關於CR 的 Assumption 類型的完整介紹

首先，我們(men) 來定義(yi) 下assumption。

我們(men) 知道一個(ge) argument由 premise 和conclusion 構成，用公式來表達話，就是

Argument ： Premise ? Conclusion

比如Premise 是小明經常幫助別人

Conclusion 是 小明是好人。

那麽(me) 這裏就有一個(ge) Argument，  小明幫助別人 ? 小明是好人.

這裏的 “?” 可以理解為(wei) “因此”

所以，上麵的Argument 就是，“小明幫助別人，因此小明是好人。”

顯然，這個(ge) Argument 是不見的成立的，而assumption 這個(ge) 邏輯結構存在的意義(yi) ，就是當 premise + assumption 的時候，一定可以得出 conclusion。

也就是 premise  + assumption ? argument

如果要小明是好人，一定成立，那麽(me) 上麵那個(ge) 中文例子的 assumption 就是 “幫助別人，就是好人”

我們(men) 可以看到 “小明幫助別人” +“幫助別人，就是好人” ? “小明是好人“

這是比較理想的bridge 類型的assumtion， 也可以把這種類型叫做sufficient （充分類型的 assumption）【上麵這個(ge) 例子的甚至可以理解為(wei) 是充分必要類型的】

關(guan) 於(yu) 充要類型的，我來舉(ju) 一個(ge) 實際GMAT的例子

Although the school would receive financial benefits if it had soft drink vending machines in the cafeteria, we should not allow them.[Conclusion] Allowing soft drink machines there would not be in our students' interest. If our students start drinking more soft drinks, they will be less healthy.[Premise]

The argument depends on which of the following?

(A) If the soft drink vending machines were placed in the cafeteria, students would consume more soft drinks as a result.

(B) The amount of soft drinks that most students at the school currently drink is not detrimental to their health.

(C) Students are apt to be healthier if they do not drink soft drinks at all than if they just drink small amounts occasionally.

(D) Students will not simply bring soft drinks from home if the soft drink vending machines are not placed in the cafeteria.

(E) The school's primary concern should be to promote good health among its students.

argument 的結構已經在題目中標出，我們(men) 可以看到，正確選項A 很好的銜接起來了【bridge】 premise 和 conclusion 的部分，和我們(men) 上麵舉(ju) 的中文的例子是類似的。

從(cong) 一板一眼的邏輯角度來說，上麵的兩(liang) 個(ge) 例子中的assumption類型其實都是 充要的類型，也就是最完美的assumption 類型。什麽(me) 是充要的assumption 類型呢？

就是這個(ge) assumption即是符合充分性的，又是符合必要性的。

那麽(me) 什麽(me) 是充分性和必要性的assumption 呢？

以下部分看了，你會(hui) 發現，並不複雜。

assumption 的充分性： 就是從(cong) premise + assumption 可以自然的一定得到這個(ge) conclusion。

比如logic reasoning 裏麵的例子：

Ramon has $50 in his wallet 是一個(ge) 充分的assumption， 因為(wei) ?的這個(ge) 箭頭方向上一定成立。但是這不是一個(ge) 必要的assumption。

怎麽(me) 判斷一個(ge) assumption 的必要性呢？

就是對於(yu) assumption 取反了以後這個(ge) argument 是不是就不成立的。

上例的assumption 取反就是 “Ramon does not have $50 in his wallet”。 沒有50 不見的把這個(ge) argument 不成立了，因為(wei) 有可能是45，46，47....

所以?這個(ge) 例子的必要性的assumption 是怎樣的呢？

可以看到，現在premise （The sweater costs $ 40） + assumption (Ramon has at least $20 in his wallet) 不見的可以得出 Conclusion （Ramon has enough money ni his wallet to buy the sweater）. 因為(wei) 有可能 Ramon 隻有35，36....

但是如果對於(yu) 這個(ge) assumption 取反 （Ramon does not at least have $20 in his wallet）. 連 $20 都沒有，顯然是可以讓上麵的argument 不成立的。

所以，判斷一個(ge) assumption 是不是必要性assumption 的方式就是看看，對於(yu) 這個(ge) assumption 取反以後，是不是可以削弱這個(ge) argument。

以上講解了充分性的和必要性的assumption， 那麽(me) 有沒有充分+必要性的，也就是充要性的assumption 呢？

有！

可以看到Ramon does not at least have $40 in his wallet。 首先在這個(ge) 箭頭的方向上可以使得這個(ge) argument 成立，另外如果對於(yu) 這個(ge) assumption 取反，也是可以削弱這個(ge) argument 的，所以就是一個(ge) 充要形式的argument。

回到下麵這道題目裏麵的A 選項，就是一個(ge) 充要形式的argument

Although the school would receive financial benefits if it had soft drink vending machines in the cafeteria, we should not allow them.[Conclusion] Allowing soft drink machines there would not be in our students' interest. If our students start drinking more soft drinks, they will be less healthy.[Premise]

The argument depends on which of the following?

(A) If the soft drink vending machines were placed in the cafeteria, students would consume more soft drinks as a result.

GMAT 裏麵的assumption題目也有是單純的必要性形式的assumption， 比如

Although there is no record of poet Edmund Spenser's parentage, we do know that as a youth Spenser attended the Merchant Tailors' School in London for a period between 1560 and 1570. Records from this time indicate that the Merchant Tailors' Guild then had only three members named Spenser: Robert Spenser, listed as a gentleman; Nicholas Spenser, elected the Guild's Warden in 1568; and John Spenser, listed as a "journeyman cloth-maker." Of these, the last was likely the least affluent of the three- and most likely Edmund's father, [Conclusion] since school accounting records list Edmund as a scholar who attended the school at a reduced fee. [Premise]

Which of the following is an assumption on which the argument depends?

(A) Anybody in sixteenth-century London who made clothing professionally would have had to be a member of the Merchant Tailors' Guild.

(B) The fact that Edmund Spenser attended the Merchant Tailors' School did not necessarily mean that he planned to become a tailor.

(C) No member of the Guild could become Guild warden in sixteenth-century London unless he was a gentleman.

(D) Most of those whose fathers were members of the Merchant Tailors' Guild were students at the Merchant Tailors' School.

(E) The Merchant Tailors' School did not reduce its fees for the children of the more affluent Guild members.

答案E 放到邏輯鏈條 【Premise + E ? Conclusion】,是不是箭頭方向不見的成立，

也就是說 “學校會(hui) 計記錄Edmund 減免過學費” + ” 學校不給富人減免學費“，不見的可以得出，Edmund 的父親(qin) 就是沒錢的那個(ge) 【不管怎麽(me) 說，題目裏麵也隻是說是三個(ge) 裏麵沒錢的，不見的就是絕對意義(yi) 上的沒錢的那個(ge) 】；也就是說E選項這個(ge) assumption 的充分性是不成立的。

但是它的必要性是存在的，如果我們(men) 把E 取反，就是“學校給富有的人也減免學費”那麽(me) 就肯定得不出Edmund的父親(qin) 到底是哪一位了。

上麵這個(ge) 必要性的題目還是比較容易解的，我們(men) 來看一題稍微複雜些的

180. Many gardeners believe that the variety of clematis vine that is most popular among gardeners in North America is jackmanii.[Conclusion] This belief is apparently correct since, of the one million clematis plants sold per year by the largest clematis nursery in North America, ten percent are jackmanii.[Premise]

Which of the following is an assumption on which the argument depends?

(A) The nursery sells more than ten different varieties of clematis.

(B) The largest clematis nursery in North America sells nothing but clematis plants.

(C) Some of the jackmanii sold by the nursery are sold to gardeners outside North America.

(D) Most North American gardeners grow clematis in their gardens.

(E) For all nurseries in North America that specialize in clematis, at least ten percent of the clematis plants they sell are jackmanii.

大多數同學不會(hui) 選A

因為(wei) 覺得Premise 是10% 是jackmanii （clematis 的一種），哪怕再加上這個(ge) assumption （有10種不同類型的clematis），並不能得出，jackmanii 是這幾個(ge) 裏麵最受歡迎的，因為(wei) 另外的9種可以有20%的，有2%... 這樣，10%不就肯定不是最popular。 但是這個(ge) 思考過程隻是否定了這個(ge) assumption 的充分性，並沒有否定它的必要性。其實從(cong) 問法【...an assumption on which the argument depends?】也可以看出來，題目要的是必要性的assumption。

那麽(me) A 選項符不符合必要性呢？

來取個(ge) 反： nursery 裏有少於(yu) 10種的clematis， 這樣10% 是不是肯定不是最popular 的了，顯然把conclusion 給削弱了。所以這個(ge) 答案就是我們(men) 要的必要性的assumption.

總結：

1. assumption 難一些的話就是那些隻是必要性assumption 的題目，那麽(me) 這個(ge) 時候用取反的方式去驗證一下就可以。

2. 簡單一些的assumption 題目就是那些即符合充分性，又符合必要性的。這種類型的就比較一目了然了。再不行，反正也可以用取反的方式去驗證的。

所以在GMAT 裏麵，用取反的方式去驗證assumption的正確答案是很靠譜的方式。