Modal logic studies arguments whose validity depends on “necessary,” “possible,” and similar notions. This chapter covers the basics, and the next gets into further modal systems.

To help us evaluate modal arguments, we’ll construct a little modal language. For now, our language will build on propositional logic, and thus include all the vocabulary, wffs, inference rules, and proofs of the latter. Our language adds two new vocabulary items: “◊” and “□” (diamond and box):

Calling something possible is a weak claim-weaker than calling it true. Calling something necessary is a strong claim; it says, not just that the thing is true, but that it has to be true-it couldn’t be false.