Bayle Shanks's website: ideas-philosopy-semanticsOfPossible

What are the various possible semantics of the word 'possible'?

Kant has a trichotomy between necessity, possibility, and actuality.
In some modal logics, 'necessary' and 'possible' are algebraically analogous to 'forall' and 'exists'; 'it's possible that x' is equivalent to 'it's not necessary that not(x)'
- The Kripke structure interpretation of this is that there is a set of 'possible worlds' and 'it's possible that x' means that there exists a possible world in which x is true
- In this sort of logic, the scope of 'necessary' may vary depending on what is taken as 'axiomatic'. Necessary given the laws of physics? Necessary given human nature? Necessary given the law of the organization under discussion?
  - Taking the laws of physics as axiomatic is somewhat preferred, although converational context can easily override this.
Sometimes 'neccessary' and 'possible' are used as synonms for 'required' and 'permissible'. E.g. to a child: 'it's necessary that you eat your peas'. Both pairs can fit with the modal semantics discussed in the previous bullet point. One can interpret 'required' in this sense as equivalent to 'necessary if my set of demands are taken as axiomatic/given'.
Sometimes possibility is used as a conversational pragmatic meaning 'this is sufficiently likely that i consider it worthwhile to discuss this further now, if you'd like' (and 'impossible' means the opposite, 'let's not discuss this further right now, i consider it an unlikely outcome'). This can fit with both the 'accessible' and the 'negotiative' uses, e.g. 'Jane: Well if we get $100,000,000 then it's easy to solve our problem...; Mary: Impossible.' vs. 'Jane: I want a raise. Mary: Impossible.'. This usage explains why sometimes people give advice like 'find out what most people think is impossible and then do it' to people seeking a startup idea; they don't necessarily mean things like 'make things levitate with only your mind like in Star Wars' (physical impossibility), but rather they mean to find something that people have implicitly accepted as immovable constraints, and find ways to move them.