William of Ockham


Born: about 1288 in Ockham (near Ripley, Surrey), England
Died: 9 April 1348 in Munich, Bavaria (now Germany)


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.

Article by: J J O'Connor and E F Robertson

February 2005


MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Ockham.html]