|Proving Cleanthes Wrong|
Laureano Luna Cabañero
Hume’s famous character Cleanthes claims that there is no difficulty in explaining the existence of causal chains with no first cause since in them each item is causally explained by its predecessor. Relying on logico-mathematical resources, we argue for two theses: (1) if the existence of Cleanthes’ chain can be explained at all, it must be explained by the fact that the causal law ruling it is in force, and (2) the fact that such a causal law is in force cannot explain the occurrence of the events in the chain. In order to perform (1), we manage to express in mathematical terms the intuitive idea that indefinitely delayed explanation is ultimately no explanation. In order to achieve (2), we identify a logical relation we can prove to be as strong as the causal relation at issue in the Cleanthes passage, according to a precise notion of strength of relations. Keywords: cause; chain; autonomous causal chain; ungrounded causal chain; causal law; $ L $-nomologically possible worlds.