Q15 - Proofs relying crucially on computers

[tamwaiman]

I wonder whether (C) is too extreme to be wrong.
Since the stimulus only says we human cannot verify "computer-dependent" proofs.
Thank you.

[giladedelman]

That's exactly right! Computer-dependent proofs provide less certainty than proofs that can be done with human calculation, but that doesn't mean that if you choose to use a computer for some calculation, you lose certainty.

As for the others:

(B) is correct, supported by the second line: "Human cognition alone cannot verify computer-dependent proofs," so it must be the case that a proof relying on computers could have errors we humans don't detect.

(A) is incorrect in two ways: not using a computer is not the same as not needing a computer, and "any degree of certainty" is too strong; we just know that computer-dependent proofs are less certain.

(D) is also too extreme. Corroborating something by human calculation provides more certainty, but that doesn't mean it's completely certain.

(E) is sort of an overly broad generalization. Just because in certain cases computers are used as conveniences, rather than supplements, that doesn't mean we can never supplement human cognition through artificial devices.

[eunjung.shin]

That's exactly right! Computer-dependent proofs provide less certainty than proofs that can be done with human calculation, but that doesn't mean that if you choose to use a computer for some calculation, you lose certainty.

Yes, I agree with you but that's not what the answer choice C says.
It says "the degree of certainty provided by the proof is reduced."
doesn't says certainty is lost.

so...why is C wrong?

[giladedelman]

Read my above post this way: "Computer-dependent proofs provide less certainty than proofs that can be done with human calculation, but that doesn't mean that if you choose to use a computer for some calculation, you lose SOME certainty."

I was using "lost" in the same sense as "reduced," as in, "I lost weight / I reduced my weight." So the point is that we can't infer that simply choosing to use a computer will reduce the amount of certainty behind a given proof.

[crazinessinabox]

I thought (C) became obviously wrong when I thought of the calculator example the stimulus provides where it seems to state explicitly that this replacement (calculator replaces human calculation) wouldn't necessarily reduce the certainty (apparently because humans can still independently verify the proof, even if they sometimes use calculators to make arithmetic easier). Computer-dependent proofs can't be proven by human cognition alone, which is why they are less certain.

[xinglipku]

I initially chose B correctly but then I got confused about E. Though E is over broad to some extent, I though this is to "strengthen" but not "assumption". So my understanding is that E can strengthen the statement since if no human cognitive ability can be substituted by computer, neither can human's ability to identify/correct the errors that computers make. Therefore proofs that solely rely on computers can never correct itself (by computer s), thus less credible than those can be verified by human.

Can you please explain more why E (esp thinking in this way) is still incorrect?

[zagreus77]

I wonder whether (C) is too extreme to be wrong.
Since the stimulus only says we human cannot verify "computer-dependent" proofs.
Thank you.

It is too extreme to be right.

The argument in the stimulus only talks about proofs relying crucially on computers, So C goes far beyond this, way out of scope. If C had said, whenever a computer is crucially relied on ...the certainty would be reduced, it would have been right. The key language is "crucially relied upon." The right answer does trade on this language, does address exactly the point in the stimulus, and is thus correct.

[disguise_sky]

Could anyone kindly explain what "attends" mean in the sentence "such proof can never provide the degree of certainty that attends our judgement concerning ...."?

Sorry if the question seems stupid. I'm not a native speaker. Thanks for your help!

[tommywallach]

Attends just means "comes along with".

I.e. The musician had all the riches that attend a big hit record.

-t

[steves]

I had this one narrowed down to (B) and (C), but I'm still not sure, even with the above discussions, why (C) is not correct or less supported than (B). Usually, extreme language like "whenever" is a red flag. However, the passage says that computer-dependent proofs can NEVER provide the degree of certainty that attends our (human) judgments.

[rinagoldfield]

Steves, you are absolutely right that the passage says that computer-dependent proofs can NEVER provide the degree of certainty that attends our (human) judgments. The key here, as Gilad alludes to above, is that “computer-dependant proofs” is NOT synonymous with “whenever a computer replaces a human calculation in a proof.”

In fact, the stimulus outlines a scenario in which this is not the case. People may use a calculator to compute arithmetic, yet humans are able to verify that arithmetic. Thus, arithmetic is not computer-dependent. Calculating arithmetic is an example of a computer replacing a human, but not of a computer-dependant proof.

The author is fine with computers replacing humans; he is skeptical of proofs that depend on computers.

Thus (C) is indeed too strong.

[ganbayou]

Hi, so "proofs" here means propositions of math, right?
(At first I thought it means evidence or something.)

Thank you

[tommywallach]

Yes.

[zhupon]

I didn't pick C because it says "we can NEVER be completely sure ..." rather than simply saying "we can NOT be completely sure ..." How do we get the support for "never?" How do we know because we cannot verify computer-dependent proofs NOW we cannot do it in the future? Thanks!

[maria487]

I didn't pick C because it says "we can NEVER be completely sure ..." rather than simply saying "we can NOT be completely sure ..." How do we get the support for "never?" How do we know because we cannot verify computer-dependent proofs NOW we cannot do it in the future? Thanks!

Hi zhupon,

I will attempt to answer your question, though I am no expert. Remember the question stem--"the statements above, if true, most strongly support which one of the following"--this question is not asking for something that absolutely must be true under any circumstance, but rather for what is most strongly supported (kind of like a less intense version of a must be true question). So, here your concerns are valid--it may be true that in the future, we cannot verify the proofs. But with these type of questions, we are only looking for exactly what the stem is asking us for: what can be most strongly supported.

(B) is the only answer choice that can be supported given the facts in the stimulus. The support from it comes from the second sentence of the stimulus, where we find out that humans alone cannot verify computer-dependent proofs.

I'm with you that this seems way too strong (the "never" caught my attention also and I ultimately chose (C) because of this), but now I am seeing why (B) is correct though it does use strong language. I would say that strong language is acceptable as an answer choice if there are no other viable correct answers. Here, there are no viable choices out of the answer choices; therefore, by default, (B) is our answer despite the strong language. If we were down to 2 that both seem correct, I would be more wary of the strength of the language and choose the weaker language. I wouldn't say that this strategy is infallible, but rather just a rule of thumb to go by