Whether humans can verify a proof without the aid of computers is a factor in the level of certainty that the proof provides.
A
Only if a proof’s result is arrived at without the help of a computer can one judge with any degree of certainty that the proof is correct.
B
We can never be completely sure that proofs relying crucially on computers do not contain errors that humans do not detect.
C
Whenever a computer replaces human calculation in a proof, the degree of certainty provided by the proof is reduced.
D
If one can corroborate something by human calculation, one can be completely certain of it.
E
It is impossible to supplement the cognitive abilities of humans by means of artificial devices such as computers.
Madden: Industrialists address problems by simplifying them, but in farming that strategy usually leads to oversimplification. For example, industrialists see water retention and drainage as different and opposite functions—that good topsoil both drains and retains water is a fact alien to industrial logic. To facilitate water retention, they use a terrace or a dam; to facilitate drainage, they use drain tile, a ditch, or a subsoiler. More farming problems are created than solved when agriculture is the domain of the industrialist, not of the farmer.
Summary
Industrialists solve problems by simplifying them, but if this strategy were applied to farming the result would be oversimplification. For example, an industrialist sees water retention and drainage as opposite functions when in fact these factors aren’t necessarily so. Industrialists would facilitate retention by using a terrace or dam, and they would facilitate drainage using a drain tile, ditch, or subsoiler. In farming, more problems are created than solved using the industrialists’ methods.
Strongly Supported Conclusions
Problems associated with farming should be addressed by recognizing the complexity of a given problem.
A
The handling of water drainage and retention is the most important part of good farming.
This answer is unsupported. We don’t know whether drainage and retention are the most important factors of good farming. These factors were given as an example to illustrate how industrialists would oversimplify these issues.
B
The problems of farming should be viewed in all their complexity.
This answer is strongly supported. The Madden’s criticism with industrialists is that industrialists tend to simplify problems. Applying this strategy to farming would result in oversimplification.
C
Farmers are better than anyone else at solving farming problems.
This answer is unsupported. We don’t know whether farmers are better than anyone else. At best, we only know that farmers are better suited than industrialists to solve farming problems.
D
Industrial solutions for problems in farming should never be sought.
This answer is unsupported. Saying industrial solutions should “never” be sought is too strong. We only know from the stimulus that these solutions usually lead to oversimplification. There could be some instances where these solutions don’t lead to oversimplifications.
E
The approach to problem solving typical of industrialists is fundamentally flawed.
This answer is unsupported. The Madden is not arguing that an industrialist approach to solving problems is “fundamentally flawed.” Rather, the Madden is arguing that these approaches are flawed when specifically applied to farming.