In the light of logic
In the light of logic
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从逻辑上看
DOI：
10.1007/bf02985859
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Andrew P. Arana
中科院分区：
文献类型：
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作者：
Andrew P. Arana
一、基本问题1.拒绝不可判定的：与希尔伯特问题搏斗2。数学中的无穷大：康托尔是必要的吗？3.数学发现的逻辑与数学的逻辑结构II：基本方法4。第五章.工作基础三：GODEL 6。戈德尔的生活和工作7.库尔特·哥德尔：信念和谨慎8。哥德尔1993年第四讲：证明理论9的介绍性说明。关于数学证明，逻辑能告诉我们什么？10.什么取决于什么？数学的证明理论分析11.哥德尔的辩证法解释及其双向延伸V：可数可约数学12.数学中的无穷大：康托是必要的吗？（结论）13.魏尔辩护：Das Kontinuum 70 years later 14.为什么一点点就能走很长的路：科学适用数学的逻辑基础
I: FOUNDATIONAL PROBLEMS 1. Declining the undecidable: Wrestling with Hilbert's Problems 2. Infinity in Mathematics: Is Cantor necessary? 3. The logic of mathematical discovery vs. the logical structure of mathematics II: FOUNDATIONAL WAYS 4. Foundational Ways 5. Working Foundations III: GODEL 6. Godel's life and work 7. Kurt Godel: conviction and caution 8. Introductory note to Godel's 1993 lecture IV: PROOF THEORY 9. What does logic have to tell us about mathematical proofs? 10. What rests on what? The proof-theoretic analysis of mathematics 11. Godel's Dialectica interpretation and its two-way stretch V: COUNTABLY REDUCIBLE MATHEMATICS 12. Infinity in mathematics: Is Cantor necessary? (Conclusion) 13. Weyl vindicated: Das Kontinuum 70 years later 14. Why a little bit goes a long way: Logical Foundations of scientifically applicable mathematics