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This is the context:

Computers can do many wonderful things. However, there are many tasks that they cannot perform. Computers cannot determine whether a painting is beautiful; they do not “understand” moral issues; and they cannot fall in love. Such “human” processes are beyond computation. Whether a painting is beautiful is subject to taste, and computers don’t have taste. They also don’t have a sense of ethics to deal with moral questions. All of these questions are subjective and computers don’t do well with subjective questions. In this chapter, we will explore certain problems that have objective answers but that nevertheless cannot be solved by computers.

Source: The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us By Noson S.Yanfosky

What is the meaning of "don't do well with" in this context? Does it mean "doesn't have a good relationship with subjective questions?" If not, what then? Thanks in advance.

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    don't do well with [..] means that cannot understand them, they cannot interpret them, cannot give a particular solution to the problem. Oct 16 '20 at 21:30
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The confusion may be related to the fact that "do" has over 30 meanings.

The meaning is likely the second main entry from that link.

(transitive) To perform; to execute. Synonyms: accomplish, carry out, functionate All you ever do is surf the Internet. What will you do this afternoon?

"well" roughly means "good". More correctly: it means accurately, competently, satisfactorily.

The phrase can be translated:

computers don’t perform well with subjective questions.
computers don’t function well with subjective questions.

Next, what is the task being "performed"? What is the job they don't do well?

That information can be found earlier in the paragraph. Jobs such as "determine whether a painting is beautiful" or "understand moral issues". In other words, "think like a human being".

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