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Full Idea
Lewis's different systems of modal logic differed about such formulae as □P implies □□P; ◊□P implies □P; and ◊S implies □◊S
Clarification
'Nec' (usually a square) and 'poss' (a diamond) are necessarily and possibly
Gist of Idea
The main modal logics disagree over three key formulae
Source
Stephen Yablo (Apriority and Existence [2000], §06)
Book Ref
'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.203
A Reaction
Yablo's point is that the various version don't seem to make much difference to our practices in logic, mathematics and science. The problem, says Yablo, is deciding exactly what you mean by 'necessarily' and 'possibly'.
| 9403 | There are three different deductions for actual terms, necessary terms and possible terms [Aristotle] |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| 16456 | For modality Lewis rejected boxes and diamonds, preferring worlds, and an index for the actual one [Lewis, by Stalnaker] |
| 14670 | Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N] |
| 7689 | The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette] |
| 8859 | The main modal logics disagree over three key formulae [Yablo] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 8480 | S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein] |
| 7787 | Possible worlds logics use true-in-a-world rather than true [Girle] |
| 7788 | Modal logic has four basic modal negation equivalences [Girle] |
| 7796 | Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle] |