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250 years of history

mathematics and science, philosophy and religion

Dutch history

to the heavens and back

imitating christ

I'd like to express extreme appreciation to the Mathematics Genealogy Project and Wikipedia.

Last time we had gotten back as far as Thomas à Kempis.  Thomas was educated as a copyist by the newly formed Brethren for the Common Life.

Thomas was under the care and supervision of Florens Radewyns from the age of 13 until the age of 21.  We probably have more knowledge of the beginnings of this group of educators than we ought because Thomas wrote of them:  Being the Lives of Gerard Groote, Florentius Radewin and their Followers (translation by J.P. Arthur).  Whether because of that or because of the impact of they had on western society, however, is probably not important.  Here's another link, to a piece by William F. Wertz, Jr. at the Schiller Institute website.

Radewyn's house was the site of the founding of the the first community of the brothers.  Later, the Congregation of Windesheim was also established in that house.

Radewyn was known for his unusually brilliant intellect and received his Master of Arts degree at Prague.  {Can I follow this academic line even further back in this direction?  Possibly, with much more time and patience.  And that is truthfully what should be done.}  He was appointed the canon of St. Peter's in Utrecht and was leading the life of the wealthy until he heard a sermon by Geert Groote and was converted to the life of a poor clerical scholar.

Groote himself had been appointed canon in both Utrecht and Aachen and was leading the high life until chastised by one of his former college classmates in Paris, Henry de Calcar.  Rejecting his former vanity, Groote became a missionary preacher, traveling throughout Utrecht, preaching wherever he could find an audience.  And according to Kempis, people walked away from their work and their meals in able to hear him speak.  Churches had not enough seating to hold his audiences.

Although he was not a priest, he was supported in his efforts by the Bishop of Utrecht, who even suggested some topics for his sermons.  But his typical targets were

the prevailing sins of the laity, but also against heresy, simony, avarice, and impurity among the secular and regular clergy.
This did not make him popular with the clergy.  He was charged with heterodoxy and an edict was issued, and later upheld by Urban VI, prohibiting the preaching of sermons by those who were not priests.  Groote died of the plague in 1384.

The Brotherhood founded by Groote and Radewyns lived on, however, through the schools they created at Zwolle, Deventer and elsewhere throughout Germany and the Netherlands, dozens of them, which offered a course of education in the humanities, philosophy, and theology.  At the time of Erasmus, Deventer had as many as 2200 students.

Because of its focus upon copying manuscripts, the Brotherhood placed an emphasis upon original classical sources, as opposed to secondary textbooks.  Moreover, its approach to education, in contrast to the Aristotelian method prevalent in the universities of the time, was not based upon rote learning and merely formal knowledge.


With the coming of printing technology, those schools became the centers of publication, with the help of their friend and close associate, Johannes Gutenburg.  Brotherhood schools produced one-quarter of all the books in pre-Reformation Europe.

Groote was educated at the Sorbonne, where he studied scholasticism and theology, Canon law, medicine, astronomy and magic, with a smattering of Hebrew.  All we know about his teacher is that he was a student of William of Ockham.  And we know that his teacher passed on to Groote the philosophy of nominalism.  

The trail will end, for now, with William of Ockham.  Although we know he worked on his master's degree at Oxford from 1309 to 1321, he never did finish that degree, earning the appellation, Venerabilis Inceptor (Worthy Beginner).  Later he would be called Doctor Invincibilis (unconquerable Doctor).  

In 1323, he wrote Summa Logicae (The Sum of Logic), from which this sketch is taken.  He developed what would later be called DeMorgan's Laws and a three-valued logic system that would arise again in the 19th and 20th centuries.

Philosophically, he studied scholasticism, the forerunner of the Scientific revolution, when inductive reasoning came into vogue.  He advocated a simplification of the philosophy's method and content.  His work on that put him among the giants in the field, along with Peter Abelard, Albertus Magnus, Duns Scotus, Bonaventure and Thomas Aquinas.

He was one of the pioneers of nominalism, to the point that some consider him to be the father of modern epistomology

because of his strongly argued position that only individuals exist, rather than supra-individual universals, essences, or forms, and that universals are the products of abstraction from individuals by the human mind and have no extra-mental existence.
Some consider him a conceptualist rather than a nominalist.  I will not weigh in on that debate:  I am a mathematician, not a philosopher.

He is, of course, best remembered for his statement on ontological parsimony:

For nothing ought to be posited without a reason given, unless it is self-evident (literally, known through itself) or known by experience or proved by the authority of Sacred Scripture.
This later became known as Occam's Razor, which was interpreted by Bertrand Russell as meaning:
one should always opt for an explanation in terms of the fewest possible number of causes, factors, or variables.
Ockham wrote extensively about natural philosophy.  He rejected Aristotle's Prohibition of Metabasis (explanations should be appropriate to the phenomena that they explain and methods from one subject cannot be applied to other subjects), anticipating the Scientific Revolution.  He applied his Razor to objects in motion and concluded that motion is essentially self-conserving in itself without need of any causal force, anticipating Newton's First Law by over three centuries.  Even then, Ockham's view was not totally accepted...not until Einstein's relativistic rewrite of Newton.

He wrote on the theory of knowledge and the difference between intuitive and abstract cognition.

His work in political science was monumental and earned him excommunication.  He believed in government with limited responsibility.  He advocated for the separation of church and state and in favor of the concept of property rights.

In 1327 the Franciscan Minister General, Michael of Cesena, was summoned by Pope John XXII to Avignon to answer charges of heresy, since the Franciscans claimed that in taking their vows of poverty, they were following the path of Christ and the Apostles.  William, professor of philosophy at the Franciscan school in Avignon, was summoned to review the case.  In the scholastic tradition, Ockham studied all the available writings, including those of Pope John, and agreed with the Franciscans, declaring further that Pope John was himself guilty of heresy for refusing to accept the Franciscan claim.

Ockham, Cesena, and the other Franciscans fled Avignon forthwith.  They reappeared in Bavaria, in the court of the Holy Roman Emperor, Louis IV, who had been excommunicated in 1324.

To insure his bad graces, William also wrote A Letter to the Friar's Minor, in which he explained the situation, Against Benedict (the pope who followed John XXII), Eight Questions on the Power of the Pope, and my favorite title, perhaps ever, A short discourse on the tyrannical government over things divine and human, but especially over the Empire and those subject to the Empire, usurped by some who are called Highest Pontiffs [i.e. Popes].

And there was Dialogus, which is perhaps the most famous.  The sketch is the frontispiece to that manuscript.  The Dialogue...

greatly influenced the Conciliar movement and assisted in the emergence of liberal democratic ideologies
But one has to know that if one opposes papal infallibility, one is in for some resistance.

In the final months of his life, William of Ockham wrote On the Power of Emperors and Pontiffs.

I have the sneaking suspicion that if he were alive today, he would have been a blogger.

And so we come to an end of the search, at least temporarily.  There are some loose ends.  Who advised Radewyns at Prague, for example?  Exactly who was Groote's teacher at the Sorbonne?  There are so many other stories to explore, like the story of Erasmus' close friend Georg Bauer (aka Georgius Agricola), who founded the disciplines of geology and metallurgy, which was an immense aid to the advancement of the printing press.

One could spend a lifetime following the threads.

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