Downward causation, property emergence and Aristotelian causal modes

The problem of downward causation is a key subject in the formulation of non-reductive physicalism as well as in the understanding of property emergence. Two possible interpretations of downward causation, to which Aristotelian thought is relevant, are examined. In the mathematical understanding of nature in classical mechanics, the principle of causality should meet requirements that entailed the rejection of three among the four Aristotelian causal modes. Those requirements do not seem equally important in the special sciences and one may suggest, then, that Aristotle's contribution may be taken into account. A definition of an emergent property is proposed, in which downward causation is interpreted according to the formal and functional causal modes.