In my previous post I briefly sketched out some of the things that God cannot do. Someone might ask, well what if God could do any of these things? The law of identity is an axiom that shows why contradictions cannot exist. All of the things I wrote about that God cannot do would be violations of principles that rely on the law of identity. For example, if God could somehow withdraw from space and time, He would violate the law of identity. How much time does it take to leave time? It is a contradiction to say that God can both move in a sequence of events and also withdraw from the sequences of events at the same time. The question, "Can God create a rock so big that he cannot lift it?" shows that God cannot violate the law of identity.
Well, what if God could violate the law of identity? If God could violate the law of identity, then the law of identity would not be an axiom. If it is not an axiom, then we could not reason since the law of identity, which implies the law of non-contradiction, is the foundation of reason. By reason, I mean the capacity of human beings to make sense of things and to establish and verify facts.
According to the law of identity a fact cannot be true and false at the same time. If facts can both be true and false at the same time, then we could not establish or verify facts. Therefore we could not have knowledge, nor could we have any reasonable expectation for our actions. This implies that we could not be anxiously engaged in good causes, nor could we do many things of our own free will. Why? Because we could never know what was a good cause or not. God would have to tell us everything to do. We would be utterly dependent on Him. We could not ever learn and grow. Since the glory of God is intelligence, it would be impossible to become like God since we could never gain any knowledge of reality.
If God could violate the law of identity, then we would know what it would be like to be insane. Imagine going through one door and then not knowing if you would come out that door or a different random door. Imagine eating and not ever knowing if would make you full or sick or purple. One day ducks could be ducks, the next day, they could be toasters, or suspenders, or Bart Simpson. The world would not make sense.
If God could violate the law of identity, then it would be completely useless to even talk because we could never know if our words could ever refer to objects in reality. It would be useless to agree or disagree since two opposing arguments could both be right at the same time.
Therefore, any argument against these principles is necessarily self-refuting.