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In mathematics and logic, plural quantification is the theory that an individual variable x may take on ''plural'', as well as singular, values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London etc. for x, we may substitute both Alice and Bob, or all the numbers between 0 and 10, or all the buildings in London over 20 storeys. The point of the theory is to give first-order logic the power of set theory, but without any "existential commitment" to such objects as sets. The classic expositions are Boolos 1984, and Lewis 1991. == History == The view is commonly associated with George Boolos, though it is older (see notably Simons 1982), and is related to the view of classes defended by John Stuart Mill and other nominalist philosophers. Mill argued that universals or "classes" are not a peculiar kind of thing, having an objective existence distinct from the individual objects that fall under them, but "is neither more nor less than the individual things in the class". (Mill 1904, II. ii. 2,also I. iv. 3). A similar position was also discussed by Bertrand Russell in chapter VI of Russell (1903), but later dropped in favour of a "no-classes" theory. See also Gottlob Frege 1895 for a critique of an earlier view defended by Ernst Schroeder. The general idea can be traced back to Leibniz. (Levey 2011, pp. 129–133) Interest revived in plurals with work in linguistics in the 1970s by Remko Scha, Godehard Link, Fred Landman, Roger Schwarzschild, Peter Lasersohn and others, who developed ideas for a semantics of plurals. 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「plural quantification」の詳細全文を読む スポンサード リンク
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