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Quite simply, cognition refers to thinking. There are the obvious applications of conscious reasoning—doing taxes, playing chess, deconstructing Macbeth—but thought takes many subtler forms, such as interpreting sensory input, guiding physical actions, and empathizing with others.
A bias is a tendency, inclination, or prejudice toward or against something or someone. Some biases are positive and helpful, such as choosing to eat foods that are considered healthy, or staying away from someone who has knowingly caused harm.