Albert of Saxony & Impetus

After the previous post on impetus, I wanted to introduce you to Albert of Saxony, who took Avicenna's idea a step further.

Albert of Saxony (c.1320 - 8 July 1390) was the son of a German farmer who became a bishop of Halberstadt after studying at the University of Prague, the University of Paris, and the Sorbonne. He went to Pope Urban V as an envoy of Austria to negotiate the founding of the University of Vienna, whose rector he became in 1353.

A pupil of Jean Buridan in his youth, he was influenced by Buridan's teachings on logic and physics. He worked out his own theory of impetus, based on his predecessors and adding the third or "final" stage of a moving object. Prior to this, it was accepted that
1. the initial force causes the object to move in a straight line (A-B)
2. the object deviates from its path as impetus fades (B)

To this theory, Albert added the third stage:
3. the impetus or force which causes the initial movement is spent, and gravity draws the object downward vertically (C), where it stops (D).

Modern physics would describe this progression as an example of inertia. It seems obvious to us, but these ideas and their descriptions had to start somewhere!

The careful, methodical way in which he laid out his thoughts, and his commentaries on Aristotle's Physics, made him more widely read in the Middle Ages than Buridan. The widespread distribution of his works spread the ideas of the University of Paris throughout Italy and central Europe.

The Theory of Impetus

1582 woodcut demonstrating
impetus with artillery

Impetus is the force or energy with which a body started to move. The term itself entered the English language in the 17th century, but the concept was studied long before that.

Aristotle thought that, for an object in motion to continue to move, it must have a continuous force behind it. John Philoponus in the 6th century thought rather that the initial force was necessary and did not need anything else, but that the initial force would therefore be only temporary; hence an object in motion's observed tendency to slow and stop. Avicenna in the 11th century agreed with him, calling the phenomenon "projectile motion."

In the 12th century, an Islamic philosopher, Hibat Allah Abu'l-Barakat al-Baghdaadi, recognized (finally!) that the motive force diminishes with distance from the mover.

Jean Buridan, writing in French in the 14th century, called this force "impetus" (from Latin impetere, "to assail"), and even expressed it mathematically: impetus = weight x velocity. Even he, however, treated impetus as if it were momentum. Modern physics distinguishes the two thusly: impetus is the initial force behind a moving object, momentum is "the quantity of motion of a moving body." It seems universally understood by anyone who has ever thrown a ball that Aristotle's option of a continuous motivating force is simply quaint.

Buridan understood that there was resistance (such as the air) that caused the impetus to fade. There was a case, however, in which impetus did not have resistance. God, when putting the celestial spheres in motion, did so in a way that created infinite impetus so that they would (obviously!) never stop moving.

To which the medieval world replied: Thank Heavens.

The Liar Paradox

Medieval philosophers categorized several logic puzzles as insolubilia, unsolvable things. Probably the most common of these was (and still is*) the Liar Paradox.

Consider the statement "I am lying." If I am truly lying at that moment, then what I just said was true. If the statement is therefore true, however, then to say "I was lying" would be a lie. So which is it?

One 20th century philosopher used Jean Buridan (c.1300-c.1361, mentioned elsewhere in this blog) to claim that it wasn't really a paradox. Arthur Prior said it wasn't really paradoxical because every statement includes an assertion of its own truth. The statement "I am lying." is therefore taken as true—it carries its own truth independent of other sentences or context— and considering it a paradox is an unnecessary complication.

Buridan actually used the Liar Paradox to prove the existence of God. He put forth two statements:
"God exists."
"None of the sentences in this pair is true."

The only consistent way to assign truth values, that is, to have these two sentences be either true or false, requires making “God exists” be true. In this way, Buridan has “proved” that God does exist. [Internet Encyclopedia of Philosophy]

This particular paradox first appears in the middle of the 4th century BCE. Eubulides of Miletus made a list of seven puzzles, one of which was “A man says that he is lying. Is what he says true or false?” His commentary on whether it is true or false is lost to time.

*Those readers of a certain vintage will remember the Star Trek: The Original Series episode "I, Mudd" in which a controlling super-robot is rendered useless by its inability to process the two statements "Everything Harry Mudd says is a lie." followed by Mudd saying "I am lying."

The College of Sorbonne

A university meeting

Today is the birthday of the founder of the Sorbonne. The Collège of Sorbonne is arguably the best-known college in France, its name becoming synonymous with excellence, especially in the field of theology. It was founded in 1257 by Robert de Sorbon.

Robert de Sorbon (9 October 1201-15 August 1274) was born in a lower-class family in the Champagne-Ardennes region of northeast France, a wild part of the country prone to spawn legends and tales of adventure. Robert joined the church and studied at Reims and Paris. His devout bearing brought him to the attention of Louis IX, and he was named canon of Cambrai (next door to the Ardennes region) in 1251.

He became a teacher in 1253; in 1257 he created a college in Paris which he called Maison de Sorbonne [House of Sorbon] to teach theology to students who could not otherwise afford a university education. The Maison grew in popularity, however, and was endorsed by the King and by Pope Alexander IV (previously mentioned here and here). The College of Sorbonne grew to become the heart of the University of Paris (which produced such lights as Jean Buridan as well as conflicts). Sorbon became its chancellor until his death in 1274.

Sorbon created an academic environment that was (in the words of one scholar) "as opposed to mere hostel foundations and elementary forms of collegial living."

... Robert of Sorbon, formulated the central idea of the future college system in exemplary fashion: vivere socialiter et collegialiter, et moraliter, et scholariter*—a formulation which implies the existence of a study community organized in the form of a brotherhood and living together in regulated and moral fashion. [P. Glorieux, Les Origines du collège de Sorbon, quoted in A History of the University in Europe: Volume 1, Universities in the Middle Ages]

Among the students were Pope Clement VI and Nicholas Oresme.

*[roughly] "To live socially and collegially and morally and scholarly"

The Beast of Provence

The "Beast of Provence" (also known as the "Giant of Provence" or "Bald Mountain") is actually Mont Ventoux [Mount Windy] in Provence. You have probably seen it on television: it is a major part of the Tour de France. It is made challenging not only because it is the highest mountain in the region, but also because of the high winds near the summit.

Winds blow over 50 miles per hour for the majority of the year, and speeds of 200 miles per hour have been recorded. The road over the mountain is often closed due to wind conditions.

The history of the Beast has always included an aura of foreboding, not just because of the wind. Its limestone peak—which can be seen from miles away—allows only sparse vegetation to grow, and so "Bald Mountain" appears to be barren and imposing.

Today is the anniversary of Petrarch's (1304-1374) ascent of Mont Ventoux in 1336. The writer claimed he was the first to do so since antiquity, even though his very own account mentioned meeting an old shepherd who had climbed it 50 years earlier. Petrarch has been cited as the first person to climb mountains for pleasure, incidentally creating "environmental writing" along the way by describing the surroundings and being inspired to introspection by them. (One of his musings at the peak is on his years of love for Laura.)

It is unlikely, however, that Petrarch was the first person to climb the mountain since antiquity—even besides the old shepherd. Jean Buridan (c.1300-1361) took a break from teaching at the University of Paris to climb the Beast, probably years before Petrarch. As for doing it "for pleasure": there are German writings from the 10th and 11th centuries about climbing mountains as a pleasant pastime.

The Rotating Earth

Nicholas Oresme

While re-examining Aristotle, Jean Buridan used observation and brainpower to anticipate some of the ideas we attribute to Galileo and Newton. He carried his ideas further when he put his mind to the question of the Earth's movement.

For most scholars of the Classical and early Medieval eras, the Earth was fixed, and the Heavens rotated around the Earth once each day. Buridan didn't like this: the Heavens are so much larger than the Earth; why would God design such an inelegant system? Moving the Earth would be easier.

Ptolemy knew this could not be, because if the Earth were rotating, there would be a constant rushing of wind as the air of the atmosphere passed over the land underneath it. Buridan scoffed at this: the atmosphere would be rotating just as the land does. There was no reason to dismiss the idea that Earth rotated daily.

For Buridan, however, empirical evidence was crucial. Of course, his predecessors argued, the Earth clearly does not move; we can see that. Buridan, however, likened the situation to being in a boat on a river. An observer on a second boat that was tied to the bank would see the first boat moving, but if the observer on the second boat could not see the surrounding landscape, then he would not know which of the boats were moving. The problem, Buridan knew, was that without an outside frame of reference, one cannot tell if it is the Earth or the Heavens that is moving. He needed an experiment, and he thought of one.

...and that's when he made his mistake.

Here was his idea: shoot an arrow straight up above your head. If it comes back down where you are standing, then the Earth is stationary. If the Earth rotated under it, then the arrow would come down somewhere off to the side.

He didn't realize that the same property that moves the atmosphere along with the ground would carry the arrow along as well. It would be Buridan's most brilliant student, Nicholas Oresme (c.1325-1382), who would realize and state that the arrow moves along with the Earth and atmosphere. Lacking a way to definitively prove his ideas, however, Oresme would ultimately fall back on the Bible for guidance on this issue.

Nominalism vs Realism

Realism [link]

At the foundation of philosophy is a question: what defines reality? There are several questions that are connected to this. Let us start with: when we say that a lot of different animals are all dogs, to what quality are we referring that makes the Dachsund and the Great Dane both dogs? Is there an essential quality of "dog-ness"? Some universal concept that is inclusive of all dogs, despite the particular differences between breeds?

There it is: universals and particulars.

Realism says that both universals and particulars exist. That is, we recognize that different dogs/houses/trees are those things because, although they have different particulars, there is a universal essence of dogs/houses/trees that exists. Plato and Aristotle were Realists.

Nominalism says that the world is made only of particulars. Things we see are put into categories by our thought processes and our language, not by the existence of some abstract universal. William of Ockham and Jean Buridan were Nominalists.

In the two diagrams shown, we see that in Realism, although John and David have different Particulars, they are defined by their Universal quality as human beings. Nominalism, however, shows John and David only defined by their Particulars. The category of Humanity is created by us. There is no abstract "Humanity" essence that exists independent of John and David.

Nominalism [link]

Getting at the truth produced some fascinating thought experiments. One—The Puzzle of Theseus' Ship—was posed by Plutarch (46-120 CE). The ship of Theseus was preserved in Athens for several generations. As pieces of it decayed, they were replaced with new wood, so that the ship would stay intact. If a thing is based on its particulars, then with the particulars of this ship having changed over the years, is it still Theseus' ship? If there is some universal of Theseus' ship (as Realism says) then it is still his ship. If there are only particulars (as Nominalism says) then it isn't.

British philosopher Thomas Hobbes (1588-1679) took this a step further: if all the removed pieces were assembled into a complete ship, then which is Theseus' ship? Are they both Theseus' ship? He concludes that this would be absurd.

Even the early scholars understood that there were problems with these concepts, and struggled to reconcile the issues. Still, they did their best to understand how reality worked, and how that would help them to understand everything else.

...such as whether we have individual souls. That discussion will take us back to Averroes tomorrow.

Pre-Inertia

Expositio & questiones manuscript

Jean Buridan (c.1300-c.1361) was a University of Paris scholar who was not afraid to tackle some of the big scientific and philosophical issues of the day. That meant, in some cases, taking a critical look at one of the most revered figures in science and philosophy, Aristotle. Buridan, like William of Ockham (c.1288-c.1348),  believed in the observable reality around him, and believed that observation of the world was the key to understanding it. Challenging Aristotle could be risky, but as more and more scholars observed the world around them, they realized that Aristotle's theories needed amendment. He wrote Expositio & questiones (Expoition and questions) to analyze Aristotle's work.

For example, Aristotle believed that an object set in motion—let's say, a rock thrown by a human hand—continues to move after it has left the hand because there must be some continuous external force exerted on it. He theorized that, in the same way a hand swished through water creates little eddies and swirls in the water around it, so the rock's movement is continued by eddies and currents of the air. If there were no movement in the medium that helped carry the rock forward, he believed, the rock would stop its forward course (and presumable drop the the ground). The currents eventually faded, allowing the rock to end its forward flight.

Buridan was not satisfied with this. Building on the work of others (such as John Philoponus and Avicenna, both of whom deserve their own entries some day), he believed that there must be a property in the rock itself that accounts for its action once it has left the motive force of the hand. He called this property of the object impetus (from Latin impetere, literally "to rush toward, to attack").

The property or quality of impetus was clearly changeable. To hurl a heavy rock required you to give it more impetus than to hurl a pebble. Also, impetus was obviously used up over time, allowing the rock to cease its movement and fall. He also explained that a falling object gained impetus the longer it fell (are you paying attention, Galileo?). Unlike Aristotle, who believed that the medium of air in which the object moves helps it along, Buridan saw the air as resistance, causing the object to use up its impetus.

He expanded this theory by looking up. A question had bothered some philosophers for ages: why don't the planets slow down? Will they move forever? Buridan extrapolated his theory to say that a thrown rock in a vacuum would experience no resistance and its impetus would last indefinitely. If the planets were moving in a vacuum...

Well, actually, he couldn't go that far. He agreed with Aristotle that a vacuum couldn't exist in space, since there was no container to keep matter from rushing into the empty area. If above our atmosphere were filled with quintessence, however, Aristotle's "fifth element" that was pure, unchangeable, and frictionless, then the impetus imparted to the planets by whatever initial agency would continue to move forever! The idea of an eternal universe was supportable by science!

Buridan's Ass

Buridan's Ass is the name given to a paradox: that a hungry and thirsty ass placed exactly in the middle between water and hay will be unable to choose because neither choice is preferable or closer; he will therefore die of thirst and hunger. The paradox is named for Jean Buridan (c.1300-c.1361), who studied and taught at the University of Paris. He had a reputation for being a bright and charismatic figure who had a way with the ladies, but that last part might have been spread by his detractors.

But Buridan, who wrote several works including answers to puzzles such as the liar paradox, never discussed the dilemma of the ass; he might have, because it had been around for hundreds of years.

Aristotle mocked the paradox in his De Caelo (On the Heavens). There was an idea circulating that one could explain the unmoving nature of the Earth simply because it was round and centered among all that existed, and therefore all forces acted upon it equally, maintaining an equilibrium. Aristotle mocked this idea by saying it was as ridiculous as if to say that "a man, being just as hungry as thirsty, and placed in between food and drink, must necessarily remain where he is and starve to death." Other early philosophers commented in this dilemma as well.

Why did it get ascribed to Buridan? In his works, he does consider that a rational choice could not be made by a rational person between two equally good options:

Should two courses be judged equal, then the will cannot break the deadlock, all it can do is to suspend judgement until the circumstances change, and the right course of action is clear.

This was just a "thought experiment" for him, however. He did not believe this would in fact lead to total inaction: he believed in a moral determinism that would lead one to a choice, even though that choice or preference might come through an unknowable thought process. Later writers mocked him by laying the burden of the ass paradox on him.

Buridan and Aristotle would cross paths on another issue, however: when a thrown object leaves the hand of the thrower, what keeps it moving? Aristotle had a theory that was clung to by many for centuries. Buridan had a different idea, one that anticipated Newton by about 300 years.

But that's a story for another day.