I discuss Steinhart’s argument against Benacerraf’s famous multiple reductions argument to the effect that numbers cannot be sets. Steinhart offers a mathematical argument according to which there is only one series of sets to which the natural numbers can be reduced (namely, the finite von Neumann ordinals), and thus attacks Benacerraf’s assumption that there are multiple reductions of numbers to sets. I will argue that Steinhart’s argument is problematic and should not be accepted.

中文翻译：

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为 Benacerraf 的多重归约论证辩护†

我讨论了 Steinhart 的论点，反对 Benacerraf 著名的多重归约论点，即数字不能被设置。Steinhart 提供了一个数学论证，根据该论证，自然数可以归约到的集合（即有限冯诺依曼序数）只有一个系列，因此攻击 Benacerraf 的假设，即数字可以多次归约到集合。我会争辩说斯坦哈特的论点是有问题的，不应该被接受。