Before and after (BA) get used in several different ways, but it’s crucial to distinguish two:
- In time. In this sense, childhood is before old age and the stone age was before the bronze age. This sense of BA is synonymous with being earlier and later, and natural science measures it in seconds.
- In causality. In this sense, the teams are determined after the last player is chosen, conception happens after fertilization, and we have to turn the steering wheel before the car will turn. This sense of “after” is synonymous with when, and natural science measures some of these ways of being before in units of force, work, energy, etc.
It’s clear that it is a serious mistake to identify causal and temporal BA, or even to make all causal BA essentially temporal BA (as Hume does). Setting up an essential relation between temporal and causal BA means either that saying “old age happens after youth” = old age happens when youth happens, or saying “my trip to the store became pointless after the store burned down” = the store burned down and then, at some later time, my journey to it became pointless.
These different senses of BA require different senses of simultaneous, and so saying that causal simultaneity demands temporal simultaneity iterates the mistake just made. Some cases of causal simultaneity will involve absolute temporal simultaneity (e.g. when conception is after fertilization or the teams are determined after the last person is chosen) others will have what is for all intents and purposes a temporal simultaneity (e.g. when the car turns after we turn the steering wheel) and other cases will involve a causal simultaneity with some temporal duration (e.g. when a building burns down after the arsonist sets the fire or the water boils after it is put on a fire). This last use the word “after” is ambiguous and can refer either to being non-simultaneous in time or being simultaneous in causality, an ambiguity which makes the possibility of confusion and ill-founded doubt about the “simultaneous causes” spoken of of in the Five Ways particularly likely. I wrote a whole series of posts that suffered under this confusion. I’m in good company though, since it is almost impossible to extract Hume’s account of natural science from this sort of confusion about causes.