I think it might go beyond two intelligences. For instance, there are 500 million neurons that independently govern the gut - https://en.wikipedia.org/wiki/Enteric_nervous_system

For reference, a cat has ~200 million neurons in its brain - https://en.wikipedia.org/wiki/Cat_intelligence

Perhaps we have dozens of intelligences, with varying degrees of cognition? What is actually happening when the amygdala takes over the nervous system to avoid a car accident before you are aware what is happening? What is really going on with Tourette syndrome?

Might the human gut have its own hopes and dreams?