Philosophy Word of the Day – Modal Logic

Study of reasoning about what must or might be the case, as well as what merely happens to be the case. The formalization of modal logic for the propositional calculus introduces special operators designating necessity and possibility (L and M). “It is necessary that p” (Lp) is interpreted to mean that p must be true in all possible worlds, and “It is possible that p” (Mp) that p is true in at least one possible world. On these interpretations,

Lp º ~M~p is tautologous.

(Via Philosophical Dictionary)

In addition,

In classical modal logic, a proposition is said to be

  • possible if and only if it is not necessarily false (regardless of whether it is actually true or actually false);
  • necessary if and only if it is not possibly false; and
  • contingent if and only if it is not necessarily false and not necessarily true (ie. possible but not necessary).

(Via Wikipedia)

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