色诺克拉底Xenocrates

色诺克拉底是柏拉图的学生，大约在公元前376年进入雅典的科学院。大约在公元前367年，色诺克拉底在狄奥尼修斯一世去世后陪同柏拉图前往锡拉库扎。色诺克拉底在公元前347年柏拉图去世后与亚里士多德一起离开雅典，当时他们都被邀请到阿索斯。色诺克拉底在阿索斯停留了大约五年。

柏拉图的侄子斯彪西波在柏拉图去世后成为科学院的负责人，但在公元前340年，他派人请色诺克拉底返回雅典，准备成为他的继任者。尽管色诺克拉底已被斯彪西波选为科学院的负责人，但在斯彪西波去世后，还是举行了一次选举来寻找他的继任者。这是色诺克拉底、皮拉的梅内德谟和赫拉克利德斯·彭提乌斯赫拉克利德斯·彭提乌斯之间的一场势均力敌的较量，但色诺克拉底仅以几票之差获胜。

色诺克拉底在雅典多年，却拒绝成为该城邦的公民，因为他不赞成雅典与马其顿的密切关系。在这方面，他与前任斯彪西波形成鲜明对比，后者曾大力支持雅典与马其顿之间的政治联系。显然，此时的科学院远非许多人描绘的那样，即学者们与周围世界隔绝，坐而论道。相反，Academy深深卷入当时的政治，不同的政治观点争相占据上风。

公元前322年，色诺克拉底发现自己担任了一个直接的政治职务，当时他率领一个团队与马其顿谈判政治解决方案。说“政治解决方案”也许相当不准确，因为他们实际上必须谈判雅典投降的条件。色诺克拉底不是雅典公民这一事实成为马其顿人的一个痛处，他被认为没有资格担任雅典的大使。

色诺克拉底余生一直担任雅典科学院的主持人。作为一个勤奋的人，色诺克拉底被描述为[1]：-

……性情温和、文雅体贴，但……他缺乏其老师柏拉图的那种优雅风度。

色诺克拉底写过哲学和数学方面的著作。第欧根尼·拉尔修给出了色诺克拉底两部数学著作的书名，即On numbers和The theory of numbers。他的所有著作都已失传，而且看来每部著作都只有他亲笔书写的一份。

在许多方面，色诺克拉底并不是一位特别有独创性的思想家。当然，他认为作为科学院的主持人，自己的职责就是尽可能准确地推广柏拉图的观点。正如Dorrie在[1]中所写：-

色诺克拉底毕生的工作在于对柏拉图的哲学进行某种编纂——因而必然也是一种改造。但很快就显而易见，其他人，尤其是亚里士多德，在某些关键问题上对柏拉图的理解完全不同。

色诺克拉底相信物质由不可分割的单元组成，因此他可以被视为原子论的早期信奉者。他赞同毕达哥拉斯关于数在哲学中重要性的观点，并将一种原子论的声学观归于毕达哥拉斯，认为被感知为单一实体的声音由离散的声音组成。

色诺克拉底相信人具有三重存在：心智、身体和灵魂。不清楚他是否是这一信念的发起者。他还相信人会死两次，一次在地球上，然后第二次在月球上，此时心智与灵魂分离并前往太阳。

普鲁塔克写到色诺克拉底试图计算由字母表中的字母可以构成的总音节数。根据普鲁塔克的说法，色诺克拉底得到的结果是1,002,000,000,000。如果属实，这很可能代表了解决一个涉及排列的组合问题的首次尝试。

Xenocrates of Chalcedon was a student of Plato who entered the Academy in Athens in about 376 BC. In about 367 BC Xenocrates accompanied Plato on his journey to Syracuse following the death of Dionysius I. Xenocrates left Athens with Aristotle after Plato's death in 347 BC when they were both invited to Assos. Xenocrates remained for around five years in Assos.

Plato's nephew Speusippus had become head of the Academy on Plato's death, but in 340 BC he sent for Xenocrates to return to Athens to prepare to become his successor. Despite Xenocrates having been chosen to head the Academy by Speusippus, an election took place to find a successor to Speusippus after his death. It was a close battle between Xenocrates, Menedemus of Pyrrha and Heraclides Ponticus but Xenocrates triumphed by just a few votes.

Although Xenocrates had been many years in Athens he had refused to become a citizen of that state since he did not approve of its close relations with Macedonia. In this respect he contrasted strongly with his predecessor Speusippus who had strongly supported the political ties between Athens and Macedonia. It is clear that the Academy at this time was far from what many picture it as, namely an institution where scholars sat thinking, isolated from the world around them. On the contrary, the Academy was highly involved in the politics of the day and different political views strove for supremacy.

In 322 BC Xenocrates found himself in a directly political post when he headed a team negotiating a political settlement with Macedonia. To say 'political settlement' is perhaps rather wide of the mark since effectively they had to negotiate terms for the surrender of Athens. The fact that Xenocrates was not an Athenian citizen became a sore point with the Macedonians and he was deemed to be illegitimate as an ambassador for Athens.

Xenocrates remained head of the Academy in Athens for the rest of his life. A hard working man, Xenocrates is described as [1]:-

... good-natured, gentle and considerate but ... he lacked the graciousness of his teacher Plato.

Xenocrates wrote on philosophy and mathematics. Diogenes Laertius gives the titles of two mathematics books by Xenocrates, namely On numbers and The theory of numbers. All his books are lost and it would appear that there only ever existed a single copy of each in his own hand.

In many ways Xenocrates was not a particularly original thinker. Certainly he saw it his duty as the head of the Academy to promote the views of Plato as exactly as he possibly could. As Dorrie writes in [1]:-

Xenocrates' lifework consisted of producing a kind of codification - and thus of necessity, a transformation - of Plato's philosophy. But it immediately became apparent that others, especially Aristotle, understood Plato in a wholly different way with respect to certain key questions.

Xenocrates believed that matter is composed of indivisible units, so he may be regarded as an early believer in the atomic theory. He agreed with Pythagoras regarding the importance of numbers in philosophy and attributed to Pythagoras an atomic view of acoustics where sound, perceived as a single entity, consists of discrete sounds.

Xenocrates believed in human beings having threefold existence, mind, body and soul. It is not clear whether he was the instigator of this belief. He also believed that people die twice, once on Earth, then for a second time on the Moon when the mind separates from the soul and travels to the Sun.

Plutarch writes about an attempt by Xenocrates to calculate the total number of syllables which could be made from the letters of the alphabet. The result which Xenocrates obtained was, according to Plutarch, 1,002,000,000,000. If true this probably represents the first attempt at solving a combinatorial problem involving permutations.