Is God a logical contradiction?

[Objectivist]

No, I don't think that I am using any terms incorrectly. On my view when one talks of Nature one is speaking of existence, all of it, the sum total.  We call it nature when it is seen as a collection of entities acting and interacting with each other according to their natures or identities and according to the Law of Causality.  To speak of something outside of Nature would be to speak of an entity that is outside the concept entity, outside of the Law of identity and outside the Law of causality.  It is wracked with contradictions.  I think you're right to say that the supernatural is a synonym for the non-existent since to exist is to be something specific, to possess identity.  And yet "God" is supposed to transcend all that.  If a god existed "outside of Nature"  it would exist outside of existence and it would bo nothing.   

On your view, the world we live in is analogous to a video game.  I think this is a good analogy given what Christianity has to say about the Universe being a creation.  In a video game, the action is dictated by the programmer who creates the virtual world of the game and by the choices of the player, which in this case would be this fictional god.  The characters in the game (us Humans) would be like puppets.  

On my view however, the Universe is not analogous to a computer game.  Reality is an absolute, and everything is what it is and does what it does independent of any ruling consciousness.

I agree with your definition of nature; which is why I disagree with your application of supernatural. I have no problem viewing God as natural, since by definition his very existence would define him as natural. However, I think most people who prefer describing God as supernatural, aren't defining nature the way you are. Instead, they're cleaving the whole of reality/existence in two, that which is natural and that which is supernatural. So I think you're coming across contradictions because you mean different things by nature, and the definitions are incompatible.

As far as the video game analogy, what are your thoughts on the Simulation Theory? From what I understand, within such a view reality is still absolute it just so happens that reality is a simulation. The theory is born out of computer science, not theology.

I realize that many people do divide reality into two opposing realms.  I recognize this and I call them on this reverse package dealing.  There's no legitimate reason to divide a fundamental concept like existence the way they are doing.  I don't think "supernatural" is a legitimate concept to begin with.  It's actually an anti-concept.  I wonder what those people who divide reality into the natural and the supernatural use as their concept denoting the whole of existence.  Do they understand the purpose of definitions and that definitions, if they are to be true, must be objective?  Objectivism avoids such errors by having a sound theory of concepts, something most theists don't have access to.  They certainly won't find anything resembling a theory of concepts in ancient texts written by people who were ignorant of such things.  

I think those that promote the notion that we live in a simulation are guilty of the fallacy of the stolen concept.  Notice what those who promote this hypothesis are doing.  We are expected to know and accept that there is such a thing as computers, that computers can run simulations, that someone exists that could program such a simulation and that such simulated realities are absolute, but we aren't able to know whether the things we perceive are real.  They don't realize that all these higher-level concepts rest on much more fundamental concepts and ultimately axiomatic concepts that they are denying with their hypothesis. They don't understand this because they don't have a conceptual understanding of knowledge.

I tell you what, if everyone knew about and thoroughly understood stolen concepts, such notions as the simulation theory would be laughed off the stage.

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Are you speaking about this?

Indeed 

You're right! The notion that we are living in a simulation is an updated and secularized replacement for the cartoon universe theory.