Neuroscientist Maxwell Bennett and philosopher Peter Hacker defend the need to eradicate the mereological fallacy of cognitive neuroscience. This fallacy attributes to the parts of an animal psychological predicates that make sense only when applied to the whole animal. In contrast, philosopher Daniel Dennett argues that it is possible to explain behavior and cognitive abilities by applying the Intentional Stance to the brain, a stance that attributes increasingly simple psychological capacities to increasingly less intelligent homunculi. So, among other things, taking (...) the intentional stance requires i) attributing psychological predicates to the brain and its parts, and ii) gradually replacing psychological predicates with non-psychological predicates.If the criticism of Bennett and Hacker is accepted, these requirements lead to two dilemmas. According to the first, the intentional stance would be inapplicable or fallacious: because it implies incurring in the mereological fallacy, and to deny is equivalent to rejecting the intentional stance. The horns of the second dilemma are dualism and explanatory vacuity: can be interpreted in a dualistic sense because it presupposes the distinction between psychological and non-psychological predicates; however, failing to respect generates an infinite regress. In this article I intend to show that both dilemmas are resolved by focusing on the details of the relationship between the intentional stance and the design stance. (shrink)