Hey Bob, good post. I’ve had the same thought (i.e. the unit of moral analysis is timelines, or probability distributions of timelines) with different formalism
The trolley problem gives you a choice between two timelines (t,¯t∈T). Each timeline can be represented as the set containing all statements that are true within that timeline. This representation can neatly state whether something is true within a given timeline or not: “You pull the lever” ∈t, and “You pull the lever” ∉¯t. Timelines contain statements that are combined as well as statements that are atomized. For example, since “You pull the lever”, “The five live”, and “The one dies” are all elements of t, you can string these into a larger statement that is also in t: “You pull the lever, and the five live, and the one dies”. Therefore, each timeline contains a very large statement that uniquely identifies it within any finite subset of T. However, timelines won’t be our unit of analysis because the statements they contain have no subjective empirical uncertainty.
This uncertainty can be incorporated by using a probability distribution of timelines, which we’ll call a forecast (f,¯f∈F). Though there is no uncertainty in the trolley problem, we could still represent it as a choice between two forecasts: f guarantees t (the pull-the-lever timeline) and ¯f guarantees ¯t (the no-action timeline). Since each timeline contains a statement that uniquely identifies it, each forecast can, like timelines, be represented as a set of statements. Each statement within a forecast is an empirical prediction. For example, f would contain “The five live with a credence of 1”. So, the trolley problem reveals that you either morally prefer f (denoted as f≻¯f), prefer ¯f (denoted as f≺¯f), or you believe that both forecasts are morally equivalent (denoted as f∼¯f).
Hey Bob, good post. I’ve had the same thought (i.e. the unit of moral analysis is timelines, or probability distributions of timelines) with different formalism