs is simply an exercise in futility. You are then trying to use a tool of which we know that it cannot deliver what you want.

If God is not the creator of logic, then logic would be primary to God. This is clearly problematic if God is to exist eternally. Therefore, God must be the creator of logic. — Teaisnice

Or, logic is simply consistent with the eternal and immutable nature of God, rather than something primary to God or created by God. This is basically a variation of the Euthyphro Dilemma, and it is exposed as a false dichotomy in the same way.

Either God can do all things or he is limited to do only logically possible things. — Teaisnice

It is not a limitation of God to be capable of doing all logically possible things, since it is God's eternal and immutable nature that determines what is logically possible.

According to your numbered argument, you conclude that God can do all things, which means that he could even do the logically impossible things, such as create a square circle or a stone heavier than he can lift. Can you explain how God would be able to do such a thing? Your reasoning attempts to prove why God could do all things, yet you don’t explain how he could physically complete such a contradictory task. What would that even look like? How could God physically make a square circle, then, or a stone heavier than he can lift?

Additionally, I’d like to object to premise 2.2 of your argument: “If God is limited by logical laws, then he is not all-powerful.”

This “limiting” idea regarding logical impossibilities often seems to be the big issue when it comes to God’s omnipotence. Many believe that God’s inability to perform logical impossibilities limits him in a negative sense, making him “lesser” or not as powerful as he should be. But I’d like to argue that it’s acceptable if God cannot perform logical impossibilities. In fact, sometimes it’s good that God cannot perform such contradictory acts. For example, God cannot do evil or sin. That would be a contradictory act, because it goes against the nature of God’s goodness and his innate God-ness. But it is good that he cannot perform that contradictory act, because it would not be good for God to do evil.

In the same way, God’s inability to do the logically impossible does not make him “less than,” because no one can perform logical impossibilities. So God still possesses the highest level of power possible and is thus still omnipotent. We just have to accept that with omnipotence comes an inability to do logically impossible things – and that’s okay; that’s not limiting.

My argument takes the following form:

1. If a being can do the logically impossible, then that being can make a contradiction true.
2. No one can make a contradiction true.
3. Therefore, no one can do the logically impossible (1, 2 MT).
4. An omnipotent being is someone.
5. Therefore, an omnipotent being cannot do the logically impossible (3, 4, MP).

So, to answer your initial question… No, God does not limit his own omnipotence with logical laws, at least not in a negative sense.

This is a very thoughtful reflection. One quick note about our argument form: I am not completely sure what 2.3 adds to the argument or what I am supposed to glean from it. This does not significantly impact my response, though. I object to premise 2.2, along similar lines to commenter philorelkook.

When thinking about God’s qualities, I like to think about all qualities, not just omnipotence. All of God’s qualities are said to be perfect. “God is omnibenevolent, so God cannot commit evil” is an example of a “God cannot” statement that I am perfectly at peace with. I view these kinds of cannots as preventions of failure. God cannot commit an action that would necessitate his failure to act with one or more of God’s perfect qualities. The argument goes something like this:

1. If God has perfect qualities, God does not fail.
2. If God does not fail, God’s actions necessarily do not cause God’s failure.
3. If God has perfect qualities, God’s actions necessarily do not cause God’s failure. (1,2 HS)
4. God has perfect qualities.
5. God’s actions necessarily do not cause God’s failure. (3, 4 MP)

If you accept this argument, you accept that God’s actions do not cause God to fail. This is significant as you posit that God can do all things, even logically impossible things. However, if God could create a boulder so heavy God could not lift it, then God’s action would necessitate God’s failure (a failure of omnipotence). Your squaring the circle example is a little harder to parse, but I think that would go against either omniscience as that thing would be impossible to perceive/know or against omniscience as God would not be able to draw that illustration in reality. The idea here is that acting out logical impossibilities would cause God to fail in some way, which is the truly impossible thing. The extension of my argument goes like this:

1. God’s actions necessarily do not cause God’s failure. (3,4 MP)
2. If God could act out the logically impossible, God’s actions would cause God to fail in one of God’s perfect qualities.
3. God cannot do the logically impossible. (1,2 MT)

I believe it is reasonable to posit that God cannot do logically impossible things. I don’t think this makes God limited by God’s own laws, that would imply that God’s omnipotence extended beyond this perceived limitation. It is not a limitation because God’s perfection necessitates God’s inability to fail. It is as much a quality in God as omnipotence, this inability to fail. It is just a perfect quality in a negative sense. We think of perfect qualities as positive things, things that God is or can do, but I believe that if we expand our notion of perfect to include things God cannot do (including evil and the logically impossible), we sacrifice little to nothing in the debate.