For a typical believer in possible worlds will, if asked to explain what they are, give an account that uses modal notions at some crucial point.
One example of the prevalence of the traditional use of modal notions can be found in the early medieval de dicto/de re analysis of examples such as 'A standing man can sit'.
To the extent that these notions are free of modality, Lewis has arguably reduced modal notions to non-modal.
On the other hand, a revised version of the indispensability argument can be used to motivate the translation into the modal language, thus emphasizing the indispensable role played by the primitive modal notions introduced by the modal structuralist.
That Lewis's truth conditions for modal statements are themselves free of modality and, hence, that his theory counts as a genuine reduction of modal notions to non-modal is not terribly controversial (albeit not undisputed — see Lycan 1991, 224 27; Divers and Melia 2002, 22 24).
(On modalism, see Forbes (1992), Melia (2003: 81 98) and Peacocke (1999: 155 159).) Instead, modal notions are properly understood in terms of primitive modal operators like the box and diamond of modal logic.
The Megarians also discussed how to define various modal notions and debated the interpretation of conditional propositions.
One kind of modal realism holds that there is a distinctive class of truths essentially involving the modal notions of necessity and possibility.
The notions just referred to necessity, possibility, impossibility, contingency, strict implication and certain other closely related ones are known as modal notions, and a logic designed to express principles involving them is called a modal logic.
Kripke began his important work on the semantics of modal logic (the logic of modal notions such as necessity and possibility) while he was still a high-school student in Omaha, Neb.
