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发布时间：2006-06-22 13:30     点击：

　　Mathematics must deal with well-defined situa- tions. Thus, mathematicians depend on an intellectual effort outside of mathematics for the crucial specifica- tion of the approximation that mathematics is to take literally. Give mathematicians a situation that is the least bit ill-defined, and they will make it well-defined, perhaps appropriately, but perhaps inappropriately. In some cases, the mathematicians' literal-mindedness may have unfortunate consequences. The mathema- ticians turn the scientists' theoretical assumptions, that is, their convenient points of analytical emphasis, into axioms, and then take these axioms literally. This brings the danger that they may also persuade the scientists to take these axioms literally. The question, central to the scientific investigation but intensely disturbing in the mathematical context-what happens if the axioms are relaxed?-is thereby ignored.

　　The physicist rightly dreads precise argument, since an argument that is convincing only if it is precise loses all its force if the assumptions on which it is based are slightly changed, whereas an argument that is convincing though imprecise may well be stable under small perturbations of its underlying assumptions.

　　21. The author discusses computing machines in the first paragraph primarily in order to do which of the following?

　　(A) Indicate the dangers inherent in relying to a great extent on machines

　　(B) Illustrate his views about the approach of mathematicians to problem solving

　　(C) Compare the work of mathematicians with that of computer programmers

　　(D) Provide one definition of intelligence

　　(E) Emphasize the importance of computers in modern technological society

　　22. According to the passage, scientists are skeptical toward their equations because scientists

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