Lange ( 2013 , 2016 ) argues that some natural phenomena can be explained by appeal to mathematical, rather than natural, facts. In these “distinctively mathematical” explanations (DMEs), the core explanatory facts are either modally stronger than facts about ordinary causal law or understood to be constitutive of the physical task or arrangement at issue. Craver and Povich ( 2017 ) argue that Lange’s account of DME fails to exclude certain “reversals”. Lange ( 2018 ) has replied that his account can avoid these directionality charges. Specifically, Lange argues that in legitimate DMEs, but not in their “reversals,” the empirical fact appealed to in the explanation is “understood to be constitutive of the physical task or arrangement at issue” in the explanandum. I argue that Lange’s reply is unsatisfactory because it leaves the crucial notion of being “ understood to be constitutive of the physical task or arrangement” obscure in ways that fail to block “reversals” except by an apparent ad hoc stipulation or by abandoning the reliance on understanding and instead accepting a strong realism about essence.

中文翻译：

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数学形式上的模态和构成

Lange（2013，2016）认为，某些自然现象可以通过诉诸于数学事实而非自然事实来解释。在这些“独特的数学”解释（DME）中，核心解释事实在模态上比关于普通因果律的事实强，或者被理解为正在讨论的物理任务或安排的构成。Craver and Povich（2017）认为，兰格对DME的描述未能排除某些“逆转”。Lange（2018）回答说，他的账户可以避免这些定向费用。兰格特别指出，在合法的二甲醚中，而不是在其“冲销”中，解释中所呼吁的经验事实“被理解为解释性地构成了有争议的物理任务或安排”。