Many-Valuation, Modality, and Fuzziness

Motivation for Modal Logic

We consider some fundamental things from history and some motivating things. Lemmon [16], pp. 20-21, describes Leibniz’s basic ideas for motivating the idea of modal logics. He says:

“Leibniz’s suggestion now becomes: a sentence is necessarily true (in this world) iff that sentence is true in all worlds alternative to this world. Actually, in many connections it is intuitively simpler to think of world t as accessible from world u rather than alternative to u. This at least has the merit of avoiding the temptation to suppose that alternativeness is a symmetric relation between worlds – that if t is alternative to u, then u must be alternative to t. Indeed, we shall not assume that each world is accessible from itself, or even that to each world there is at least one accessible world: there may be accessibility-isolated worlds. We shall find that to many such assumptions about the accessibility relation between worlds there correspond distinctive modal sentences which come out valid precisely because we have made those assumptions. If necessity means truth in all accessible worlds, then possibility will mean truth in some accessible world. Thus our remarks about the vagueness of the notion of necessity, and the various more precise accounts of it, may be repeated mutantis mutandis for the notion of possibility.”