# Suzy and Billy throwing rocks at a bottle or hitting a bell - are these examples of late preemption?

Regarding causation, late preemption occurs, when a process (cause) leads to an effect, but a backup-process is also set in motion and would have led to the same effect, if the other process wouldn't have happened.

A popular example for suche a late preemption is the following:

"Suzy and Billy both throw rocks at a bottle. Suzy is slightly quicker, and consequently it is her rock, and not Billy’s, that breaks the bottle. But Billy, though not as fast, is just as accurate: had Suzy not thrown, or had her rock somehow been interrupted mid-flight, Billy’s rock would have broken the bottle moments later." (Paul & Hall 2013, Causation. A User's Guide. p. 99)

But Paul & Hall also present a slightly different example of this situation:

"Billy and Suzy throw rocks, this time not at a bottle, but at a bell. The bell rings twice in rapid succession: the first time as a result of Suzy’s throw, the second time as a result of Billy’s. Nothing deserving the name “preemption” is going on." (Paul & Hall 2013, Causation. A User's Guide. p. 101)

Paul & Hall, on page 99, show following neuron diagram:

Just one page later, they add this diagram:

My questions are: Which of these situations is an instance of late preemption? And is the bottle-situation represented by the 2nd picture? And the bell-situation by the 1st picture? (Unfortunately I am having a hard time comprehending this english text in the mentioned book.)

In case you want to read the related 2-3 pages: The book is easily available via "libgen".

• Are they arguing that late preemption does not exist because the same event cannot occur at different times, so if the first cause had not existed, the second cause would have caused a different event? Jul 29, 2021 at 21:25
• @DavidGudeman: If I am not mistaken, these thought experiments try to attack Lewis's counterfacutal theory of causation. First, it is necessary to know what "causal dependence" means: "Where c and e are two distinct possible events, e causally depends on c if and only if, if c were to occur e would occur; and if c were not to occur e would not occur." To overcome problems with early preemption, Lewis then defines causation as "c is a cause of e if and only if there exists a causal chain leading from c to e". A causal chain consists of events connected by causal dependence. 1/2 Jul 29, 2021 at 21:55
• Now, late preemption is a problem for this idea of causation. Consider the lower picture and let's call the neuron next to C "D". "If D would not have fired, E would not have fired" is wrong, because then B would have excited E. So although C did fire, Lewis could not consider it the cause of event E. For this, one would need to distinguish between E_1 (caused by C) and E_2 (caused by A). 2/2 Jul 29, 2021 at 21:55