Continuing the thoughts around expressing Chomsky’s ethical opinion regarding US military actions as expressed by the documentary that I watched during 2016-2017 break.
It became obvious that while propositional logic and set theory are comforting languages, they are not the most convenient when operationalizing an ethic. For example, there seem to be a need to distinguish these prescriptive targets: must do, must not do, may do, may not do.
It seems “may not do” is “not may do” due to common English use even though technically both expression should be subset relation. I.e. “You may not smoke” states “you must not smoke” instead of “you can choose not to smoke.” Although that imprecision is inconsequential to the current discussions.
So in fact the expression can be simplified by including do_not_do_ actions for each action in simple TAS. We must also impose a contemporaneous interpretation to a as to mean a is an action viewed at some references moment, ostensibly now.
Then, the predicate , reads “p1 must do a to p2” is expressed as . is simply .
The need to restrict preposition to single moments in time is in retrospect necessary. All preposition can be sub-indexed with reference time: prescriptive proposition means it is ethical at time , while descriptive preposition means something is done at time t.
That’s a mouthful. But at least we can avoid the pitfalls such as the “may not” fiasco we have in English.
(Disclaimer, I watched a thirdprty documentary about Chomsky. Some videoed statements were stitched together and I watched that. doesn’t mean I am writing to explain what he actually said or meant.)