The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions maintains its validity when some of the terms included in these propositions are empty. In the following, I first argue that, just as in the case of non-modal propositions, Abelard interprets modal propositions as having existential import, so that it is a necessary condition for the truth of propositions like ‘It is possible for my son to be alive’ or ‘it is necessary that all men are animals’ that their subjects’ referents exist. Then, I present the schemata of inferences that Abelard proposes to describe the logical behaviour of de rebus modal propositions. I argue that these systems of relations are valid only as long as all the terms contained in the formulas have an existing referent. I also claim that Abelard was aware of this difficulty (at least in the Logica Ingredientibus), and, accordingly, he explicitly decided to restrict the validity of his modal system to propositions that do not contain empty terms.

中文翻译：

---

“我未来的儿子可能还活着”。阿伯拉尔模态逻辑中的存在预设与空项

本文的目的是研究阿伯拉尔模态逻辑中的存在输入问题，并询问他为模态命题提出的逻辑关系系统在这些命题中包含的某些术语为空时是否保持其有效性。在下文中，我首先论证，就像在非模态命题的情况下一样，阿伯拉德将模态命题解释为具有存在意义，因此它是诸如“我儿子有可能活着”或“所有的人都是动物是必要的”，他们的对象的指称存在。然后，我提出了 Abelard 提出的用于描述 de rebus 模态命题的逻辑行为的推理图式。我认为这些关系系统只有在公式中包含的所有术语都有一个现有的指称时才是有效的。我还声称 Abelard 意识到了这个困难（至少在 Logica Ingredientibus 中），因此，他明确决定将他的模态系统的有效性限制为不包含空项的命题。