柏拉图Plato

在详细介绍柏拉图的生平之前，我们先花一点时间讨论一下下面给出的细节有多确定。这些细节大多由柏拉图本人在书信中给出，表面上看似乎使这些细节确凿无疑。然而，柏拉图是否确实写了这些书信存在争议，因此有三种可能的解释。第一，柏拉图写了这些书信，因此细节是准确的。第二，虽然并非柏拉图所写，但这些书信出自认识他的人之手，或者至少是能够接触到关于他生平的准确信息的人之手。第三种可能，遗憾的是无法排除，即这些书信是某人纯粹虚构的。

接下来我们应该评论一下“柏拉图”这个名字。在[13]中，罗写道：-

有人声称柏拉图的真名是阿里斯托克勒斯，而“柏拉图”是一个绰号（大致意为“宽”），其来源要么是他肩膀的宽度——这是摔跤训练的结果，要么是他文风的宽广，要么是他额头的尺寸。

柏拉图是阿里斯通和佩里提俄涅最小的儿子，他们两人都出身于世代居住在雅典的著名富裕家族。当柏拉图还年轻时，他的父亲去世了，母亲改嫁，她的第二任丈夫是皮里兰佩斯。柏拉图主要是在皮里兰佩斯的家中长大的。亚里士多德写道，当柏拉图年轻时，他师从克拉底鲁，后者是赫拉克利特的学生，以其宇宙论而闻名，该学说认为火是宇宙的基本物质。几乎可以肯定，柏拉图在年轻时就成了苏格拉底的朋友，因为柏拉图母亲的兄弟卡米德斯是苏格拉底的密友。

伯罗奔尼撒战争是公元前431年至公元前404年间雅典与斯巴达之间的战争。柏拉图从公元前409年至公元前404年在军队服役，但此时他想要的是政治生涯而非军事生涯。战争结束时，他加入了公元前404年在雅典建立的三十僭主寡头政权，其领导人之一是他母亲的兄弟Charmides，但他们的暴行使柏拉图很快离开了。

公元前403年，雅典恢复了民主制，柏拉图满怀希望认为自己能够再次从政。然而，雅典政治生活的过度似乎使他放弃了政治抱负。特别是公元前399年Socrates被处死对他产生了深远的影响，他决定不再与雅典的政治有任何瓜葛。

苏格拉底被处死后，柏拉图离开了雅典，游历了埃及、西西里和意大利。在埃及，他了解到一种水钟，后来将其引入希腊。在意大利，他了解到毕达哥拉斯的工作，并开始认识到数学的价值。这是一件极其重要的事件，因为从柏拉图从毕达哥拉斯的弟子那里获得的思想中，他形成了自己的观念[6]：-

……科学思想所寻求的实在必须能够用数学术语来表达，数学是我们所能拥有的最精确、最确定的思想方式。这一观念对于科学从最初起源发展到今天的重要性是巨大的。

又经历了一段战争时期，柏拉图再次入伍服役。后来为柏拉图写传记的作家声称，在他生命的这一时期，他因在战斗中的勇敢而受到嘉奖。人们还认为他是在这个时候开始撰写他的对话录的。

柏拉图回到雅典，约在公元前387年在雅典创立了他的科学院。它建在属于阿提卡英雄Academus的圣地上，这就是“Academy”这个名字的由来。Academy是一个致力于哲学和科学研究与教学的机构，柏拉图从公元前387年起主持它，直到公元前347年去世。

他建立科学院的原因与他早期涉足政治有关。他对公职人员的表现深感失望，希望培养能成为政治家的年轻人。然而，在赋予他们柏拉图所信奉的价值观后，柏拉图认为这些人将能够改善希腊各城邦的政治领导。

柏拉图生平中仅记载了另外两件事。公元前367年，在统治该城的狄奥尼修斯一世去世后，他前往叙拉古。狄奥尼修斯一世的妻弟狄翁说服柏拉图前往叙拉古教导新统治者狄奥尼修斯二世。柏拉图并不指望该计划成功，但由于狄翁和塔兰托的阿尔库塔斯都相信该计划，柏拉图便同意了。他们的计划是，如果狄奥尼修斯二世接受科学和哲学教育，他将能够阻止迦太基入侵西西里。然而，狄奥尼修斯二世嫉妒狄翁，迫使他离开叙拉古，正如柏拉图所预料的那样，计划失败了。

柏拉图回到雅典，但在公元前361年再次访问叙拉古，希望能使对手和解。他在公元前360年的一部分时间里留在叙拉古，但未能就对手间的争斗达成政治解决。狄翁于公元前357年发动政变攻击叙拉古，获得控制权，但在公元前354年被谋杀。

费尔德在[6]中写道，柏拉图的一生：-

……清楚地表明，将柏拉图视为一个超然物外、不谙世事的学者，在书房里闭门造车、脱离实际生活的流行观念，是极其离谱的。相反，他是一个阅历丰富的人，一位经验丰富的军人，游历广泛，与他自己城邦内外的许多重要事务人物都有密切联系。

柏拉图的主要贡献在哲学、数学和科学。然而，要发现柏拉图的哲学观点并不像人们想象的那么容易。原因在于柏拉图没有写下系统论述自己观点的著作，而是写了若干对话录（约30篇），以对话形式写成。首先我们应当评论这些对话录是多么出色的文学作品[6]：-

它们展现了语言的精通、刻画性格的力量、对情境的感知，以及对悲剧与喜剧两面的敏锐眼光，这使柏拉图跻身世界最伟大作家之列。他充分利用这些天赋来灌输他想传授的教益。

在柏拉图的书信中，他明确表示他明白从对话录中提炼出他的哲学理论将是困难的，但他声称读者只有经过长期思考、讨论和质疑之后才能理解它。对话录中没有把柏拉图作为角色，因此他并未宣称其中所断言的任何内容是他自己的观点。角色都是历史人物，通常以苏格拉底为主角，所以不清楚这些角色在多大程度上表达了他们自己会提出的观点。人们认为，至少在早期对话录中，苏格拉底这一角色表达了苏格拉底实际持有的观点。

通过这些对话录，柏拉图对艺术理论做出了贡献，特别是舞蹈、音乐、诗歌、建筑和戏剧。他讨论了整个系列的哲学主题，包括伦理学、形而上学，其中讨论了诸如不朽、人、心灵和实在论等主题。

他讨论了数学哲学、政治哲学——其中讨论了诸如审查制度等主题——以及宗教哲学，其中考虑了诸如无神论、二元论和泛神论等主题。在讨论认识论时，他考察了诸如先验知识和理性主义等观念。在其形式理论中，柏拉图拒绝了我们通过感官所感知的可变、欺骗性的世界，转而提出他那个恒定而真实的理念世界。

让我们用柏拉图的一个数学例子来说明他的理型论。柏拉图把数学对象视为完美的理型。例如，线是一个有长度而无宽度的对象。无论我们在感官世界中把一条线画得多么细，它都不会是这种完美的数学理型，因为它总会有宽度。在Phaedo中，柏拉图谈到现实世界中的对象试图像它们的完美理型。借此他想到的是越来越细的线，它们在极限中趋向于线的数学概念，但当然永远达不到它。Phaedo中的另一个例子见于[6]：-

那里所举的例子是相等的数学关系，并在我们在数学中所想的绝对相等与我们在用感官处理对象时不得不满足于其中的粗略、近似的相等之间作了对比。

又在Republic中，柏拉图谈到几何图形是它们所代表的完美数学对象的不完美模仿。

柏拉图对教育理论的贡献体现在他主持科学院的方式以及他对何谓受过教育的人的看法上。他还对逻辑学和法律哲学作出了贡献，包括修辞学。

柏拉图本人没有做出重要的数学发现，但他相信数学为心智提供最好的训练，这一信念对该学科的发展极为重要。在科学院的门上写着：

不懂几何者不得入内。

柏拉图专注于“证明”的观念，并坚持精确的定义和清晰的假设。这为欧几里得系统化的数学方法奠定了基础。在[2]中，他通过学生而对数学做出的贡献被总结如下：

4世纪所有最重要的数学工作都是由柏拉图的朋友或学生完成的。conic sections最早的学生，可能还有泰阿泰德，即立体几何的创立者，都是学园的成员。欧多克索斯——欧几里得的《几何原本》中所阐述的比例学说的作者、用exhaustion求曲线图形面积和体积方法的发明者，以及被亚里士多德采纳并修改的同心球天文学体系的提出者——为了与柏拉图合作，把他的学派从卡里普斯迁到雅典；在柏拉图某次缺席期间，他似乎担任过学园的负责人。阿尔库塔斯，机械科学的发明者，是柏拉图的朋友和通信者。

在数学中，柏拉图的名字与柏拉图立体联系在一起。在Timaeus中，有一种对元素（土、火、气、水）的数学构造，其中立方体、四面体、八面体和二十面体被分别赋予土、火、气、水的原子形状。第五个柏拉图立体，即正十二面体，是柏拉图对整个宇宙的模型。

柏拉图关于宇宙的信念是：恒星、行星、太阳和月亮在晶体球壳中绕地球运动。月亮的球壳离地球最近，然后是太阳的球壳，再然后是水星、金星、火星、木星、土星，最远的是恒星的球壳。他相信月亮靠反射太阳光而发光。

也许，考察柏拉图认为适当的教育课程应由什么组成，可以获得对他的观点最好的概览。以下是他[2]的课程：

……精确科学——算术、平面几何与立体几何、天文学和和声学——将首先学习十年，以使心灵熟悉那些只能通过思想才能把握的关系。随后五年将用于研究更为艰深的辩证法。辩证法是一门对话、提问与回答的艺术；根据柏拉图，辩证法的技能就是就事物的本质提出并回答问题的能力。辩证学家用可靠的知识取代假设，他的目标是把一切科学、一切知识都建立在某种“非假设的第一原理”之上。

Plato's Academy一直繁荣到公元529年，被基督教皇帝查士丁尼关闭，他声称这是一所异教机构。它存续了900年，是已知存续时间最长的大学。

Before giving details of Plato's life we will take a few moments to discuss how definite the details are which we give below. The details are mostly given by Plato himself in letters which seem, on the face of it, to make them certain. However, it is disputed whether Plato did indeed write the letters so there are three possible interpretations. Firstly that Plato wrote the letters and therefore the details are accurate. Secondly that although not written by Plato, the letters were written by someone who knew him or at least had access to accurate information on his life. The third possibility, which unfortunately cannot be ruled out, is that they were written by someone as pure fiction.

Next we should comment on the name 'Plato'. In [13] Rowe writes:-

It was claimed that Plato's real name was Aristocles, and that 'Plato' was a nickname (roughly 'the broad') derived either from the width of his shoulders, the results of training for wrestling, or from the breadth of his style, or from the size of his forehead.

Plato was the youngest son of Ariston and Perictione who both came from famous wealthy families who had lived in Athens for generations. While Plato was a young man his father died and his mother remarried, her second husband being Pyrilampes. It was mostly in Pyrilampes' house that Plato was brought up. Aristotle writes that when Plato was a young man he studied under Cratylus who was a student of Heracleitus, famed for his cosmology which is based on fire being the basic material of the universe. It almost certain that Plato became friends with Socrates when he was young, for Plato's mother's brother Charmides was a close friend of Socrates.

The Peloponnesian War was fought between Athens and Sparta between 431 BC and 404 BC. Plato was in military service from 409 BC to 404 BC but at this time he wanted a political career rather than a military one. At the end of the war he joined the oligarchy of the Thirty Tyrants in Athens set up in 404 BC, one of whose leaders being his mother's brother Charmides, but their violent acts meant that Plato quickly left.

In 403 BC there was a restoration of democracy at Athens and Plato had great hopes that he would be able to enter politics again. However, the excesses of Athenian political life seem to have persuaded him to give up political ambitions. In particular, the execution of Socrates in 399 BC had a profound effect on him and he decided that he would have nothing further to do with politics in Athens.

Plato left Athens after Socrates had been executed and travelled in Egypt, Sicily and Italy. In Egypt he learnt of a water clock and later introduced it into Greece. In Italy he learned of the work of Pythagoras and came to appreciate the value of mathematics. This was an event of great importance since from the ideas Plato gained from the disciples of Pythagoras, he formed his idea [6]:-

... that the reality which scientific thought is seeking must be expressible in mathematical terms, mathematics being the most precise and definite kind of thinking of which we are capable. The significance of this idea for the development of science from the first beginnings to the present day has been immense.

Again there was a period of war and again Plato entered military service. It was claimed by later writers on Plato's life that he was decorated for bravery in battle during this period of his life. It is also thought that he began to write his dialogues at this time.

Plato returned to Athens and founded his Academy in Athens, in about 387 BC. It was on land which was sacred to the Attic hero Academus, and this is where the name "Academy" came from. The Academy was an institution devoted to research and instruction in philosophy and the sciences, and Plato presided over it from 387 BC until his death in 347 BC.

His reasons for setting up the Academy were connected with his earlier ventures into politics. He had been bitterly disappointed with the standards displayed by those in public office and he hoped to train young men who would become statesmen. However, having given them the values that Plato believed in, Plato thought that these men would be able to improve the political leadership of the cities of Greece.

Only two further episodes in Plato's life are recorded. He went to Syracuse in 367 BC following the death of Dionysius I who had ruled the city. Dion, the brother-in-law of Dionysius I, persuaded Plato to come to Syracuse to tutor Dionysius II, the new ruler. Plato did not expect the plan to succeed but because both Dion and Archytas of Tarentum believed in the plan then Plato agreed. Their plan was that if Dionysius II was trained in science and philosophy he would be able to prevent Carthage invading Sicily. However, Dionysius II was jealous of Dion whom he forced out of Syracuse and the plan, as Plato had expected, fell apart.

Plato returned to Athens, but visited Syracuse again in 361 BC hoping to be able to bring the rivals together. He remained in Syracuse for part of 360 BC but did not achieve a political solution to the rivalry. Dion attacked Syracuse in a coup in 357, gained control, but was murdered in 354.

Field writes in [6] that Plato's life:-

... makes it clear that the popular conception of Plato as an aloof unworldly scholar, spinning theories in his study remote from practical life, is singularly wide of the mark. On the contrary, he was a man of the world, an experienced soldier, widely travelled, with close contacts with many of the leading men of affairs, both in his own city and elsewhere.

Plato's main contributions are in philosophy, mathematics and science. However, it is not as easy as one might expect to discover Plato's philosophical views. The reason for this is that Plato wrote no systematic treatise giving his views, rather he wrote a number of dialogues (about 30) which are written in the form of conversations. Firstly we should comment on what superb pieces of literature these dialogues are [6]:-

They show the mastery of language, the power of indicating character, the sense of a situation, and the keen eye for both its tragic and its comic aspects, which set Plato among the greatest writers of the world. He uses these gifts to the full in inculcating the lessons he wants to teach.

In letters written by Plato he makes it clear that he understands that it will be difficult to work out his philosophical theory from the dialogues but he claims that the reader will only understand it after long thought, discussion and questioning. The dialogues do not contain Plato as a character so he does not declare that anything asserted in them are his own views. The characters are historic with Socrates usually the protagonist so it is not clear how much these characters express views with which they themselves would have put forward. It is thought that, at least in the early dialogues, the character of Socrates expresses views that Socrates actually held.

Through these dialogues, Plato contributed to the theory of art, in particular dance, music, poetry, architecture, and drama. He discussed a whole range of philosophical topics including ethics, metaphysics where topics such as immortality, man, mind, and Realism are discussed.

He discussed the philosophy of mathematics, political philosophy where topics such as censorship are discussed, and religious philosophy where topics such as atheism, dualism and pantheism are considered. In discussing epistemology he looked at ideas such as a priori knowledge and Rationalism. In his theory of Forms, Plato rejected the changeable, deceptive world that we are aware of through our senses proposing instead his world of ideas which were constant and true.

Let us illustrate Plato's theory of Forms with one of his mathematical examples. Plato considers mathematical objects as perfect forms. For example a line is an object having length but no breadth. No matter how thin we make a line in the world of our senses, it will not be this perfect mathematical form, for it will always have breadth. In the Phaedo Plato talks of objects in the real world trying to be like their perfect forms. By this he is thinking of thinner and thinner lines which are tending in the limit to the mathematical concept of a line but, of course, never reaching it. Another example from the Phaedo is given in [6]:-

The instance taken there is the mathemtical relation of equality, and the contrast is drawn between the absolute equality we think of in mathematics and the rough, approximate equality which is what we have to be content with in dealing with objects with our senses.

Again in the Republic Plato talks of geometrical diagrams as imperfect imitations of the perfect mathematical objects which they represent.

Plato's contributions to the theories of education are shown by the way that he ran the Academy and his idea of what constitutes an educated person. He also contributed to logic and legal philosophy, including rhetoric.

Although Plato made no important mathematical discoveries himself, his belief that mathematics provides the finest training for the mind was extremely important in the development of the subject. Over the door of the Academy was written:-

Let no one unversed in geometry enter here.

Plato concentrated on the idea of 'proof' and insisted on accurate definitions and clear hypotheses. This laid the foundations for Euclid's systematic approach to mathematics. In [2] his contributions to mathematics through his students are summarised:-

All of the most important mathematical work of the 4th century was done by friends or pupils of Plato. The first students of conic sections, and possibly Theaetetus, the creator of solid geometry, were members of the Academy. Eudoxus of Cnidus - author of the doctrine of proportion expounded in Euclid's "Elements", inventor of the method of finding the areas and volumes of curvilinear figures by exhaustion, and propounder of the astronomical scheme of concentric spheres adopted and altered by Aristotle - removed his school from Cyzicus to Athens for the purpose of cooperating with Plato; and during one of Plato's absences he seems to have acted as the head of the Academy. Archytas, the inventor of mechanical science, was a friend and correspondent of Plato.

In mathematics Plato's name is attached to the Platonic solids. In the Timaeus there is a mathematical construction of the elements (earth, fire, air, and water), in which the cube, tetrahedron, octahedron, and icosahedron are given as the shapes of the atoms of earth, fire, air, and water. The fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.

Plato's beliefs as regards the universe were that the stars, planets, Sun and Moon move round the Earth in crystalline spheres. The sphere of the Moon was closest to the Earth, then the sphere of the Sun, then Mercury, Venus, Mars, Jupiter, Saturn and furthest away was the sphere of the stars. He believed that the Moon shines by reflected sunlight.

Perhaps the best overview of Plato's views can be gained from examining what he thought that a proper course of education should consist. Here is his course of study [2]:-

... the exact sciences - arithmetic, plane and solid geometry, astronomy, and harmonics - would first be studied for ten years to familiarise the mind with relations that can only be apprehended by thought. Five years would then be given to the still severer study of 'dialectic'. Dialectic is the art of conversation, of question and answer; and according to Plato, dialectical skill is the ability to pose and answer questions about the essences of things. The dialectician replaces hypotheses with secure knowledge, and his aim is to ground all science, all knowledge, on some 'unhypothetical first principle'.

Plato's Academy flourished until 529 AD when it was closed down by the Christian Emperor Justinian who claimed it was a pagan establishment. Having survived for 900 years it is the longest surviving university known.