It is also possible to make a similar analysis of the deductive method, that is to say, of formal axiom systems. This is accomplished by analyzing more carefully the new version of Berry's paradox that was presented. Here we only sketch the three basic results that are obtained in this manner. (See the Appendix).
In a formal system with n bits of axioms it is impossible to prove that a particular binary string is of complexity greater than n+c.
Contrariwise, there are formal systems with n+c bits of axioms in which it is possible to determine each string of complexity less than n and the complexity of each of these strings, and it is also possible to exhibit each string of complexity greater than or equal to n, but without being able to know by how much the complexity of each of these strings exceeds n.
Unfortunately, any formal system in which it is possible to determine each string of complexity less than n has either one grave problem or another. Either it has few bits of axioms and needs incredibly long proofs, or it has short proofs but an incredibly great number of bits of axioms. We say “incredibly”' because these quantities increase more quickly than any computable function of n.
见：Gregory J. Chaitin. Information-Theoretic Computational Complexity. IEEE Transactions on Information Theory, IT-20 (1974), pp. 10-15.
以下的俗解完全有可能是不恰当的，期待您的改进与批评！
（1）如果土豆、西红柿、茄子等比“洗菜盆”小，则可以在该盆里洗；
（2）显然这个洗菜盆不能洗大冬瓜；但从土豆、西红柿、茄子的个头越来越大的次序看，应该存在大冬瓜；
（3）不幸的是，洗菜是两难之一：用小洗菜盆洗，则需要多次换水；用另外一个大洗菜盆洗，就可以少换几次水。
尽管古希腊、我国先秦时期就发现了（形式）逻辑里面的悖论，但后来的数学家们似乎忘记了这些。直到罗素悖论（Russell's paradox，也称为理发师悖论，1901年提出），数学家们才重新认真看待这些问题。
1931年Gödel incompleteness theorem是著名的。1974年的前几年，Chaitin定理出现。
问题2：为什么毛主席要求我们“批评与自我批评”？
问题4：我不知道我死了（计算机停机问题）。别人也就不能知道我死了吗？
问题5：语言、视觉都有局限性。不能眼、耳、口直接交流的信息，就不存在吗？
问题6：佛陀释迦摩尼的“若以色见我，以音声求我，是人行邪道，不能见如来。”是什么意思？
以上内容，定有错误。看在真理的份上，请您指正！谢谢！
管窥蠡测
出自：东汉·班固《汉书·东方朔传》：“以管窥天，以蠡测海，以莛撞钟，岂能通其条贯，考其文理，发其音声哉。”
相关链接：
[1] 《中国“科学网大学”逻辑基础研讨中心》活动之一：逻辑基础资源
http://bbs.sciencenet.cn/home.php?mod=space&uid=107667&do=blog&id=430666
http://bbs.sciencenet.cn/home.php?mod=space&uid=107667&do=blog&id=440876
http://blog.sciencenet.cn/home.php?mod=space&uid=107667&do=blog&id=301287
相关专题：众议“科学网大学”
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