logicists
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Logicism holes that mathematics can be reduced to logic, but the logicists were beaten by the discovery of the set paradox, because they have not discerned the intrinsic differences between logic and mathematics.
逻辑主义认为数学可以化归为逻辑,集合论悖论的发现给逻辑主义者造成重大的打击,逻辑主义失败的原因在于他们没有看到逻辑与数学之间存在着质的区别。
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"Logicists supposed that abstract mathematical objects can be entirely developed starting from basic ideas of sets and rational, or logical, thought; a variant of logicism, known as mathematical Platonism, views these objects as existing external to and independent of an observer"
逻辑主义认为抽象的数学对象全部可以从基本的几组想法以及合理的或逻辑的思想发展出来,称为数学的柏拉图主义的一个变型把这些对象看作是观察者之外的、独立的存在
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"Logicists suppose d that abstract mathematical objects can be entirely developed starting from basic ideas of sets and rational, or logical, thought; a variant of logicism, known as mathematical Platonism, views these objects as existing external to and independent of an observer"
逻辑主义认为抽象的数学对象全部可以从基本的几组想法以及合理的或逻辑的思想发展出来,称为数学的柏拉图主义的一个变型把这些对象看作是观察者之外的、独立的存在
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Hisresearch on philosophy has the important relations with the mathematicaldevelopment and especially with the investigations of the logicists, formalists andintuitionists on the mathematical foundation.
因为他的诸多哲学思考都与当时的数学发展特别是数学中逻辑主义、形式主义和直觉主义对数学基础的探讨有着重要的联系。
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Eventually, the different facets of the controversy factioned the creatures of the region into many little bands of quarrelling doctrinaires: Formalists, Logicists, Intuitionists, Neo-intuitionists, Finitists, etc.
最终,参加争论的各方分解为若干个数学流派,它们的理论相互冲突,这些派别分别是:形式主义、逻辑实证主义、直觉主义、新直觉主义以及有限论者等等。