This study aims to develop a hybrid model to represent the human mind from a functionalist point of view that can be adapted to artificial intelligence. The model is not a realistic theory of the neural network of the brain but an instrumentalist AI model, which means that there can be some other representative models too. It had been thought that the provability of an axiomatic system requires the completeness of a formal system. However, G？del proved that no consistent formal system can prove its own consistency. There is a paradoxical limit to provability. Both consistency and completeness are impossible together. These formal limits form the basis of our model: the hybrid model of the mind consists of a formal axiomatic system and an evolutionary algorithm (EA) of intelligence, which also includes the genetic algorithm (GA) of consciousness. The GA of consciousness operates based on intentions, functioning in conjunction with the principles of EA. This collaboration allows it to transcend the paradoxical formal limits of intelligence. However, GA overcomes the problem of paradoxicality at the cost of producing illusions. Following this collaboration gives us a GA operating system. After all, if the rational optimization task of the GA in question produces illusions, then the rationality must lie elsewhere in the paradox.
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