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

【小題1】D

【小題2】B

【小題3】A

【小題4】C

【小題5】B

解析:

【小題1】科學研究/探索的方法。文章一開始就提出問題，為什么從希臘文化頂峰時期后兩千年來歸納法和數(shù)學科學發(fā)展如此緩慢，而后的兩百年又超越了前人，是應用新，舊方法關系還是其它（見難句譯注1，2）。第二段講埃及古代在科學探索中運用了演繹推理法，而現(xiàn)在應用了歸納法。這種解釋太狹隘，經(jīng)仔細審核，難以很清晰地點明古代和現(xiàn)代科學教義和探究上明顯的差別。因為一切知識都基于觀察，通過分析，綜合，或綜合分析，歸納演繹推理，有可能的話，經(jīng)過校正或經(jīng)由演繹指導下再觀察而向前推進。第三段進一步闡明不用這些方法觀察，實驗；忽略相關事實，推理不慎；不能答出理論的結論，再用實驗或觀察來檢驗等或用得不全，不論在古代還是現(xiàn)代都會失敗。但這不能說明為什么現(xiàn)代科學具有較高的功效，通過什么方式方法，超越了前人，更不用說說明最近科學突飛猛進的原因。第四，五段涉及事實和理論的關系。

A. 數(shù)學的哲學，文內沒有提。        B. 近來科學的發(fā)展。       C. 事實的驗證，只是最后兩段提及驗證方法之作用。

【小題2】B. 是上天的安排，這是作家在用方法論等失敗后得出的結論。見難句譯注4，第一段最后一句話。

A. 兩個階段的相似性。      . 兩者都試圖應用歸納法。      D. 由于演繹法的衰落。

【小題3】A. 后者需要證實。答案在第四，五段，死段試圖在事實的對立面和理論，或事實和思想中發(fā)現(xiàn)上述現(xiàn)象的解釋看起來有餓太狹隘，也會因模糊不清遭批評。因為，對立面不全面，事實和理論不是同類的事物。理論，如果是真正的理論，就是事實——一種特殊類別的事實，一般復雜，但仍是事實。而事實，從詞的狹義來說，如果很復雜，如果各成分中存在著邏輯的聯(lián)系，就具有理論的一切主要特征。第五段第二句，事實是一個提議，通過運用知識的源泉和經(jīng)驗而證實的提議直接而又簡單。而理論，若是真理論，就有事實的一切特性（除非其證實只能通過非直接的，遙遠的和困難的方式方法），把理論轉成事實必須用簡單的核實，理論因此具有事實的一切特性。

B. 前者簡單。         C. 是現(xiàn)代科學家和古希臘的差異。         D. 幫助我們了解演繹法，三項都不對。

【小題4】C. 是推理演繹科學，這個問題常識就能回答。

A. 歸納法科學。        B. 需要簡單證實。           D. 基于事實和理論。

【小題5】     B. 是一個悖論，見第四，五段注釋。

A. 比喻。      C. 對歸納法和演繹法的贊揚。        D. 雙關語。