THE QUESTION

Which if any of the many systems of modal logic in the literature is it whose theorems are all and only the right general laws of necessity? That depends on what kind of necessity is in question, so I should begin by making distinctions.

A first distinction that must be noted is between metaphysical necessity or inevitability – “what could not have been otherwise” – and logical necessity or tautology – “what it is self-contradictory to say is otherwise.” The stock example to distinguish the two is this: “Water is a compound and not an element.” Water could not have been anything other than what it is, a compound of hydrogen and oxygen; but there is no self-contradiction in saying, as was often said, that water is one of four elements along with earth and air and fire.

The logic of inevitability might be called mood logic, by analogy with tense logic. For the one aims to do for the distinction between the indicative “it is the case that…” and the subjunctive “it could have been the case that…,” something like what the other does for the distinction between the present “it is the case that…” and the future “it will be the case that…” or the past “it was the case that…” The logic of tautology might be called endometalogic, since it attempts to treat within the object language notions that classical logic treats only in the metalanguage.