内容概述
故事先介绍柏拉图及其雅典学院，然后讨论柏拉图格言“不懂几何者不得入内”所体现的数学教育观：数学研究是训练心智的理想场所。接着引出近几十年来关于“训练迁移”的争论——一派认为数学培养真理感、正直品格、整洁习惯与精密思考能力；另一派认为这种迁移并不彻底、自动、不可避免。最后指出心理学家倾向于折中观点：迁移只有在带着特定目的教学时才可能发生。
中文正文
58° 柏拉图格言和训练转移
柏拉图
“西方世界一切哲学家中最崇高、最迷人、最受人爱戴的”柏拉图，公元前427年出生在雅典（或雅典附近）。他在那儿跟苏格拉底学哲学，然后开始他的智慧漫游，在南非海岸跟昔兰尼（Cyrene）的西奥多罗（Theodorus）研究数学，成为著名的毕达哥拉斯弟子阿尔希塔斯（Archytas）的亲密朋友。大约公元前387年，他回到雅典，建立了著名的雅典学院，一个系统探求哲学和科学的机构。他的后半生都在管理他的学院，公元前347年，老人死了，享年80岁。公元前4世纪的重要数学工作，几乎都是柏拉图的朋友和学生们完成的，他的学院因而成为承前启后的纽带，联系着之前的毕达哥拉斯学派和之后的亚历山大数学学院。雅典学院延续了900年，直到公元529年，基督徒们从东罗马帝国皇帝拿到一纸法令，才永久地关闭了它的大门。
柏拉图对数学的影响不是因为他有什么数学发现，而在于他热忱地相信，数学研究是思想训练的理想场所，从而对哲学家的培养，对理想国的未来统治者的成长，都是至关重要的。难怪他在学院的大门写下这句著名的格言：
不懂几何者不得入内。
于是，在柏拉图看来，数学的逻辑元素和数学研究带来的纯粹的思想精神，使它成为无上崇高的东西，因为这一点，数学在学院的课程里也占据着重要的地位。
最近几十年来，关于智力训练和训练的转移，发生了激烈的争论，分化为两个极端。喜欢柏拉图的人宣称，数学的研究培养了学生对真理的尊重，从而形成正直的品格；它还培养了整洁的习惯，专心致志的作风，特别是精密思考的能力。但机械论心理学的出现，给这些主张的效能带来很大疑问，而且，事实也证明，训练的转移并不是彻底、自觉和不可避免的。在学数学的那些学生中有许多不诚实、不整洁的例子，他们也不能清晰思考非数学的问题。不分青红皂白的人却认为，这意味着训练的转移是不存在的。今天，心理学家似乎同意，真理应该在两个极端之间，假如怀着某种特定的目的来教一门学科，训练的转移才可能发生。
英文正文
58° Plato's motto and the transfer of training.
PLATO
PLATO, “the most winged, most charming, and best loved of all the philosophers of the Western World,” was born in or near Athens in 427 B.C. He studied philosophy under Socrates there, and then set out upon his extensive wanderings for wisdom, studying mathematics under Theodorus of Cyrene on the African coast and becoming an intimate friend of the eminent Pythagorean Archytas. Upon his return to Athens around 387 B.C., he founded his famous Academy there, an institution for the systematic pursuit of philosophical and scientific inquiry. He presided over his Academy for the rest of his life, and died in Athens in 347 B.C. at the venerable age of eighty. Almost all the important mathematical work of the fourth century B.C. was done by friends or pupils of Plato, making his Academy the link between the mathematics of the earlier Pythagoreans and that of the long-lived school of mathematics at Alexandria. The Athenian school lasted some nine hundred years, until the Christians obtained from Emperor Justinian a decree that in 529 A.D. closed its doors forever.
Plato’s influence on mathematics was not due to any mathematical discoveries he made, but rather to his enthusiastic conviction that the study of mathematics furnished the finest training field for the mind, and hence was essential in the cultivation of philosophers and those who should govern his ideal state. This belief explains the renowned motto over the door of his Academy:
Let no one unversed in geometry enter here.
Thus, because of its logical element and the pure attitude of mind that he felt its study creates, mathematics seemed of utmost importance to Plato, and for this reason it occupied a valued place in the curriculum of the Academy.
In recent decades there has been vigorous controversy over the question of mental discipline and transfer of training, with contentions ranging from one extreme to the other. Thus there are those who, like Plato, claim that the study of mathematics develops the pupil’s respect for truth and therefore results in honesty, that it develops neatness, power of concentration, and especially the power to think clearly. But the advent of a mechanistic psychology cast grave doubt upon the validity of such claims, and it was quite conclusively shown that transfer of training is not complete, automatic, and inevitable. There are many examples of dishonesty, lack of neatness, and failure to think clearly in nonmathematical situations on the part of students of mathematics, and many uncritical people have interpreted this to mean that transfer of training is nonexistent. Competent psychologists today seem agreed that the truth lies between the two extreme positions; transfer of training can take place if the subject is taught with this specific purpose in view.
英语学习拓展
常用词汇
motto音标/ˈmɒtəʊ/
格言；座右铭。
原文用法：the renowned motto over the door of his Academy。
transfer音标/ˈtrænsfɜː(r)/
转移；迁移。
原文用法：the transfer of training。
influence音标/ˈɪnfluəns/
影响。
原文用法：Plato’s influence on mathematics。
enthusiastic音标/ɪnˌθjuːziˈæstɪk/
热情的。
原文用法：his enthusiastic conviction。
conviction音标/kənˈvɪkʃn/
信念；深信。
原文用法：同上。
furnish音标/ˈfɜːnɪʃ/
提供；装备。
原文用法：furnished the finest training field for the mind。
curriculum音标/kəˈrɪkjələm/
课程。
原文用法：the curriculum of the Academy。
vigorous音标/ˈvɪɡərəs/
激烈的；有力的。
原文用法：vigorous controversy。
controversy音标/ˈkɒntrəvɜːsi/
争论；争议。
原文用法：同上。
contention音标/kənˈtenʃn/
主张；论点。
原文用法：with contentions ranging from one extreme to the other。
discipline音标/ˈdɪsəplɪn/
训练；纪律；学科。
原文用法：mental discipline。
mechanistic音标/ˌmekəˈnɪstɪk/
机械论的。
原文用法：mechanistic psychology。
conclusively音标/kənˈkluːsɪvli/
结论性地；确凿地。
原文用法：it was quite conclusively shown。
nonmathematical音标/nɒnˌmæθəˈmætɪkl/
非数学的。
原文用法：nonmathematical situations。
uncritical音标/ʌnˈkrɪtɪkl/
不加批判的。
原文用法：many uncritical people。
nonexistent音标/ˌnɒnɪɡˈzɪstənt/
不存在的。
原文用法：transfer of training is nonexistent。
competent音标/ˈkɒmpɪtənt/
有能力的；称职的。
原文用法：Competent psychologists。
specific音标/spəˈsɪfɪk/
特定的；明确的。
原文用法：with this specific purpose in view。
同义词与近义词
对应核心词汇：motto
对应核心词汇：motto。
辨析：motto 指个人或机构的座右铭；saying 指俗语、谚语；maxim 指格言、箴言。
对应核心词汇：influence
对应核心词汇：influence。
辨析：influence 常指潜移默化的影响；impact 强调强烈冲击；effect 指产生的结果。
对应核心词汇：controversy
对应核心词汇：controversy。
辨析：controversy 指公开且持久的争论；debate 指正式辩论；dispute 指具体争端。
对应核心词汇：show。
辨析：show 泛指表明；demonstrate 强调论证或展示；reveal 指揭示隐藏的事物。
对应核心词汇：transfer
对应核心词汇：transfer。
辨析：transfer 指迁移；generalization 指泛化；carry-over 指迁移过来的能力或习惯。
常用短语与固定搭配
- the transfer of training：训练的迁移。原文用法：the question of mental discipline and transfer of training。
- Plato’s motto：柏拉图的格言。原文用法：This belief explains the renowned motto over the door of his Academy。
- the finest training field for the mind：心智的最佳训练场。原文用法：furnished the finest training field for the mind。
- play a valued place in：在……中占有重要地位。原文用法：it occupied a valued place in the curriculum。
- the cultivation of philosophers：哲学家的培养。原文用法：essential in the cultivation of philosophers。
- mental discipline：心智训练；智力训练。原文用法：mental discipline and transfer of training。
- carry over to：迁移到。原文用法：transfer of training is not complete, automatic, and inevitable（隐含迁移）。
- the validity of such claims：这些主张的有效性。原文用法：cast grave doubt upon the validity of such claims。
- lie between the two extreme positions：位于两个极端之间。原文用法：the truth lies between the two extreme positions。
- with this specific purpose in view：怀着这一特定目的。原文用法：if the subject is taught with this specific purpose in view。
常用句式
- Pattern: A’s influence on B was not due to …, but rather to …：A 对 B 的影响并非由于……，而是由于……。原文例句：Plato’s influence on mathematics was not due to any mathematical discoveries he made, but rather to his enthusiastic conviction that …
- Pattern: Thus, because of …, A seemed of utmost importance to B, and for this reason it occupied a valued place in …：因此，由于……，A 对 B 显得极为重要，因此它在……中占有重要地位。原文例句：Thus, because of its logical element and the pure attitude of mind that he felt its study creates, mathematics seemed of utmost importance to Plato, and for this reason it occupied a valued place in the curriculum of the Academy.
- Pattern: There has been vigorous controversy over …, with contentions ranging from one extreme to the other：关于……存在激烈争论，论点从一个极端到另一个极端。原文例句：In recent decades there has been vigorous controversy over the question of mental discipline and transfer of training, with contentions ranging from one extreme to the other.
- Pattern: Competent … seem agreed that …; … can take place if …：称职的……似乎一致认为……；如果……，……就可能发生。原文例句：Competent psychologists today seem agreed that the truth lies between the two extreme positions; transfer of training can take place if the subject is taught with this specific purpose in view.
长难句解析
Thus, because of its logical element and the pure attitude of mind that he felt its study creates, mathematics seemed of utmost importance to Plato, and for this reason it occupied a valued place in the curriculum of the Academy.
- 主干：mathematics seemed of utmost importance to Plato, and it occupied a valued place.
- 修饰与从句：
- Thus 为结果状语； - because of its logical element and the pure attitude of mind 为原因状语； - that he felt its study creates 为定语从句，修饰 attitude of mind，其中 he felt 为插入语； - of utmost importance 为固定搭配，意为“极为重要”； - for this reason 为连接性状语。
- 逻辑关系：先说明原因（数学的逻辑元素和纯粹心智态度），再说明结果（数学对柏拉图极为重要，并在课程中占有重要地位）。
语言使用特点
- 正式学术文体，频繁使用抽象名词（conviction, controversy, transfer, validity）；
- 用 not … but rather … 明确区分原因；
- 用 range from one extreme to the other 描述争论双方；
- 用 seem agreed that 表达学界共识，语气委婉而客观；
- 段落结构清晰：先介绍柏拉图与学院，再引出格言，最后展开争论与结论。
迁移练习
- 翻译柏拉图的格言“Let no one unversed in geometry enter here.”并说明它在你理解中的含义。
- 用 range from one extreme to the other 造句，描述一场争论。
- 用 Competent … seem agreed that …; … can take place if … 仿写一段关于学习方法迁移的话。
点击展开参考答案
- 不懂几何者不得入内。它强调几何学是进入柏拉图学院、接受哲学与科学训练的必备心智基础。
- （示例）Opinions on whether homework should be banned range from one extreme to the other.
- （示例）Competent educators seem agreed that effective learning can take place if students are taught with clear goals and active engagement in view.