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William of Ockham

William of Ockham is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand William of Ockham rather than just read about it. In short: William of Ockham or Occam ( OK-əm; Latin: Guillelmus de Ockham; c. 1287 – 9/10 April 1347) was an English Franciscan friar, scholastic philosopher and theologian. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of the 14th century.

William of Ockham — main illustration
William of Ockham — illustration

Key takeaways

  • William of Ockham belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect William of Ockham to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of William of Ockham from memory before moving on to harder problems.

Reference excerpt

William of Ockham or Occam ( OK-əm; Latin: Guillelmus de Ockham; c. 1287 – 9/10 April 1347) was an English Franciscan friar, scholastic philosopher and theologian. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of the 14th century. The nominalists of the fifteenth century regarded him as one of the founders of their movement. He is widely known for Occam's razor, the methodological principle that bears his name. He produced significant works on logic, physics and theology. Ockham is remembered in the Church of England with a commemoration corresponding to the commonly ascribed date of his death on 10 April.

Life William of Ockham was born probably in Ockham, Surrey, around 1287. At an early age he became a member of the Franciscan Order (Order of Friars Minor) and received the first stages of his theological education in the Franciscan school in London. From some undetermined date until probably 1321 he studied in the Franciscan school in the University of Oxford. Although he completed all the requirements for a master's degree in theology, he never was a regent master. Because of this he was later called the Venerabilis Inceptor. (An inceptor was someone recognized by the university as qualified to begin ("incept") as a regent master.) A scholar seeking to become a Master of Theology was required to give lectures on Peter Lombard's Sentences. These lectures (which were usually in the form of disputed questions) were often copied and circulated, and a "Commentary on the Sentences" was often a theologian's main publication. Ockham's disputations on the Sentences were held probably in the years 1317-1319. His Sentences commentary has been edited in his Opera Theologica. After qualifying for the Mastership, Ockham was sent by his Order to one of its schools, probably the school in London where he had previously been a student. Most of the works he produced during this time were philosophical, rather than theological. They included commentaries on several logical treatises of Aristotle, a commentary on Aristotle's Physics, and a Summary of Logic. His output during this time was prodigious. The works Ockham produced during this period have been edited in his Opera Philosophica. His teaching work was interrupted in 1324 by a summons to the papal court, at that time located in Avignon, to defend his Sentences commentary. (An alternative hypothesis, recently proposed by George Knysh, is that he was initially appointed in Avignon as a professor of philosophy in the Franciscan school there, and that his disciplinary difficulties did not begin until 1327.) The Pope, Pope John XXII, directed former Oxford chancellor John Lutterell, who had come to Avignon looking for advancement, to prepare a collection of suspect passages from Ockham's Sentences commentary, and a committee of theologians was appointed to review them. The committee's preliminary reports were critical, but the process was never brought to a conclusion. While he was in Avignon, Ockham became involved in the dispute about Apostolic poverty. The Rule of Saint Francis commanded members of the Order to practice the poverty of Jesus and his apostles, who, the Franciscans maintained, owned nothing either individually or "in common" (i.e. as a group). In several papal bulls or "constitutions" Pope John rejected the Franciscan doctrine and practice. In Ad conditorem canonem John argued that no-one could justly consume (i.e. destroy by use) something owned by someone else (for example, food, clothing), so that provision of consumables was a transfer of ownership. He also argued that it was not possible to transfer durables to another person's use permanently without thereby transferring ownership. In Cum inter nonnullos John condemned as heresy the statement that Christ and the Apostles did not have anything individually or as a group. The Minister General (head) of the Franciscan order, Michael of Cesena, asked Ockham to study the pope's bulls. Ockham found in them "a great many things that were heretical, erroneous... adverse to orthodox faith". Together with Michael, Bonagratia of Bergamo, Francis of Marchia and perhaps other members of the Order, Ockham secretly left Avignon on 26 May 1328. The dissident Franciscans eventually took refuge in Munich, under the protection of the Holy Roman Emperor Louis IV of Bavaria, who was also engaged in a dispute with Pope John over the question whether he ought to have obtained the Pope's approval to become Emperor. On June 6, 1328, Ockham and the other dissidents were excommunicated for leaving Avignon without permission. Most members of the Franciscan Order submitted to the decrees of Pope John. Ockham and other members of the small band of dissident Franciscans in Munich (the "Michaelists") campaigned for years to get John XXII and his successors Benedict XII and Clement VI deposed from the papacy. The writings Ockham published during those years are often called his "political writings" (Opera Politica), because they deal with many matters relevant to political philosophy. After he left Avignon Ockham seems to have written nothing more on the topics of his academic work in England. William of Ockham died probably on either 9 or 10 April 1347 (just before the outbreak in Munich of the Black Death).

Philosophical thought

Ockham incorporated much of the work of some previous theologians, especially Duns Scotus. From Scotus Ockham derived his view of divine omnipotence, his view of grace and justification, much of his epistemology and ethics. He disagreed with Scotus about predestination, penance, universals, and the formal distinction ex parte rei ("on the part of the thing") in creatures.

Faith and reason William of Ockham held that theology is not a science. "Only faith gives us access to theological truths. The ways of God are not open to reason, for God has freely chosen to create a world and establish a way of salvation within it apart from any necessary laws that human logic or rationality can uncover." Science includes empirical knowledge and conclusions demonstrated from self-evident premises.

… excerpt ends here. Continue reading the full article.

Illustrations

William of Ockham illustration
William of Ockham illustration
William of Ockham illustration
William of Ockham illustration
William of Ockham: Sketch labelled "frater Occham iste", from a manuscript of Ockham's Summa Logicae, 1341
Sketch labelled "frater Occham iste", from a manuscript of Ockham's Summa Logicae, 1341

Worked examples

Example 1 — a first encounter with William of Ockham

Start with the simplest possible case. Write down what William of Ockham claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to William of Ockham before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about William of Ockham ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of William of Ockham

In research
William of Ockham appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses William of Ockham in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
William of Ockham is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1287 births, 1347 deaths, 14th-century Christian theologians, so understanding it makes those chapters shorter.
In everyday life
Look for William of Ockham outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study William of Ockham in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what William of Ockham means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain William of Ockham out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is William of Ockham in simple terms?

William of Ockham or Occam ( OK-əm; Latin: Guillelmus de Ockham; c. 1287 – 9/10 April 1347) was an English Franciscan friar, scholastic philosopher and theologian. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political contr…

Why does William of Ockham matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study William of Ockham?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on William of Ockham.

Tags

  • 1287 births
  • 1347 deaths
  • 14th-century Christian theologians
  • 14th-century English mathematicians
  • 14th-century English philosophers
  • 14th-century English writers
  • 14th-century writers in Latin
  • 14th century in science
  • Alumni of the University of Oxford
  • Anglican saints
  • Catholic clergy scientists
  • Catholic philosophers

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