Possible World - Possibility, Necessity, and Contingency

Possibility, Necessity, and Contingency

Further information: Modal logic#The ontology of possibility

Those theorists who use the concept of possible worlds consider the actual world to be one of the many possible worlds. For each distinct way the world could have been, there is said to be a distinct possible world; the actual world is the one we in fact live in. Among such theorists there is disagreement about the nature of possible worlds; their precise ontological status is disputed, and especially the difference, if any, in ontological status between the actual world and all the other possible worlds. One position on these matters is set forth in David Lewis's modal realism (see below). There is a close relation between propositions and possible worlds. We note that every proposition is either true or false at any given possible world; then the modal status of a proposition is understood in terms of the worlds in which it is true and worlds in which it is false. The following are among the assertions we may now usefully make:

• True propositions are those that are true in the actual world (for example: "Richard Nixon became President in 1969").
• False propositions are those that are false in the actual world (for example: "Ronald Reagan became President in 1969").
• Possible propositions are those that are true in at least one possible world (for example: "Hubert Humphrey became President in 1969"). Note: This includes propositions which are necessarily true, in the sense below.
• Impossible propositions (or necessarily false propositions) are those that are true in no possible world (for example: "Melissa and Toby are taller than each other at the same time").
• Necessarily true propositions (often simply called necessary propositions) are those that are true in all possible worlds (for example: "2 + 2 = 4"; "all bachelors are unmarried").
• Contingent propositions are those that are true in some possible worlds and false in others (for example: "Richard Nixon became President in 1969" is contingently true and "Hubert Humphrey became President in 1969" is contingently false).

The idea of possible worlds is most commonly attributed to Gottfried Leibniz, who spoke of possible worlds as ideas in the mind of God and used the notion to argue that our actually created world must be "the best of all possible worlds". However, scholars have also found implicit traces of the idea in the works of Al-Ghazali (The Incoherence of the Philosophers), Averroes (The Incoherence of the Incoherence), Fakhr al-Din al-Razi (Matalib al-'Aliya) and John Duns Scotus. The modern philosophical use of the notion was pioneered by David Lewis and Saul Kripke.