Symbols in Principia Mathematica

“(x)φx” — “There exists an x for which φx is true,” or “there exists an x satisfying φx” page 16. 1st ed.

“(inverted iotax)φx” — “the x which satisfies \varphi(\hat{x}) .” Page 31. 1st ed.

“E!(inverted iotax)φx”  — “the x satisfying φx exists”. Page 32. 1st ed.

“𝜾 ‘x” — “the class whose only member is x.” page 37, 1st ed.

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It is meaningless to say a set is or is not a member of itself.

A defining function \phi(\hat{z}) can be used to determine a set whose members are arguments that satisfy \phi(\hat{z}) . Let \hat{z}(\phi z) denote the set determined by \phi(\hat{x}) . To say \hat{z} is or is not a member of itself is to use \hat{z}(\phi z) as an argument for \phi(\hat{z}) , namely \phi(\hat{z}(\phi(z))) , thus violates vicious-circle principle.

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Go back to China at your own risk

pidou萧光琰是1968年12月10日晚自杀的。1920年萧光琰出生于日本(祖籍福建福州),后移居美国。1942年毕业于坡摩那大学化学 系,1945年获得芝加哥大学研究院物理化学博士学位,后任芝加哥大学化学系助理研究员、冶金研究所研究员、美孚石油公司化学师。1950年回国,后到大 连化学物理研究所担任研究员。在抗美援朝、反右运动等一系列运动中,萧光琰都因直率的个性惹来不大不小的麻烦。文革开始后,他却未能逃此劫难,被人怀疑是 特务为美国提供情报,1968年10月5日被关进“牛棚”。有人对他进行审问,对他拳打脚踢,甚至使用皮鞭,打得他遍体鳞伤。当时还有人给他起了个外号叫 “白屎”(博士的谐音)。在饱受了心灵和肉体的双重折磨之后,萧光琰在牛棚服用安眠药(巴比妥)自杀。当天下午,萧光琰的妻子,正在营城子农场劳动改造的 美籍华人甄素辉被拉到化学物理所,被要求继续交待萧光琰的罪行。在萧光琰夫妇被揪斗后,他们15岁的女儿小洛连在嘲骂、追打中过着痛苦的孤独生活。12月 14日,甄素辉和小洛连也一起服用巴比妥自杀了。图为萧光琰在某次博士论文答辩会上留影。


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An example of vicious-circle fallacy in proving identity

Define “\large x is identical with y” as meaning “whatever is true of x is true of y,” i.e.

\phi(x) always implies \phi(y).”            (1)


If  x is identical with  a and “ x is identical with  y , then  y is identical with a.

Although the conclusion is sound, the above reasoning embodies a vicous-circle fallacy. The following is the above demonstration written out in full:

 x is identical with  a ” is, by definition, “(\phi)\cdot\phi(x) \supset \phi(a).”   (2)

\vdash .  [(1).   \frac{ (\phi) \cdot \phi(x) \supset \phi(a) }{ \phi(x) } ]                        (3)

\supset \vdash (\phi) \cdot \phi(x) implies \phi(a) .implies.  (\phi) \cdot \phi(y) implies \phi(a) .             (4)

\supset \vdash y is identical to a

(1) is a function in the form of f(\phi(\hat{z}), x, y)

(2) is a function of x and can be written as \psi(x) in which \phi is an apparent variable instead of a real variable.

In step (3), (2) is taken as a possible value of \phi ,  but (2) involves the totality (all possible values) of \phi , thus a value of \phi is determined by its totality and violates vicious-circle principle.

Note: A value of \phi\hat{x} is obtained by assigning a \phi , namely \phi(x), \psi(x), \chi(x), etc. A value of \phi(x) is obtained by assigning an x , namely \phi(a), \phi(b), \phi(c), etc. The latter determination is NOT used in this post.

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Reminiscent of 1914: “War among European nations is in essence a civil war.” –Bertrand Russell

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The right sources of national pride

  • Sparkling teeth;
  • Beautiful women, frank and affectionate;
  • Handsome men, frank and affectionate;
  • Magnificent animals in natural habitats;
  • High quality of living;
  • Contributions to science and technology;
  • Contributions to philosophy and art;
  • Fresh air;
  • Clean water;
  • Blue sky.
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The corruption and anarchy in Chinese politics do much less harm than one would be inclined to expect.

Honourable_Bertrand_RussellNine-tenths of the activities of a modern Government are harmful; therefore the worse they are performed, the better. In China, where the Government is lazy, corrupt, and stupid, there is a degree of individual liberty which has been wholly lost in the rest of the world. –Bertrand Russell. Problem of China. 1922

Quoter’s note: The most honest government is also the most persecuting, from the Puritans in 1600’s New England to Mao’s regime in the 1960’s. If equality becomes an end, the most likely result will be universal poverty, as is shown by former communist states in their most pious periods.

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