PrepTest 130, Section 4, Question 15
Proofs relying crucially on computers provide less certainty(63 more words not shown)
The statements above, if true,(8 more words not shown)
- AOnly if a(24 more words not shown)
- BWe can never(18 more words not shown)
- CWhenever a computer(16 more words not shown)
- DIf one can(12 more words not shown)
- EIt is impossible(15 more words not shown)
Reading the argument
Think of a proof as reasoning meant to establish a result. The passage distinguishes results we can verify by human calculation from proofs that crucially require a computer.
At first, we might wonder whether the computer itself makes a result less certain, or whether the problems needing a computer are harder to check. Five plus two equals seven is easy to verify. A very complicated calculation could require help beyond what a person can independently check.
The passage focuses on that verification limit. Human cognition alone cannot verify computer-dependent proofs, so those proofs provide less certainty than simple arithmetical facts we can check ourselves.
Using a calculator is not automatically the same as crucially depending on one. We might enter seventeen plus thirteen to get thirty, yet still be able to check the addition by hand. The calculator is convenient in that case; it does not supply an ability beyond human verification.
What we’re looking for
I do not have a more specific result to predict for the most-supported question. We should look for a statement that respects the distinction between essential dependence and optional assistance, while keeping “less certain” separate from “no certainty.”
Working the answers
- A
This is too strong about any degree of certainty. The passage says computer-dependent proofs provide less certainty, not none at all. It also allows using a calculator for a calculation humans can verify. Merely receiving computer help does not prevent all justified confidence in a result.
- BCorrect
If a proof crucially relies on a computer and humans cannot independently verify it, we cannot be completely sure that no undetected error remains. That fits the passage's explanation of the reduced certainty. B does not claim that every such proof contains an error; it says that complete confidence in the absence of undetected errors is unavailable.
- C
This treats every use of a computer in place of human calculation as reducing certainty. But a calculator could add five and two, and we could still independently verify seven. The relevant distinction is whether the proof requires computer abilities beyond human verification, not simply whether someone chose to use a computer.
- D
Greater certainty is not automatically complete certainty. The passage compares computer-dependent proofs with human-verifiable arithmetic; it does not supply a universal guarantee that anything corroborated by human calculation is absolutely certain. D turns a comparison into that guarantee.
- E
The passage allows computers to supplement human cognition. That is why some proofs depend on them. Its concern is the resulting limit on independent human verification, not an inability of artificial devices to extend what humans can calculate.
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