Gottlob Frege (戈特洛布·弗雷格弗里德里希·路德维希·戈特洛布·弗雷格德语Friedrich Ludwig Gottlob Frege,宽式IPA:/ˈɡɔtlop ˈfʁeːɡə/;1848年11月8日-1925年7月26日),著名德国数学家逻辑学家哲学家。是数理逻辑分析哲学的奠基人。

ontological /╷ɒntə╵lɒdʒikl;╷ɑntə╵lɑdʒikəl/ 
adj: ontological speculation 本体论的演绎.

Chapter 5. Self-reference / liar paradox

Eubulides 欧布利德斯 BC400 希腊逻辑学家

Russell’s paradox
Now, consider the set of all those sets that are not members of themselves. Call this R. Is R a member of itself, or is it not? If it is a member of itself, then it is one of the things that is not a member of itself, and so it is not a member of itself. If, on the other hand, it is not a member of itself, it is one of those sets that are not members of themselves, and so it is a member of itself. It would seem that R both is and is not a
member of itself.

This paradox was discovered by Bertrand Russell, whom we met in Chapter 4, and so is called Russell’s paradox.Like the liar paradox, it has a cousin. What about the set of all sets that are members of themselves. Is this a member of itself, or is it not? Well, if it is, it is; and if it is not, it is not. Again, there would seem to be nothing to determine the matter either way.

Chapter 9 . Identity and change

Leibniz 莱布尼茨

Chapter 10. Vagueness / slope slippery (Fuzzy theory)

sorites paradoxes 连锁诡辩

A standard form of the argument is to the effect that by adding one grain of sand at a time, one can never form a heap; ‘sorites’ comes from soros’, the Greek for heap.)

Example: A person who is 5 years old is a (biological) child. If someone is a child, they are still a child one second later. In which case, they are still a child one second after that, and one second after that, and one second after that. . . . So after 630,720,000 seconds, they are still a child. But then they are 25 years old!

Chapter 11

actuaries 精算师

Chapter 13. Decision theory (expectation, 期望值理论)

Blaise Pascal 帕斯卡 17世纪法国科学家、神学家。

Pascal’s Wager

Chapter 15

Euclid 欧几里得 BC4-3世纪希腊数学家

Kurt Gödel 库尔特·哥德尔 出生於奧匈帝國數學家邏輯學家哲學家维也纳学派(维也纳小组)的成员。哥德尔是二十世纪最伟大的逻辑学家之一,其最杰出的贡献是哥德尔不完备定理 (等效于图灵停机问题,但早于图灵5年提出并证明)和连续统假设的相对协调性证明。