more from this thinker | more from this text
Full Idea
Modal logic by its very nature is not monolithic, but fragmented into multiple systems of modal qualifications, reflected in the plurality of accessibility relations on modal model structures or logically possible worlds.
Gist of Idea
Modal logic is multiple systems, shown in the variety of accessibility relations between worlds
Source
Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §3)
Book Ref
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.4
A Reaction
He implies the multiplicity is basic, and is only 'reflected' in the relations, but maybe the multiplicity is caused by incompetent logicians who can't decide whether possible worlds really are reflexive or symmetrical or transitive in their relations.
| 16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
| 16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
| 10760 | With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg] |
| 16468 | Non-S5 can talk of contingent or necessary necessities [Stalnaker] |
| 9456 | Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette] |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |