我是否搞懂lawyer大神的例题，欢迎拍砖！

laiweizhou · 发表于 2011-10-22 11:17:05

No mathematical proposition can be proven true by observation. It follows that it is impossible to know any

mathematical proposition to be true.

The conclusion follows logically if which one of the following is assumed?

(A) Only propositions that can be proven true can be known to be true

(B) Observation alone cannot be used to prove the truth of any proposition

(C) If a proposition can be proven true by observation then it can be known to be true.

(D) Knowing a proposition to be true is impossible only if it cannot be proved true by observation
第一步：先把主项的否定转到谓语的否定，根据句意需要，修改主语的全称或者特称
前提1：No mathematical proposition can be proven true by observation
修改为 All mathematical proposition can't be proven true by observation
结论：It follows that it is impossible to know any mathematical proposition to be true.
修改为 All mathematical proposition to be true can't be known
简化前提和结论为：M代表All mathematical proposition S代表be proven true by observation M和S的关系是M不在S里面
M代表All mathematical proposition P代表to know M和P的关系是M不在P里面
因为 M不在S。所以 M不在Q。
或者: 因为 M属于非S。所以 M属于非Q。
非S和非Q的关系，必须是非Q包含非S。即非Q的外延大于非P。例如M是女人，所以M是人因为人的外延包含了女人集合
或者：M是非人，所以M是非女人。因为非女人的外延大于非人
非Q包含非S 等价于S包含Q
所以是：be proven true by observation is （includes） to know
我似乎感觉到包含和if then 的关系有得时候可以这样等价
if A ,then B 等价于B 包含A
所以答案也可以改为：
If a proposition can be known to be true, then it can be proven true

以上的解析还需要各位NN们指点下，我感觉有点拗，如有考试出现这种题，我肯定挂了

我是否搞懂lawyer大神的例题，欢迎拍砖！

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