作者Senkousha ( )
看板logic
標題only if, only when
時間Fri May 19 09:29:12 2006
有一個問題困擾我好一陣子了，一段敘述如下：
A person's cholesterol level will decline significantly if that
person increases the number of meals eaten per day, but only if
there is no significant increase in the amount of food eaten.
However, most people who increase the number of meals they eat
each day will eat a lot more food as well.
上面第二行結尾的 only if，被補習班老師解釋為 "->"，
強調後面的敘述要放在 "->" 符號的右邊，並列了一個式子：
A and B -> C
其中，
A代表"a person increases the number of meals eaten per day"
B代表"a person's cholesterol level will decline significantly"
C代表"there is no significant increase in the amount of food eaten"
用簡單的中文代替則是:
A: 多餐
B: 低膽
C: 少量
多餐又低膽 -> 少量
這與多數人的直覺都不符，我個人認為應該套入 1st-order logic 的觀念寫作：
for all x [多餐(x) and 少量(x) -> 低膽(x)] and
for all y [多餐(y) and 多量(y) -> 高膽(y)]
但是我對自己於 "only if"的解釋也感到很奇怪。
想請問大家，問題究竟在哪裡？是其中的"will"嗎？
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