Question

Why the inductive and mathematical sciences, after their first rapid development at the culmination of Greek civilization, advanced so slowly for two thousand years—and why in the following two hundred years a knowledge of natural and mathematical science has accumulated, which so vastly exceeds all that was previously known that these sciences may be justly regarded as the products of our own times—are questions which have interested the modern philosopher not less than the objects with which these sciences are more immediately conversant. Was it the employment of a new method of research, or in the exercise of greater virtue in the use of the old methods, that this singular modern phenomenon had its origin? Was the long period one of arrested development, and is the modern era one of normal growth? Or should we ascribe the characteristics of both periods to so-called historical accidents—to the influence of conjunctions in circumstances of which no explanation is possible, save in the omnipotence and wisdom of a guiding Providence?

The explanation which has become commonplace, that the ancients employed deduction chiefly in their scientific inquiries, while the moderns employ induction, proves to be too narrow, and fails upon close examination to point with sufficient distinctness the contrast that is evident between ancient and modern scientific doctrines and inquiries. For all knowledge is founded on observation, and proceeds from this by analysis, by synthesis and analysis, by induction and deduction, and if possible by verification, or by new appeals to observation under the guidance of deduction—by steps which are indeed correlative parts of one method; and the ancient sciences afford examples of every one of these methods, or parts of one method, which have been generalized from the examples of science.

A failure to employ or to employ adequately any one of these partial methods, an imperfection in the arts and resources of observation and experiment, carelessness in observation, neglect of relevant facts, by appeal to experiment and observation—these are the faults which cause all failures to ascertain truth, whether among the ancients or the moderns; but this statement does not explain why the modern is possessed of a greater virtue, and by what means he attained his superiority. Much less does it explain the sudden growth of science in recent times.

The attempt to discover the explanation of this phenomenon in the antithesis of “facts” and “theories” or “facts” and “ideas”—in the neglect among the ancients of the former, and their too exclusive attention to the latter—proves also to be too narrow, as well as open to the charge of vagueness. For in the first place, the antithesis is not complete. Facts and theories are not coordinate species. Theories, if true, are facts—a particular class of facts indeed, generally complex, and if a logical connection subsists between their constituents, have all the positive attributes of theories.

Nevertheless, this distinction, however inadequate it may be to explain the source of true method in science, is well founded, and connotes an important character in true method. A fact is a proposition of simple. A theory, on the other hand, if true has all the characteristics of a fact, except that its verification is possible only by indirect, remote, and difficult means. To convert theories into facts is to add simple verification, and the theory thus acquires the full characteristics of a fact.

     The title that best expresses the ideas of this passage is

[A]. Philosophy of mathematics.              [B]. The Recent Growth in Science.

[C]. The Verification of Facts.                [C]. Methods of Scientific Inquiry.

According to the author, one possible reason for the growth of science during the days of the ancient Greeks and in modern times is

[A]. the similarity between the two periods.

[B]. that it was an act of God.

[C]. that both tried to develop the inductive method.

[D]. due to the decline of the deductive method.

     The difference between “fact” and “theory”

[A]. is that the latter needs confirmation.

[B]. rests on the simplicity of the former.

[C]. is the difference between the modern scientists and the ancient Greeks.

[D]. helps us to understand the deductive method.

     According to the author, mathematics is

[A]. an inductive science.           [B]. in need of simple verification.

[C]. a deductive science.            [D]. based on fact and theory.

     The statement “Theories are facts” may be called.

[A]. a metaphor.                  [B]. a paradox.

[C]. an appraisal of the inductive and deductive methods.

[D]. a pun.

Answer 1

【小题1】D

【小题2】B

【小题3】A

【小题4】C

【小题5】B

解析:

【小题1】科学研究/探索的方法。文章一开始就提出问题，为什么从希腊文化顶峰时期后两千年来归纳法和数学科学发展如此缓慢，而后的两百年又超越了前人，是应用新，旧方法关系还是其它（见难句译注1，2）。第二段讲埃及古代在科学探索中运用了演绎推理法，而现在应用了归纳法。这种解释太狭隘，经仔细审核，难以很清晰地点明古代和现代科学教义和探究上明显的差别。因为一切知识都基于观察，通过分析，综合，或综合分析，归纳演绎推理，有可能的话，经过校正或经由演绎指导下再观察而向前推进。第三段进一步阐明不用这些方法观察，实验；忽略相关事实，推理不慎；不能答出理论的结论，再用实验或观察来检验等或用得不全，不论在古代还是现代都会失败。但这不能说明为什么现代科学具有较高的功效，通过什么方式方法，超越了前人，更不用说说明最近科学突飞猛进的原因。第四，五段涉及事实和理论的关系。

A. 数学的哲学，文内没有提。        B. 近来科学的发展。       C. 事实的验证，只是最后两段提及验证方法之作用。

【小题2】B. 是上天的安排，这是作家在用方法论等失败后得出的结论。见难句译注4，第一段最后一句话。

A. 两个阶段的相似性。      . 两者都试图应用归纳法。      D. 由于演绎法的衰落。

【小题3】A. 后者需要证实。答案在第四，五段，死段试图在事实的对立面和理论，或事实和思想中发现上述现象的解释看起来有饿太狭隘，也会因模糊不清遭批评。因为，对立面不全面，事实和理论不是同类的事物。理论，如果是真正的理论，就是事实——一种特殊类别的事实，一般复杂，但仍是事实。而事实，从词的狭义来说，如果很复杂，如果各成分中存在着逻辑的联系，就具有理论的一切主要特征。第五段第二句，事实是一个提议，通过运用知识的源泉和经验而证实的提议直接而又简单。而理论，若是真理论，就有事实的一切特性（除非其证实只能通过非直接的，遥远的和困难的方式方法），把理论转成事实必须用简单的核实，理论因此具有事实的一切特性。

B. 前者简单。         C. 是现代科学家和古希腊的差异。         D. 帮助我们了解演绎法，三项都不对。

【小题4】C. 是推理演绎科学，这个问题常识就能回答。

A. 归纳法科学。        B. 需要简单证实。           D. 基于事实和理论。

【小题5】     B. 是一个悖论，见第四，五段注释。

A. 比喻。      C. 对归纳法和演绎法的赞扬。        D. 双关语。