Quarter Wit, Quarter Wisdom: Stuck in Assumptions Again

There is a particular issue in assumption questions that I would like to discuss today. We discussed in our previous posts that assumptions are ‘necessary missing premises’. Many students get stuck between two options in assumption questions. The correct option is the necessary premise. The incorrect one is often a sufficient premise. Due to the sufficiency, they believe that that particular option is a stronger assumption. But the point to remember is that an assumption is only necessary for the conclusion to be true. It may not actually lead to the conclusion beyond a reasonable doubt. You only have to answer what has been asked (which is an assumption), not what you think is better to make the conclusion true.

Let me explain this with an example:

Question: Exports of United States cotton will rise considerably during this year. The reason for the rise is that the falling value of the dollar will make it cheaper for cloth manufacturers in Japan and Western Europe to buy American cotton than to get it from any other source.

Which of the following is an assumption made in drawing the conclusion above?

(A) Factory output of cloth products in Japan and Western Europe will increase sharply during this year.
(B) The quality of the cotton produced in the United States would be adequate for the purposes of Japanese and Western European cloth manufacturers.
(C) Cloth manufacturers in Japan and Western Europe would prefer to use cotton produced in the United States if cost were not a factor.
(D) Demand for cloth products made in Japan and Western Europe will not increase sharply during this year.
(E) Production of cotton by United States companies will not increase sharply during this year.

Solution:

First, let’s analyze the given argument:

Premises:
– Dollar is falling.
– It will be cheaper for cloth manufacturers in Japan and Western Europe to buy American cotton than to get it from any other source.

Conclusion:
– Exports of United States cotton will rise considerably during this year.

The conclusion links ‘sale of cotton’ to ‘cost of cotton’. It says that since the cost of American cotton will be lower than the cost of cotton from any other source, American cotton will sell. We are assuming here that the American cotton is adequate in all other qualities that the cloth manufacturers look for while buying cotton or that lower cost is all that matters. We are assuming that lowest cost will automatically lead to sale.

Let’s look at each of the options now:

(A)   Factory output of cloth products in Japan and Western Europe will increase sharply during this year.

Notice that we don’t NEED the factory output to increase. Even if it stays the same or in fact, even if it falls, as long as the manufacturers find American cotton suitable, the cotton exports of US could rise. Hence this is not the assumption.

(B)   The quality of the cotton produced in the United States would be adequate for the purposes of Japanese and Western European cloth manufacturers.

This option says that the quality is adequate and hence this is an assumption. Notice that it is necessary for our conclusion. If the quality is not adequate, no matter what the cost, US cotton sale may not increase. Hence, answer is (B).

(C)   Cloth manufacturers in Japan and Western Europe would prefer to use cotton produced in the United States if cost were not a factor.

This is the tricky non-correct option! Many people will swing between (B) and (C) for a while and then choose (C).  This option says that Japanese and Europeans prefer to use US cotton if cost does not matter. Do we NEED this to be true? No. It is good if it is true because it means that if cost of US cotton goes down, US cotton will sell more (hence, it is sufficient for the conclusion to be true – assuming all else stays constant). But do we NEED them to prefer US cotton? No. It is not necessary for our conclusion to be true. Even if the manufacturers don’t particularly prefer US cotton, US cotton exports could still increase if the price is the lowest.

Beware of this difference between ‘necessary’ and ‘sufficient’ conditions. Remember that assumptions are NECESSARY conditions; they don’t need to be sufficient. We end up incorrectly choosing sufficient conditions because they seem to be all encompassing and hence more attractive for our conclusion. If the sufficient condition is satisfied, then the conclusion has to be true. But mind you, that is not what the question is asking you. The question is looking for only a necessary condition, not a sufficient one. Also notice that sufficient conditions may not be necessary.

(D)   Demand for cloth made in Japan and Western Europe will not increase sharply during this year.

This is incorrect. We are not assuming that the demand for their cloth will not increase.

(E)    Production of cotton by United States companies will not increase sharply during this year.

It doesn’t matter what happens to the production of cotton in US. All we care about is that exports should rise.