弗协调的弗雷格(英文)

Paraconsistent Frege

本文表明,二阶弗协调概括与弗雷格的第五公理是足道的。也表明,如果等数关系是初始符号,那么通过弗协调推理可以从第五公理可以推出休谟原则。最后表明,弗协调的休谟原则不能用作逻辑主义数学的基础。

This paper shows the non-triviality of second-order paraconsistent comprehension and Frege’s infamous Basic Law V. Then, it shows that Hume’s Principle can be derived from Basic Law V by means of paraconsistent inference provided that equinumerosity is regarded as primitive. Finally, it shows that paraconsistent Hume’s Principle cannot serve as a foundation for mathematics of Logicism.