從國小開始多少有聽過些自相矛盾的情況、對話,今日在「計算理論」課程中再度提到此議題,阿喜老師舉的例子之多,讓我差點闔上的眼睛又張大開來~以下是節錄自講義:
- 【羅素悖論】某村裡只有一位理髮師,他替而且只替所有不自己理髮的村民理髮,問他是否替自己理髮?
- 全能的上帝可否造出一個自己搬不動的石頭?
- 莎朗史東在「魔鬼專家」電影中說:「I’m not a woman you can trust.」
- 你要我說謊話還是真話?
- 古希臘的幾何學家Zeno Paradox(詭論):龜吐賽跑,龜時速10km,兔時速20km,龜先出發一小時,問兔永遠追不上龜?
我知道第5道的矛盾,在於他假設總共時間不到兩小時,於是1小時後相差10km,經過1/2小時後相差5km,接著經過1/4小時後相差2.5km,再經過1/8小時後相差1.25km,繼續經過1/16……
使用數學計算1/2+1/4+1/8+1/16+…,最後的加總結果為接近1,也就表示若不等於2小時,兔是永遠追不上龜的~了改!這我國小就聽過嚕。
WiKi對Paradox也有一番定義與論述:
- Self reference – An example is “This statement is false“, a form of the Liar paradox. The statement is referring to itself. Another example of self reference is the question of whether the barber shaves himself in the Barber paradox. One more example would be “Is the answer to this question no?" In this case, if you replied no, you would be stating that the answer is not no. If you reply yes, you are stating that it is no, because you said yes. But because you answered yes the answer is not no. However you could reply “It isn’t." indicating a negative response without saying the word “no".
- Contradiction – “This statement is false“—the statement cannot be false and true at the same time.
- Vicious circularity or infinite regress – “This statement is false“—if the statement is true, then the statement is false, thereby making the statement true. Another example of vicious circularity is the following group of statements:
- “The following sentence is true."
- “The previous sentence is false."
所以下次我就可以來頑愚性(餘興)節目,問朋友說,我現在在說謊~是真還是假XD?
隨意留個言吧:)~