The Structure of the Ordinals and the Interpretation of ZF in Double Extension Set Theory

Andrzej Kisielewicz has proposed three systems of double extension set theory of which we have shown two to be inconsistent in an earlier paper. Kisielewicz presented an argument that the remaining system interprets ZF, which is defective: it actually shows that the surviving possibly consistent system of double extension set theory interprets ZF with Separation and Comprehension restricted to ₀ formulas. We show that this system does interpret ZF, using an analysis of the structure of the ordinals.     

A dialogue on Zeno's paradox of Achilles and the tortoise

The five participants in this dialogue critically discuss Zeno of Elea's paradox of Achilles and the tortoise. They consider a number of solutions to and restatements of the paradox, together with their philosophical implications. Among the issues investigated include the appearance-reality distinction, Aristotle's distinction between actual and potential infinity, the concept of a continuum, Cantor's continuum hypothesis and theory of transfinite ordinals, and, as a solution to Zeno's puzzle, the distinction between infinite and indeterminate or inexhaustible divisibility.     

先天易的数学基础初探——试论先天卦序与二进位制

本文从自然数及其记数法的基本慨念出发。辨析了与二进位制相关的几个容易混淆的概念,指出序数概念的引入在近代数学发展中有重要意义。作为邵雍数学学派的数学基础,先天易是数学史上第一个专门定义的序数体系,该序数体系在数学史上率先采用了二进位制记数法。先天易作为二进制序数体系这一事实在明清时期引起不同的反响,反对者认为它使易道沦落,大数学家汪莱则从P进制的角度论证它的优越性。本文最后还对近年来反对先天易与二进制有关的两种典型观点进行了剖析．指出其谬误所在。