一句话：在函数扩展框架下将莱布尼茨三原则分别解释为分离性、紧致性与有向性，并证明三者不能同时成立。
论文研究莱布尼茨的三个原则：不可分辨者的同一、可能性即一致性，以及理想元素正确决定实在事物（转移原则）。作者在 Functional Extensions 这一同时推广紧化、完备化和模型初等扩张的数学结构中，为这些原则给出精确的逻辑-数学表述。在该解释下，三原则分别表现为拓扑或代数性质：分离性、紧致性与有向性。基于这一对应，论文得到一个略显意外的结论：这些莱布尼茨原则可以两两同时满足，但不能三者同时成立。论证以形式化解释和数学推导为主，不涉及经验评估。
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object" (Identity of indiscernibles), "everything can possibly exist, unless it yields contradiction" (Possibility as consistency), and "the ideal elements correctly determine the real things" (Transfer). Here we give a precise logico-mathematical formulation of these principles within the framework of the Functional Extensions, mathematical structures that generalize at once compactifications, completions, and elementary extensions of models. In this context, the above Leibnizian principles appear as topological or algebraic properties, namely: a property of separation, a property of compactness, and a property of directeness, respectively. Abiding by this interpretation, we obtain the somehow surprising conclusion that these Leibnizian principles may be fulfilled in pairs, but not all three together.Comment: arXiv admin note: substantial text overlap with arXiv:1012.4341
@article{paperbot391,
title = {A topological interpretation of three Leibnizian principles within the functional extensions},
author = {Marco Forti},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 3},
year = {2018},
doi = {10.23638/lmcs-14(3:5)2018}
}