How can the whole have a causal effect on its parts? This is considered impossible because, if the supervenient whole is completely determined by its parts, then the whole-to-parts causation would be redundant. However, the exclusion argument did not assume a hierarchy of multiple supervenient functions and the existence of an inter-level negative feedback control mechanism. Here, we propose that this mechanism enables a causal effect from the whole to its parts. Feedback control typically involves two mechanisms: observing and controlling of the feedback error. These mechanisms can be implemented at two different levels of the hierarchy. We assume that the macro-level consists of a set of mathematical functions that supervene on physical neural states. An algebraic structure of these functions describes a macro-level equation that determines the feedback error. This equation is independent of an external cause, introducing new causal power to the micro-level while avoiding overdetermination. Modifying the micro synaptic weights within the neural networks via inter-level negative feedback control is a whole-to-parts causation mechanism. It should be noted that this paper does not intend to take a position on the ontology surrounding downward causation.
Ohmura et al. (Tue,) studied this question.