Computational theory of the mind is that human's ability to reason and think is explained by the ability of the brain to compute information. This provides a mechanistic explanation for why human's think, that is that the brain as a purely physical object through mechanical processes is able to make decisions based on information. This would lead to conception that the brain is a type of biological computer and that our consciousness is a analogous to a program being run by the computer.
This isn't to say that computational theory of the mind holds that a mind is similar to a modern day electronic computer just that both have inputs and create outputs with step by step functions in between. Their are similar principles at play but not neccessarily similar mechanisms. The inputs in our case are our senses and the outputs are our actions.
An example of step by step function in a human could be a person avoiding a snake. The person sees a snake on the ground which is his input. Their mind formulates that the long slithering object fits with the symbolic idea of a snake in their memory. They know that some snakes can carry deadly poisons and therefore be dangerous. They decide to take action by walking a wide path around the snake and this represents their output.
The importance of computationalism to AI is that it is a conception of the mind that holds the possibility that an Artificial Intelligence could be truly sentient and hold a similar state to the one we describe as a mind. It is not neccessarily the only theory of the mind that leads to this possibility but it would be one with the simplest path to a sentient Artificial Intelligence.
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