奥卡姆的威廉William of Ockham

奥卡姆的威廉的名字有时写作奥卡姆的威廉 Occam。他也被称为“超过微妙的博士”或“可敬的初学者”。在他十四岁进入方济各会之前，关于他的父母或早年生活一无所知。他在方济各会修道院接受教育，几乎可以肯定是在伦敦修道院，因为它是他所居住地区的教育中心。我们确实知道，他于1306年在伦敦南华克被坎特伯雷大主教任命为副执事，这肯定支持他在伦敦接受培训。此后，一些学生被送到巴黎进一步培训，其余的在修道院教学。没有直接证据支持奥卡姆的威廉遵循了哪种选择，但一定是其中之一。然后他被送到牛津攻读神学学位。

奥卡姆的威廉就Peter Lombard的Book of Sentences进行了讲授。Peter是12世纪的意大利神学家，他撰写这部著作是为了明确阐述《圣经》和教父关于基督教教义的立场。Peter Lombard是一位保守的神学家，他撰写这部文本是为了反对当时一些人将亚里士多德的逻辑应用于神学。要求每位攻读神学高级学位的学生都要讲授并评论Book of Sentences，这正是奥卡姆的威廉于1317-1319年在牛津所做的。该文本被用作框架，让学生发展自己的原创立场，并与老师和同学辩论。1318年6月，奥卡姆的威廉获准听取告解，到1320年他完成了学士学位的学习。

奥卡姆的威廉从1321年到1324年在一所方济各会学校讲授逻辑学和自然哲学，同时等待返回大学攻读博士学位。在这些年里，他写了许多关于哲学和逻辑学的深刻著作。Corcoran写道：-

奥卡姆的威廉无疑是中世纪最具想象力、最有能力且最多产逻辑学家之一。在他著作中发现的明显原创的概念、问题和结果，其范围即使不令人震惊，也令人印象深刻。

特别是Ockham在这四年间写下了不朽的三部分Summa logicae，Corcoran说：-

……可能是亚里士多德的《工具论》和伯纳德·波尔查诺的《知识学》(1837)之间时期所写的最全面的原创逻辑论著。

奥卡姆的威廉的观点引起了强烈反对，他被方济各会省分会传唤[3]：-

……解释他对源自其关于亚里士多德范畴，特别是“关系”范畴教学的十三个命题的看法。

奥卡姆的威廉解释了他的观点，没有对他采取任何行动，但显然他已被挑出为不适合教学，而且这件事没有被允许就此了结。他于1324年被召到阿维尼翁，接受对其讲座和著作的异端或错误教导审查。奥卡姆的威廉于1324年夏天渡过英吉利海峡前往法国，并继续前往普罗旺斯，他现在居住在阿维尼翁修道院。相当令人惊讶的是，将要阅读奥卡姆的威廉对彼得·隆巴德的Book of Sentences的评论的人是弗瑞兹·约翰 Lutterell，他在奥卡姆的威廉在牛津大学学习时曾担任牛津大学校长。也许Lutterell就是奥卡姆的威廉现在受到审查的原因，因为他可能在奥卡姆的威廉在牛津学习时就认定他的观点是危险的。无论如何，Lutterell仔细审查了奥卡姆的威廉的著作，并列出了一份56条陈述的清单，他认为这些陈述是错误的或异端的。由于这份清单现在成为指控奥卡姆的威廉的基础，一个委员会被设立来审判他。

首先，委员会决定，奥卡姆的威廉关于物理学的教导，即关于时间、运动和位置的教导，应从指控清单中删除，除非它是神学陈述的一部分。到1326年，有51项针对奥卡姆的威廉的指控，后来减少到49项。委员会在攻击奥卡姆的威廉时遇到的困难之一是，他实际上是一位相当保守的神学家，他的宗教陈述大多得到方济各会主要成员的拥护。因此，他没有因他的教导而受到正式谴责。

奥卡姆的威廉在阿维尼翁修道院等待委员会得出结论期间并没有闲着。他一直在研究教皇们关于集体贫穷，特别是基督和使徒贫穷的声明。作为他研究的结果，他认定现任教皇约翰二十二世在这个问题上发表的声明与前任教皇们的声明相矛盾。对奥卡姆的威廉来说逻辑是清楚的；教皇约翰二十二世不是真正的教皇，他以书面指控谴责了他。奥卡姆的威廉使其他主要方济各会士相信了他论点的逻辑，他们于1328年5月26日一起逃往比萨。他们在寻求巴伐利亚皇帝路德维希的保护方面选择得很好，因为路德维希不是教皇的朋友，并且已被开除教籍！奥卡姆的威廉和他来自阿维尼翁修道院的方济各会朋友们也被教皇约翰二十二世开除教籍，后者发出了逮捕他们并遣返阿维尼翁的令状。然而，教皇没有成功，从未实现他的目标。当巴伐利亚皇帝路德维希的宫廷从意大利返回慕尼黑时，奥卡姆的威廉也去了慕尼黑，并在那里的方济各会修道院度过了余生。他继续攻击教皇权力，在论证中总是运用逻辑推理。在慕尼黑期间，他写了许多关于教会与国家关系的论著。人们可能会说，遗憾的是，在这些晚年里，他偏离了哲学和逻辑的工作。

在哲学方面，奥卡姆的威廉坚定地致力于亚里士多德的思想。他做出贡献的主要问题之一是共相问题：现实中是否有任何东西对应于我们的一般词语和概念，如果有，它是什么样的？这里与数学有很强的联系，因为对奥卡姆的威廉来说，数学概念不是绝对术语。他以条件形式陈述数学术语，因此他不必假设点、线等数学实体的真实存在，就可以有效地使用它们。奥卡姆的威廉采取唯名论的方法（事实上他常被称为唯名论之父），认为点、线等仅仅是抽象，并不真正存在。

在对数学逻辑的研究中，奥卡姆的威廉做出了重要贡献，这些贡献在今天仍然意义重大。他考虑了一种三值逻辑，其中命题可以取三个真值之一。这在20世纪对数学变得重要，但值得注意的是，它最早是由奥卡姆的威廉在600年前研究的。他也非常接近陈述奥古斯塔斯·德摩根的定律。在Summa logicae中，奥卡姆的威廉将合取命题定义为由“和”连接的两个或多个直言命题的复合。类似地，他将析取命题定义为由“或”连接的两个或多个直言命题的复合。一个合取命题为真当且仅当每个合取支都为真，一个析取命题为真当且仅当某个析取支为真。奥卡姆的威廉指出，一个合取命题蕴含每个合取支，但不一定被每个合取支单独蕴含。他明确补充说，如果一个合取支蕴含其他合取支，它就蕴含整个合取命题。类似地，他指出，一个析取命题被每个析取支蕴含，但不一定蕴含每个析取支，并且一个析取命题与其中一个析取支的否定一起蕴含其余析取支的析取。他还指出，合取命题的矛盾是各合取支矛盾的析取。他还对析取命题的矛盾陈述了类似的陈述，只是做了明显的改变。

最后让我们提一下奥卡姆的威廉剃刀。这是奥卡姆的威廉的原则之一，今天他的名字因此广为人知。很难让“奥卡姆的威廉剃刀”的含义与他思考这一原则的方式完全一致，但让我们说，它指出在构建理论时，人们应该始终偏向简单性。容易误解的地方在于，奥卡姆的威廉并不是说自然总是遵循最简单的过程。相反，他是在建议人们不应构建不必要和过度复杂的解释。

考特尼将奥卡姆的威廉对当今观念的影响总结如下[3]：-

……随着二十世纪下半叶对中世纪晚期思想兴趣的复兴，奥卡姆的威廉重新成为经院思想的主要人物之一，通常被列为与托马斯·阿奎那和约翰邓斯·司各脱同等水平。而从1980年代和1990年代哲学的角度来看，奥卡姆的威廉对词项逻辑、语言理论和符号学的兴趣使他处于那些被用作当代哲学讨论来源的中世纪思想家的前列。

William of Ockham's name is sometimes written William Occam. He is also known as the "More than Subtle Doctor" or the "Venerable Inceptor". Nothing is known of his parents or his early life before he entered the Franciscan order at the age of fourteen. His education was in a Franciscan convent and it was almost certainly the London convent since it acted as the educational centre for the area in which he lived. We do know that he was ordained a subdeacon by the archbishop of Canterbury in Southwark, London, in 1306 which certainly supports him being trained in London. After this some students were sent to Paris for further training, the rest taught at a convent. There is no direct evidence to support which of these alternatives Ockham followed but it must have one of them. He was then sent to Oxford to study for a theological degree.

At Oxford Ockham lectured on the Book of Sentences of Peter Lombard. Peter was a 12th century Italian theologian who had written the work to state clearly the position found in the Scriptures and that of the Church fathers on Christian doctrine. Peter Lombard, a conservative theologian, wrote the text as a reaction against some who at the time were applying Aristotle's logic to theology. It was required that every student working for a higher degree in theology would lecture and comment on the Book of Sentences which is what Ockham did at Oxford in 1317-1319. The text was used as a framework for students to develop their own original positions and to debate with their teachers and fellow students. In June 1318 Ockham was granted a licence to hear confessions and by 1320 he completed study for his bachelor's degree.

Ockham lectured on logic and natural philosophy in a Franciscan school from 1321 to 1324 while he waited to return to university to study for his doctorate. During these years he wrote many deep works on philosophy and logic. Corcoran writes:-

William of Ockham was certainly among the most imaginative, competent, and prolific of Medieval logicians. The scope of the apparently original concepts, problems, and results found in his works is impressive, if not astounding.

In particular Ockham wrote the monumental three-part Summa logicae during these four years which Corcoran says:-

... is probably the most comprehensive original logical treatise written in the period between Aristotle's "Organon" and Bolzano's "Wissenschaftslehre" (1837).

Ockham's opinions aroused strong opposition and he was summoned by the Franciscan provincial chapter [3]:-

... to explain his views on thirteen propositions derived from his teaching on the Aristotelian categories, especially the category of 'relation'.

Indeed Ockham explained his views and no action was taken against him but clearly he had been singled out as unsuitable to teach, and the matter was not allowed to rest. He was summoned to Avignon in 1324 to have his lectures and writings examined for heretical or mistaken teaching. Ockham went to France, crossing the Channel in the summer of 1324, and continued to Provence where he now resided at the Avignon convent. Rather surprisingly, the person who was to read Ockham's commentary on the Book of Sentences of Peter Lombard was John Lutterell who had been chancellor of Oxford University when Ockham studied there. Perhaps Lutterell was the reason that Ockham was now being tested for he may have decided that Ockham's views were dangerous when he was a student at Oxford. Anyway Lutterell went through Ockham's work and made a list of 56 statement which he deemed to be erroneous or heretical. With the list being now the basis for the charge against Ockham, a commission was set up the try him.

First the commission decided that Ockham's teaching on physics, namely on time, motion and place, should be removed from the list of charges unless it was part of a theological statement. By 1326 there was a list of 51 charges against Ockham which was later reduced to 49. One of the difficulties the commission had in attacking Ockham was that he was in fact a fairly conservative theological and his religious statements mostly had adherents among the leading Franciscans. As a result, he was not formally condemned for his teaching.

While Ockham had been in the Avignon convent waiting for the commission to come to its conclusions he had not been idle. He had been studying the pronouncements made by popes regarding collective poverty, in particular the poverty of Christ and the apostles. As a result of his researches he decided that the current pope, John XXII, had made pronouncements of the issue which contradicted those of previous popes. The logic was clear to Ockham; Pope John XXII was no true pope and he denounced him with written charges. Ockham had convinced other leading Franciscans of the logic of his arguments, and together they fled to Pisa on 26 May 1328. They had chosen well in seeking the protection of Emperor Ludwig of Bavaria for Ludwig was no friend of the Pope and had been excommunicated! Ockham and his Franciscan friends from the Avignon convent were also excommunicated by Pope John XXII who issued a warrant for their arrest and return to Avignon. The Pope, however, was unsuccessful and never achieved his aims. When the court of Emperor Ludwig of Bavaria returned from Italy to Munich, Ockham also went to Munich and he lived out the rest of his life in the Franciscan convent there. He continued to attack papal power, always employing logical reasoning in his arguments. He wrote many treatises while in Munich on the relations between church and state. One might argue that it was a pity that he became distracted from his work on philosophy and logic during these latter years.

In terms of philosophy Ockham was strongly committed to the ideas of Aristotle. One of the main problems he contributed to was the problem of universals: is there anything in reality which corresponds to our general words and concepts, and if so, what is it like? Here there are strong connections to mathematics, for mathematical notions are not absolute terms for Ockham. He states mathematical terms in conditional form so that it was not necessary for him to suppose the real existence of such mathematical entities as points and lines in order to make useful use of them. Ockham takes a nominalist approach (indeed he is often called the father of nominalism) believing that points, lines, etc. are mere abstractions and do not really exist.

In his studies of mathematical logic Ockham made important contributions to it which are significant today. He considered a three valued logic where propositions can take one of three truth values. This became important for mathematics in the 20th century but it is remarkable that it was first studied by Ockham 600 years earlier. He also came very close to stating De Morgan's laws. In the Summa logicae Ockham defines a conjunctive proposition as a composite of two or more categorical propositions joined by 'and'. Similarly he defines a disjunctive proposition as a composite of two or more categorical propositions joined by 'or'. A conjunctive is true if and only if every conjunct is true and a disjunctive is true if and only if some disjunct is true. Ockham notes that a conjunctive implies, but is not necessarily implied by, each conjunct separately. He explicitly adds that if one conjunct implies the others it implies the whole conjunctive. Similarly, he notes that a disjunctive is implied by, but does not necessarily imply, each disjunct and that a disjunctive together with a negation of one of its disjuncts implies the disjunctive of the rest. He also notes that the contradictory of the conjunctive is the disjunctive of the contradictories of the conjuncts. He also states a similar statement for the contradictory of the disjunctive, with the obvious changes.

Finally let us mention Ockham's razor. This is one of Ockham's principles for which his name is widely known today. It is quite difficult to get the meaning of 'Ockham's razor' to coincide precisely with the way that he thought of the principle, but let us say that it states that one should always take a bias towards simplicity when constructing a theory. Where it is easy to get the wrong meaning is that Ockham was not saying that nature always follows the simplest course. Rather he was suggesting that one should not construct unnecessary and over-elaborate explanations.

Courtenay sums up Ockham's influence on present day ideas as follows [3]:-

... with the revival of interest in late medieval thought that took place in the second half of the twentieth century, Ockham has re-emerged as one of the major figures of scholastic thought, generally ranked on the level of Thomas Aquinas and John Duns Scotus. And from the standpoint of the philosophy of the 1980s and 1990s, Ockham's interest in terminist logic, linguistic theory, and semiotics has placed him in the forefront of those medieval thinkers used as sources in contemporary philosophical discussion.