Self-study
Proofs relying crucially on computers provide less certainty than do proofs not requiring computers. █████ █████████ █████ ██████ ██████ ██████████████████ ███████ ████ ██████ ███ █████ ███████ ███ ██████ ██ █████████ ████ ███████ ███ █████████ ███████████ ███ █████████ ██████ ████████████ ██████ █████ ███ ██ ████████ ██ █████ ████████████ ██ ███████ ██ █████ █████ ███ █████ ████ ██████████ ████████████ ███ ████ ███ ████████ ██ █ ███████████ ██████ ████ █ ██████████ ██ █████ ██████████
Summary
Proofs that rely on computers give less certainty than do proofs that don’t require using computers. This is because humans alone can’t verify computer-dependent proofs. With proofs that don’t require computers, we can verify them by human calculation. Note that although we often use computers to verify these non-computer-dependent proofs, we’re using these computers for convenience, not because we depend on the computers.
Strongly Supported Conclusions
Computers can provide assistance concerning tasks for which computers are not necessary.
Whether humans can verify a proof without the aid of computers is a factor in the level of certainty that the proof provides.
15.
The statements above, if true, ████ ████████ ███████ █████ ███ ██ ███ ██████████
a
Only if a ███████ ██████ ██ ███████ ██ ███████ ███ ████ ██ █ ████████ ███ ███ █████ ████ ███ ██████ ██ █████████ ████ ███ █████ ██ ████████
Unsupported. The stimulus acknowledges that computers can aid in the proof of non-computer-dependent proofs. So, it might be possible to judge that such proofs are correct even if we arrive at those proofs with the aid of computers.
b
We can never ██ ██████████ ████ ████ ██████ ███████ █████████ ██ █████████ ██ ███ ███████ ██████ ████ ██████ ██ ███ ███████
Strongly supported. We’re told that human cognition can’t verify computer-dependent proofs. And if they can’t verify such proofs, that suggests they can’t detect every single error in those proofs. So, some errors may slip by that humans can’t detect.
c
Whenever a computer ████████ █████ ███████████ ██ █ ██████ ███ ██████ ██ █████████ ████████ ██ ███ █████ ██ ████████
Unsupported. The stimulus acknowledges that we can use computers for convenience for non-computer-dependent proofs. And if such computer makes an error, we can catch the error through human calculation.
d
If one can ███████████ █████████ ██ █████ ████████████ ███ ███ ██ ██████████ ███████ ██ ███
Unsupported. Human ability to confirm something by calculation may mean we can be more certain about the thing, but that doesn’t imply we can be “completely” certain of it.
e
It is impossible ██ ██████████ ███ █████████ █████████ ██ ██████ ██ █████ ██ ██████████ ███████ ████ ██ ██████████
Unsupported. The stimulus tells us that when we use calculators to perform calculations that could be done by humans, we are not using calculators as a supplement. But that doesn’t imply it’s impossible for devices to supplement human cognition in other contexts.