Modal potentialism argues that mathematics has a generative nature, and aims to formalise mathematics accordingly using quantified modal logic. This paper shows that Øystein Linnebo’s approach to modal potentialism in his book Thin Objects is incoherent. In particular, he is committed to the legitimacy of introducing a primitive modal predicate of formulae. However, as with the semantic paradoxes, natural principles for such a predicate are inconsistent; no such predicate can underpin an account of modal potentialism. Hence, Linnebo’s intended interpretation of the primitive modality and his formal framework do not match up.

中文翻译：

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我们应该如何理解模态潜力论者的模态？


模态潜力主义认为数学具有生成性质，旨在使用量化模态逻辑相应地将数学形式化。本文表明，Øystein Linnebo 在他的《薄物体》一书中对模态势能论的方法是不连贯的。特别是，他致力于引入公式的原始模态谓词的合法性。然而，与语义悖论一样，这种谓词的自然原则是不一致的;没有这样的谓词可以支撑对模态势能论的解释。因此，Linnebo 对原始模态的意图解释和他的形式框架并不匹配。