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<p>Let’s suppose you think that there are <i>no</i> uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes—you’ve prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that a formal notion of restrictiveness suggests that it is restrictive to hold that there <i>are</i> uncountable sets.</p>

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Is (Un)Countabilism Restrictive?

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • Neil Barton

摘要

Let’s suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes—you’ve prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that a formal notion of restrictiveness suggests that it is restrictive to hold that there are uncountable sets.