Set-theoretic potentialism is one of the most lively trends in the philosophy of mathematics. Modal accounts of sets have been developed in two different ways. The first, initiated by Charles Parsons, focuses on sets as objects. The second, dating back to Hilary Putnam and Geoffrey Hellman, investigates set-theoretic structures. The paper identifies two strands of open issues, technical and conceptual, to clarify these two different, yet often conflated, views and categorize the potentialist approaches that have emerged in the contemporary debate. The final outcome is a taxonomy that should help researchers navigate the rich landscape of modal set theories.

中文翻译：

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集合论势论的分类


集合论势能论是数学哲学中最活跃的趋势之一。集合的模态帐户以两种不同的方式开发。第一个由查尔斯·帕森斯 (Charles Parsons) 发起，重点关注作为对象的集合。第二个可以追溯到希拉里·帕特南和杰弗里·赫尔曼，研究集合论结构。本文确定了技术和概念上的两个开放问题，以澄清这两种不同但经常混为一谈的观点，并对当代辩论中出现的潜在主义方法进行分类。最终结果是一种分类法，可以帮助研究人员驾驭模态集合理论的丰富领域。