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In philosophy and logic, the concept of a possible world is used to express modal claims. The concept of possible worlds is common in contemporary philosophical discourse but has been disputed. == Possibility, necessity, and contingency == 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"). (Reagan did not run for president until 1976, and thus couldn't possibly have been elected.) * Possible propositions are those that are ''true in at least one possible world'' (for example: "Hubert Humphrey became president in 1969"). (Humphrey did run for president in 1968, and thus could have been elected.) 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").〔See "A Priori and A Posteriori" (author: Jason S. Baehr), at ''(Internet Encyclopedia of Philosophy )'': "A necessary proposition is one the truth value of which remains constant across all possible worlds. Thus a necessarily true proposition is one that is true in every possible world, and a necessarily false proposition is one that is false in every possible world. By contrast, the truth value of contingent propositions is not fixed across all possible worlds: for any contingent proposition, there is at least one possible world in which it is true and at least one possible world in which it is false." Accessed 7 July 2012.〕 * 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 Rene Descartes,〔"Nor could we doubt that, if God had created many worlds, they would not be as true in all of them as in this one. Thus those who could examine sufficiently the consequences of these truths and of our rules, could be able to discover effects by their causes, and, to explain myself in the language of the schools, they could have a priori demonstrations of everything that could be produced in this new world." -The World, Chapter VII〕 a major influence on Leibniz, 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Possible world」の詳細全文を読む スポンサード リンク
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