Halliday & Matthiessen (2014: 230n):
… seen from a different perspective from that of the traditional transitive/intransitive model, these two functions, the intransitive Actor and the transitive Goal, are actually one and the same — the Medium. The differentiation of different sub-types of ‘material’ clauses is thus based on the combination of Medium + Process in the first instance. One might have expected that it would be based on Actor + Process instead, as the traditional model would suggest; but it turns out that although they have been favoured by philosophers of language drawing on action theory, distinctions based on Actor + Process such as animacy, potency and volitionality are less central to the system of ‘material’ clauses than distinctions based on Medium + Process. In fact, the grammar of transitivity is more centrally concerned with consciousness rather than with animacy, potency or volitionality.