Arrhenius’s impossibility theorems purport to demonstrate that no population axiology can satisfy each of a small number of intuitively compelling adequacy conditions. However, it has recently been pointed out that each theorem depends on a dubious assumption: Finite Fine-Grainedness. This assumption states that there exists a finite sequence of slight welfare differences between any two welfare levels. Denying Finite Fine-Grainedness makes room for a lexical population axiology which satisfies all of the compelling adequacy conditions in each theorem. Therefore, Arrhenius’s theorems fail to prove that there is no satisfactory population axiology. In this paper, I argue that Arrhenius’s theorems can be repurposed. Since all of our population-affecting actions have a non-zero probability of bringing about more than one distinct population, it is population prospect axiologies that are of practical relevance, and amended versions of Arrhenius’s theorems demonstrate that there is no satisfactory population prospect axiology. These impossibility theorems do not depend on Finite Fine-Grainedness, so lexical views do not escape them.

阿雷尼乌斯（Arrhenius）的不可能定理旨在证明，没有任何人口价值论能够满足少数几个直观上令人信服的充分条件中的每一个。但是，最近有人指出，每个定理都取决于一个可疑的假设：有限细粒度。该假设表明，在任何两个福利水平之间存在有限的轻微福利差异序列。否定有限细粒度为满足所有定理中所有令人信服的充分条件的词汇总体价值论提供了空间。因此，阿伦尼乌斯定理未能证明没有令人满意的总体价值论。在本文中，我认为阿伦尼乌斯定理可以重新利用。由于我们所有影响人口的行动带来不止一个不同人口的可能性都不为零，具有实际意义的前景价值论，以及Arrhenius定理的修订版本表明，没有令人满意的人口前景价值论。这些不可能定理不依赖于有限细粒度，因此词汇视图不能逃脱它们。