1What we are really doing here is defining a real-world morality as a relation on the Cartesian product of the set of actions and the set of manifestations. But to provide proper definitions and explanations of these terms (relation, Cartesian product), and to justify the notion of a “set of manifestations,” would take us too far afield and is out of scope for the intended audience. Instead we are using the term “data set” as an informal way of referring to the more rigourous concept of a mathematical relation, in the hope that this will be sufficiently clear and acceptable to the reader.
On this topic, we note that these various terms and ideas we are borrowing from the world of mathematics (set, mapping, domain, codomain, value) are technically not applicable in our present sphere of inquiry, since none of the things we are talking about is defined in true set-theoretic terms. Rather we are using these ideas as metaphors to help us maintain clarity and precision of thought. At the end of the day we are in the messy world of actions and consequences, not the pure one of mathematics.
