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.1
See also: Modal Logic: An Introduction
by Brian F. Chellas
5 comments :
I don't understand this at all.
An example would be great. I don't understand this fully.
An example would be great to understand this better.
The tautology on the bottom helps when you say it out loud: "It's necessary that p means that it's not possible that not p." In no possible worlds can not p exist, therefore, p is necessary, or, p exists all the time everywhere.
Anyone interested on a good summary of logic is suggested to purchase: "The Little Logic Book". The book is a collaboration of 4 philosophers from Calvin College. I think many here at Apologetics 315 will benefit from it.
In Christ,
Brian
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