基于迄今为止所取得的与“无穷概念、逻辑”相关领域的研究新成果，分析了“概念、逻辑、悖论”之间的密切关系，对比了无穷理论体系中三个组成部分新、旧内容之间的主要区别，即经典无穷观和新无穷观，与“无穷”相关的经典数量体系和新数量体系，与“无穷”相关的数量形式的新、旧处理理论和技术（比如极限论）。进一步分析芝诺悖论、贝克莱悖论和罗素悖论家族千百年来悬而未决且不断繁衍壮大的原因，事实证明了自古以来，人们在对这三个悖论所揭示问题的研究工作中那种“忽视基础理论研究（重形式-轻本体）”的思路一直是错误的。得到明确的结论，现有“概念-逻辑”、无穷理论体系基础的缺陷使人们自古以来一直无法知道芝诺悖论、贝克莱悖论和罗素悖论是“三胞胎”悖论，它们生于、养于、受保护于现有知识理论体系，与该体系共存亡，在现有知识体系中不可能单独解决其中的任何一个悖论；人类2500多年来艰辛却无果的“无穷悖论”史证明了经典无穷理论体系中与“潜无穷-实无穷”相关的各种内容是错误的、必须抛弃；注重“概念-逻辑”的研究，构建、研发以“无穷规律、性质及其载体”为基础的新无穷理论体系及其相关的逻辑体系，是解决这“三胞胎”无穷悖论悬案的唯一出路。%Basing on the new research achievements in the“infinitude concept-logic”related field, the close relationships among“con-cept, logic, paradox”are analyzed and the major differences of three components between classical and new infinitude system are com-pared:the classical and new infinitude ideas, the infinitude related classical and new number systems, the classical and new treating theories and techniques of the infinitude related number forms(such as limit theory). The reasons of why the members of the suspended Zeno’s Paradox, Berkeley’s Paradox and Russell’s Paradox families have been keeping increasing are further studied and it is proved that the working idea of“neglecting the fundamental research”since antiquity has been wrong. Two conclusions are drown:(1)The de-fects in the foundations of present“concept-logic”theory and classical infinitude theory system have been unable people to understand the fact since antiquity that Zeno’s Paradox, Berkeley’s Paradox and Russell’s Paradox are actually triplets paradoxes having been bound up with the same knowledge system with the same fate. Produced, nourished and protected together in the same knowledge sys-tem, none of the“Triplets’Paradoxes”can be solved alone.(2)Our 2500 years“hard but fruitless”history of infinitude paradoxes has proved that all the“potential infinity-actual infinity”related contents in present classical infinitude system are wrong and should be a-bandoned, a new“infinitude concept-logic”theory system basing on“infinitude law and nature-the carriers of infinitude law and na-ture”should be developed. This is the only way to solve the“Triplets’Paradoxes”as well as the defects disclosed by them.
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