『数学の原理』におけるラッセルのパラドクスと命題関数の理論

野村 恭史

doi:10.4216/jpssj.46.1-17

『数学の原理』におけるラッセルのパラドクスと命題関数の理論

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野村恭史

書誌事項

タイトル別名

Russell’s Paradox and the Theory of Propositional Functions in <i>The Principles of Mathematics</i>
『スウガクノゲンリ』ニオケルラッセルノパラドクストメイダイカンスウノリロン

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説明

Bertrand Russell has found the paradox that bears his own name in the spring of 1901 and offered a version of the so-called “simple” theory of types as measures against it in an appendix to The Principles of Mathematics (1903). This theory was devised to deal with the class-version of that paradox. But he formulated it also in terms of “predicates” and the type theory has no effect to this formulation. In this paper, I shall show that Russell offered measures also against the “predicate”-version of that paradox in the Principles and it is very interesting in a sense that it enables to avoid the paradox without forbidding self-predications of predicates in general.