下面这段内容摘自某数学论坛(记不清是哪个论坛了) ,注意我标记为红字的部分

奥地利数学家哥德尔在1931年发表了题为《论<数学原理> 及有关系统的形式不可判定命题》的论文,其中提出这样一个观点,在任何数学系统中,只要其能包含整数的算术,这个系统的相容性就不可能通过几个基础学派所采用的逻辑原理建立。简单地说,就是在任何系统中,总有些真理是游离于逻辑之外的,这些真理就叫做歌德尔命题。 比如说大家知道欧几里得的《几何原理》中的第五公设就是平行线公设:两平行线永远不能交于一点。但是打破第五公设,人们仍然可以建立完整的罗巴切夫斯基几何和黎曼几何等等非欧几何,并且在现代物理中都有重要的应用。 一本《几何原理》可以由五个公设推出所有的定理,环环相扣,逻辑严密。没有任何“人为”的痕迹,尽管最后发现“第五公设”基础是不坚实的,但中间的逻辑是清楚地,推演是严密的。

后来,数学家对个别命题的演绎证明逐渐转向了对整个数学的研究。此后很长一段时间,大家在努力构造一个完备的数学体系,包容所有的真理命题,使得所有存在命题可以通过此体系彼此证明出来。但歌德尔这位天才逻辑学家+数学家+理论物理学家在一个形式化的算术体系中构造出了命题G:“G是不可证明的。”这是一个不可判定的命题。(假设G是不可证明的,则G为真,由命题真与命题可证明等价,则G可证明;假设G可证明,则G为真,则G不可证明。)从而也就证明了不完备性定理 Ⅰ)歌德尔第一定理对于包含自然数系的任何相容(彼此矛盾的陈述不同时为公设集所包含)的形式体系F,存在F中的不可判定命题,即存在F中的命题S,使得S和非S都不是在F中可证明的。 Ⅱ)歌德尔第二定理对包含自然数系的任何相容的形式体系F,F的相容性不能在F中被证明。 这样歌德尔就说明了“人类智慧没有能力公式化它的所有数学直觉,它只能用公式表达出它们中的一些” ,而非全部。数学上总是存在着无法用理性证明的直觉,数学远非一大堆毫无生气可言的枯燥的逻辑堆砌,人类理性根本上也是不可能建立这种程式化的逻辑的。同时人类在处理包含思维的抽象体系时有极大的局限性,因为人的理性乃是根植于这个体系中的,人无法超越这个体系来理性地审视思维本身。歌德尔定理认识到了理性的局限性,人永远不能超越理性来认识理性

看完上面的内容,我突然想起以前一个朋友问我的一个问题:你如何才能确定你所在的这个世界是真实的?

正如哥德尔定理所阐述的,这种真实永远无法被证明。

我们所有的人,可能只是处在电脑芯片中的一堆0和1

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当年HostGator推出了一款头一个月只需要0.01美元的Plan,当时大批中国人去订购,HostGator于是订购了大批的服务器来招呼这些“贵客”,没想到中国人享受了几乎免费的高品质虚拟主机一个月后全跑了,一个续费的都没有,于是乎HostGator要支付大量的服务器费用。此后对中国人也是敬而远之。
以下是我和他们客服的聊天记录
FairPlease wait for a HostGator operator to respond.

Welcome to HostGator Live Chat! You are now chatting with ‘Nicole Z.’

Nicole Z.: Welcome to HostGator Live Chat, how may I assist you?

Shan Yang: if I finished the payment with west union,Can I pay for nextyear with paypal or credit card

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Nicole Z.: Is there anything else I can help you with?

Shan Yang: why other people can use paypal and credit card

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Nicole Z.:

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Nicole Z.: 2. The phone number we called to confirm may have been incorrect or was unanswered.

Nicole Z.:

Nicole Z.:

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Shan Yang: Nicole Z.: 1. Your IP may have been too far of a distance from the listed address upon order. Nicole Z.: 2. The phone number we called to confirm may have been incorrect or was unanswered.

Shan Yang: ?

Nicole Z.: correct

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Nicole Z.: From that location, yes

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Nicole Z.: For the reasons, above listed previously. For security reasons.

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Nicole Z.: Is there anything else I can help you with?

Shan Yang: No

Shan Yang: Thank hyou

Shan Yang: Thank you

Nicole Z.: You’re welcome!

Nicole Z.: I am sorry

Nicole Z.: Thank you for using HostGator Live Chat! If you could take a minute to rate your experience with HostGator as well as my overall performance, that would help us to improve our customer service. To do that, just click the button that says “close” in the upper right hand corner. The survey takes less than a minute to fill out.

Shan Yang: at last

Nicole Z.: pardon?

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Nicole Z.: and I am very sorry for the inconveniences

Shan Yang: =]

Shan Yang: thank you again

Nicole Z.: =]

Nicole Z.: You’re welcome!