John Philoponus

How to use this course

John Philoponus lived in sixth-century Alexandria, at the end of the Greek philosophical schools of antiquity. He was trained as a commentator on Aristotle and wrote some of the most careful commentaries we have. He also wrote the most thorough attack on Aristotle’s physics before the seventeenth century. Many of his objections reappear in Ibn Sina, in the Paris impetus theorists such as Jean Buridan, and in the young Galileo, who cited him by name.

Each technical lesson opens with a paragraph for the general reader, then states Philoponus’s positions as closely as the texts allow and compares them with modern physics or mathematics. Philoponus wrote in Greek prose. Formulas are our models of his claims, and we say so. His life is poorly documented: we have the dates his own works reveal, the replies of his opponents, and later Syriac, Arabic and Byzantine reports. Where a date or detail is contested, we give the range.

Timeline

Alexandria and the school of Ammonius

Alexandria around 500 was a Christian city of the Eastern Roman Empire, governed from Constantinople, with a powerful patriarch and a long tradition of Greek learning. It still had public teachers of philosophy, medicine and grammar. The leading philosopher was Ammonius, son of Hermias, who had studied in Athens under the Neoplatonist Proclus and then taught in Alexandria for decades. Ammonius was a pagan in a Christian city. According to the later philosopher Damascius, he reached some accommodation with the Christian authorities that allowed him to keep teaching.

Name and origins

Philoponus called himself John the Grammarian (Iōannēs ho Grammatikos). “Grammarian” was a professional title: a teacher of language and literature, a rank below the chair of philosophy. The surname Philoponus means “lover of work”. It may have been a nickname for his industry or a reference to the philoponoi, lay Christian associations in Alexandria that were active in church life. Arabic writers knew him as Yahya al-Nahwi, John the Grammarian. Nothing reliable is known of his family. Most scholars think he was born around 490 and was a Christian from birth, though some earlier accounts placed his origins in Caesarea and some argued for a later conversion.

The curriculum

In Ammonius’s school, students read Aristotle’s logic first, then his natural philosophy, as preparation for Plato and for Neoplatonic metaphysics. Teaching took the form of lectures on a text, often taken down by students and edited for publication. Several of Philoponus’s early commentaries carry the heading “from the seminars of Ammonius, with some observations of his own”. They show a pupil who knew Aristotle extremely well and had begun to disagree with him.

The grammarian as commentator, c. 510–517

Between about 510 and 517 Philoponus published commentaries on Aristotle’s On Generation and Corruption, On the Soul, the Categories, and the Prior and Posterior Analytics, along with a work on Greek words with several meanings. The commentaries follow the Neoplatonic convention of harmonizing Aristotle with Plato and explaining difficulties away.

The Physics commentary

The commentary on the Physics is different. In it Philoponus refers to a date that corresponds to 517, so it was finished in or soon after that year. It may have been revised later. In long digressions he rejects several of Aristotle’s central doctrines: the definition of place as the boundary of the containing body, the impossibility of void, the account of projectile motion, and the law that speed is proportional to weight and inversely proportional to the density of the medium. Lessons 04 to 06 reconstruct these arguments. They are the main reason historians of physics know his name.

Philoponus did not reject Aristotle wholesale. He kept the four elements, natural places, the distinction between natural and forced motion, and Aristotle’s logic. His method was internal criticism: he used Aristotle’s own principles, and common experience, to show where the system failed.

529: the turn against Proclus

The Neoplatonists held that the world has no beginning. Plato’s Timaeus seems to describe a creation in time, but they read the story as an allegory of eternal dependence on a cause. Proclus had collected eighteen arguments for the eternity of the world. In 529 Philoponus published On the Eternity of the World against Proclus, a long work that answers each argument in turn.

The same year is the traditional date of Emperor Justinian’s measures against pagan teaching, which ended the Neoplatonic school in Athens. Historians debate how far the coincidence was deliberate. Some see the book as a Christian scholar’s bid to show that philosophy could serve the faith; others stress that its arguments are philosophical throughout and that Philoponus quotes Plato and Aristotle against Proclus far more than Scripture.

Against Aristotle

In the early 530s he followed it with Against Aristotle on the Eternity of the World, in at least eight books. It attacked Aristotle’s fifth element, the aether, and the eternity of motion and time. The work is lost, but the Athenian philosopher Simplicius, who had also studied with Ammonius, quoted it extensively in order to refute it, so we know much of its content from its enemy. Simplicius treated Philoponus with contempt and mocked him as an outsider to philosophy. A further work, On the Contingency of the World, survives only in an Arabic summary. Lessons 07 and 08 present the arguments.

From the 530s Philoponus seems to have turned mainly to theology, though he still wrote on natural philosophy and probably on the astrolabe.

Impressed force

For the general reader. What keeps a thrown stone moving after it leaves the hand? Aristotle said the air. Philoponus showed that the air cannot do the job and proposed instead that the thrower gives the stone an incorporeal motive power, which carries it on until the power is used up. This is the first clear statement of the idea later called impetus.

The air theories

Aristotle held that a forced motion needs a mover in contact. For a projectile he offered the air: either displaced air flows round and pushes from behind (antiperistasis, which he reported but did not accept), or the thrower moves the air along with the stone and gives it a power of moving that passes from layer to layer (Physics VIII.10).

Philoponus held that this power is temporary: it is expended in producing the motion and fades of itself, even without resistance. He extended the idea to light (Lesson 09), and in On the Creation of the World he suggested that God gave the heavenly bodies a motive power at their creation, an idea that Buridan would later develop with a permanent impetus.

A model

Let \(p\) be the impressed power, and suppose the horizontal speed is proportional to it, \(v=cp\). Philoponus’s power exhausts itself; air resistance also weakens it. A simple model is

with \(\lambda>0\) the rate of self-exhaustion and \(k\ge0\) the resistance. In a void (\(k=0\)), \(p(t)=p_0-\lambda t\) and the motion stops at \(t^*=p_0/\lambda\). This is why Philoponus could accept motion in a void without accepting endless motion. Ibn Sina, who made the imparted inclination self-preserving, had to deny the void (see the Ibn Sina course, Lesson 05); Buridan, who also made it permanent, accepted endless motion where nothing resists.

Falling bodies and motion in a void

For the general reader. Aristotle said a body ten times heavier falls ten times faster, and that motion through empty space would take no time at all, which he thought absurd. Philoponus replied with a test anyone can make: drop two weights, one much heavier, from the same height, and the difference in their times is very small. He also offered a new rule for motion in a medium, in which the medium adds time to a motion that would take a definite time even in a void.

Aristotle’s rule

In Physics IV.8 Aristotle argues that the speed of a falling body is proportional to its weight and inversely proportional to the density of the medium. In modern notation \(v\propto W/\rho\), so the time to fall a height \(h\) is \(t\propto h\rho/W\). As \(\rho\to0\) the time tends to zero, and Aristotle concluded that motion in a void is impossible.

He presents this as a matter of evidence, “by observation”, and against Aristotle’s rule it is decisive. Whether he performed a careful trial or reported common experience cannot be determined.

The additive rule

As a formula for a fall through height \(h\),

with \(a,b\) constants. The void time is finite, so Aristotle’s argument from infinite speed fails. A related rule, in which the speed is the motive power minus the resistance, was held in twelfth-century Spain by Ibn Bajja (Avempace) and reported by Ibn Rushd; through Averroes it reached Thomas Aquinas and the Latin debate.

The Newtonian picture

In a true vacuum all bodies fall with the same acceleration \(g\), and \(t=\sqrt{2h/g}\) for every weight. In air, drag makes heavy compact bodies fall slightly faster than light ones. The Aristotle course shows that Aristotle’s rule describes the terminal speed in a viscous medium. Philoponus’s “very small difference” is what one actually sees from a tower.

Place as extension

For the general reader. Where is a thing? Aristotle said: inside the surface of whatever surrounds it. Philoponus said: in a three-dimensional region of space, the same size as the thing, which would still be there if the thing were removed. Such a region is never actually empty, but it is a coherent idea, and it is what we mean by place. This is close to the modern idea of space as a container.

Objections to the surface definition

• The outermost sphere. On Aristotle’s definition, the outermost heaven is not contained by anything, so it has no place, yet it moves in a circle. Motion without place is incoherent.
• Size. A place should be equal to what it contains. A surface is two-dimensional and a body three-dimensional, so a surface cannot be equal to a body.
• Natural places. Bodies move toward their natural places. A mere surface has no power to attract; an extension with an order of up and down can explain why each element has its region.

Void never actual

Philoponus distinguished conceptual possibility from physical fact. Place as extension can be conceived empty, but in nature it is always filled. He cited the clepsydra, a vessel with small holes in the bottom that holds water in while its top is stopped, and the way liquid rises in a tube when air is sucked out. These show a natural force that prevents a void from forming. This “force of the void” is real, he argued, only because a void is a meaningful idea; one cannot resist what makes no sense.

The explanation was replaced in 1643, when Evangelista Torricelli showed that the weight of the atmosphere supports a column of mercury, and later experiments produced a vacuum above it.

Against the aether

For the general reader. Aristotle split the cosmos in two. Below the Moon, things are made of earth, water, air and fire, and they change and decay. Above the Moon, everything is made of a fifth element, aether, which moves only in circles and never changes. Philoponus argued that there is no fifth element: the stars and the Sun are made of the same kinds of stuff as things on Earth, mostly fire. Then the heavens are subject to the same physics, and like everything composite, they could perish.

Aristotle’s argument

In On the Heavens I.2 Aristotle argues: every simple body has one simple natural motion. Straight motion up or down belongs to the four elements. Circular motion is also simple, so it must be natural to some simple body, which is neither heavy nor light, and which, having no contrary, cannot be generated or destroyed.

Philoponus’s objections (from Against Aristotle, via Simplicius)

• Circular motion of fire. Aristotle himself says, in the Meteorology, that the fire and upper air beneath the Moon rotate along with the heavens. So circular motion is not peculiar to a fifth body.
• Colours of the stars. The stars differ in colour and brightness. Differences of colour arise from differences in composition, as fires differ in colour with their fuel. So the stars are composite and are not made of one simple body.
• Heat of the Sun. The Sun heats and burns. Aristotle explained this by friction of the air, but the simplest explanation is that the Sun is fire.
• Composite implies perishable. What is composite can be dissolved. If the heavens are composite, nothing in their nature guarantees that they last forever; their permanence depends on God.

Philoponus also held that all bodies share three-dimensional extension as their common nature, prior to the qualities that distinguish the elements, a view sometimes compared with Descartes’s matter as extension.

A modern check

Philoponus was right that the Sun and stars are hot and are made of ordinary elements, and right that the colour of a star reveals its physical state. Spectroscopy in the nineteenth century confirmed that stars contain hydrogen, sodium, iron and other terrestrial elements. The colour of a star mainly indicates its surface temperature, through the thermal spectrum, rather than its fuel.

The world had a beginning: arguments from the infinite

For the general reader. Could the world always have existed? Aristotle said yes: there was no first motion and no first moment. Philoponus turned Aristotle’s own principle against him. Aristotle had said an infinite can never be completed or crossed. If the world had no beginning, an infinite number of days would already have passed, which is an infinite that has been completed. So, Philoponus argued, the world must have a beginning.

Aristotle’s premise

Aristotle held that the infinite exists only potentially: a magnitude can be divided without end, but no infinite collection is ever present or completed (Physics III.6). He also held that the world, time and motion have no beginning. Philoponus argued that these two theses are inconsistent.

Cantor’s verdict

After Georg Cantor, two sets have the same size (cardinality) when there is a one-to-one correspondence between them. The natural numbers \(\mathbb N\) and the even numbers have the same cardinality \(\aleph_0\), through \(n\mapsto2n\).

So arguments 2 and 3 fail in Cantorian arithmetic: adding a day, or multiplying by thirty, does not make an infinite set larger. Philoponus was assuming the Euclidean axiom that the whole is greater than the part, which fails for infinite sets. Argument 1 is different. It concerns the completion of an infinite sequence of successive events that ends now, a series with no first term. Modern philosophers still dispute it. Mathematically, the negative integers \(\dots,-3,-2,-1\) form a consistent infinite sequence that ends, with no first term, which suggests that the traversal argument needs more than mathematics to succeed.

The argument from finite power

Aristotle proved that a finite body cannot contain an infinite power (Physics VIII.10). The world is a finite body. Philoponus argued that it therefore cannot have in itself the power to exist for an infinite time; if it lasts, its continued existence must come from outside, from God. He here read “power” as a capacity to be, rather than a force to move. Simplicius objected that this changes the meaning of Aristotle’s term.

Afterlife of the arguments

Philoponus’s arguments passed into Arabic through translations and summaries. Al-Kindi used similar arguments from the infinite to prove that the world had a beginning, and the theologians of the kalam developed them. Al-Ghazali used them against the philosophers. In the Latin West, Bonaventure argued in the same way in the thirteenth century, while Thomas Aquinas held that reason alone can prove neither the eternity nor the beginning of the world.

Light as activity

For the general reader. Aristotle thought light was not a thing that moves but a state of the transparent medium, made actual by a source of fire. Philoponus reinterpreted this state as an activity, a kind of force sent out by a luminous body, which travels outward along straight lines and can even heat what it reaches. He used geometric rays going from the object to the eye, not from the eye outward.

From state to activity

For Aristotle, light is the actuality of the transparent as transparent (On the Soul II.7). It is not a body and does not travel; the whole medium becomes lit at once. In his commentary on On the Soul and in the Physics commentary, Philoponus kept the claim that light is incorporeal but treated it as an activity (energeia) emitted by the luminous body, comparable to the incorporeal motive power impressed on a projectile. It spreads in straight lines, and he used it to explain why sunlight heats: the activity of the Sun warms the bodies it reaches.

He adopted the geometrical optics of rays, but reversed their direction: visual rays run from the object to the eye. In his discussion of reflection he noted that the geometry of a ray is the same whichever way it is traversed.

The astrolabe

For the general reader. The astrolabe is a flat model of the sky: a brass disc on which the celestial sphere is drawn by a projection, with a rotating star map on top. It was used to tell the time, find the height of the Sun or a star, and solve problems of spherical astronomy without calculation. Philoponus wrote the oldest Greek treatise on its use and construction that has survived. The mathematics behind it, stereographic projection, has a remarkable property: it sends circles to circles.

Stereographic projection

Place the celestial sphere of radius \(R\) with its south pole \(S\). Project each point \(P\) of the sphere from \(S\) onto the plane of the equator: the image is where the line \(SP\) meets the plane. Points of the northern hemisphere land inside the equator circle; the south pole goes to infinity. Ptolemy described the projection in his Planisphaerium; the idea may go back to Hipparchus.

Proof sketch. Use coordinates with the sphere \(x^2+y^2+z^2=R^2\) and \(S=(0,0,-R)\). The projection is \((x,y,z)\mapsto(u,v)=\frac{R}{R+z}(x,y)\). Its inverse sends \((u,v)\) to a point on the sphere whose coordinates are rational functions of \(u,v\) with common denominator \(u^2+v^2+R^2\). A circle on the sphere is the intersection with a plane \(ax+by+cz=d\). Substituting the inverse map and clearing the denominator gives an equation of the form \(\alpha(u^2+v^2)+\beta u+\gamma v+\delta=0\), which is a circle, or a line when \(\alpha=0\), which happens exactly when the plane passes through \(S\).

Circles on the plate

For a point at declination \(\delta\) on the meridian, the image lies at distance \(r=R\tan\!\big(45^\circ-\tfrac{\delta}{2}\big)\) from the centre. The equator (\(\delta=0\)) maps to the circle of radius \(R\), the Tropic of Cancer (\(\delta=+\varepsilon\)) inside it, and the Tropic of Capricorn (\(\delta=-\varepsilon\)) outside, usually forming the rim of the plate.

Theology and condemnation

From the 530s Philoponus wrote mainly as a Christian theologian. On the Creation of the World, his only theological work to survive complete in Greek, is a commentary on the creation narrative in Genesis, dedicated to Sergius, patriarch of Antioch. It defends a creation that includes the heavens against the literalist cosmology of Cosmas Indicopleustes, who held that the universe is shaped like the Tabernacle. Philoponus combined the account in Genesis with Greek astronomy and physics, including a spherical Earth and heavens, and his view that the heavenly bodies received their motion from God.

Christology

In the controversies over the nature of Christ that divided the Eastern Church after the Council of Chalcedon (451), Philoponus took the miaphysite side, which held that Christ has one nature from two. His Arbiter, written about 552–553, defended this position with Aristotelian logic just before the Second Council of Constantinople. He argued that a nature exists in reality only as a particular, an Aristotelian principle that he applied to theology.

Tritheism

Applied to the Trinity, the same principle seemed to imply that the Father, Son and Spirit have three particular natures. In On the Trinity (567) and related works, Philoponus was understood by his opponents to teach three gods, and his followers were called tritheists. He died around 570. More than a century later, in 680–681, the Third Council of Constantinople condemned him posthumously as a tritheist. The condemnation helps explain why his Greek works were little copied in Byzantium and why several survive only in Syriac or Arabic.

Yahya the Grammarian and the road to Galileo

In late antiquity

Simplicius’s replies, written in the late 530s, ensured that Philoponus’s arguments against the eternity of the world survived even where his books did not. They also set the tone of later Greek judgments: a clever polemicist who did not understand Aristotle. Simplicius kept the Aristotelian physics that Philoponus attacked.

In the Islamic world

As Yahya al-Nahwi, Philoponus was read in Arabic from the ninth century. Al-Kindi’s proofs that the world has a beginning draw heavily on his arguments from the infinite. Al-Farabi wrote a treatise against him, defending Aristotle on the heavens. Ibn Sina knew the theory of impressed force and reworked it as violent inclination (mayl) that does not decay by itself. Abu’l-Barakat al-Baghdadi kept Philoponus’s self-exhausting version. Ibn Bajja held a rule of motion close to his, in which a finite speed in a void is reduced by the medium. Al-Ghazali and the kalam theologians used arguments like his for creation in time. Ibn Rushd defended Aristotle against them.

In Latin Europe

Some of his commentaries were translated into Latin in the thirteenth century, and his arguments against eternity reached Bonaventure. In fourteenth-century Paris, Franciscus de Marchia proposed a self-spending impressed force and Jean Buridan a permanent impetus; both stand in the tradition Philoponus started, though they knew it mostly at second hand. Greek editions and Latin translations of his commentaries were printed in the sixteenth century. In his early treatise De motu (c. 1590), Galileo used a theory of self-decaying impressed force and named Philoponus among his authorities. Galileo’s later law of fall, with equal times for all weights in a void, went beyond Philoponus’s claim that the difference is very small.

Modern assessments

Pierre Duhem and later Shmuel Sambursky presented Philoponus as a forerunner of Galileo and of modern physics. Richard Sorabji, who organized the translation of the ancient commentators into English from the 1980s, and Christian Wildberg have emphasized both his originality and his place in the debates of his own century. His case is now a standard example of how criticism from within a tradition can prepare its replacement.

Connections

People linked to John Philoponus across this collection. A name without a link has no page here yet. See John Philoponus in the network of all 337 lives →

Teachers and advisors

• Ammonius, son of Hermias

Influenced by

• Aristotle
• Proclus

Influenced

• Galileo Galilei
• Ibn Sina
• Jean Buridan
• Abu'l-Barakat al-Baghdadi
• al-Farabi
• al-Kindi
• Bonaventure
• Ibn Bajja (Avempace)

Rivals

• Simplicius

Also mentioned in this life

• Tycho Brahe
• Georg Cantor
• René Descartes
• Hipparchus
• Isaac Newton
• Plato
• Claudius Ptolemy
• Ole Rømer
• Evangelista Torricelli

Fields

• natural philosophy 12 lives
• mechanics 27 lives
• cosmology 7 lives
• astronomy 50 lives
• theology 8 lives

On CoursesHub

• Classical Mechanics
• Cosmology
• Astrophysics for Beginners

Sources and further reading

Biography and overview

1. C. Wildberg, John Philoponus, Stanford Encyclopedia of Philosophy.
2. S. Sambursky and C. Pearson, John Philoponus, Dictionary of Scientific Biography and New Dictionary of Scientific Biography.
3. John Philoponus, Wikipedia.
4. R. Sorabji (ed.), Philoponus and the Rejection of Aristotelian Science, Duckworth, 1987; 2nd ed., Institute of Classical Studies, 2010.
5. K. Verrycken, The development of Philoponus’ thought and its chronology, in R. Sorabji (ed.), Aristotle Transformed, Duckworth, 1990.

Physics, cosmology and the astrolabe

1. Philoponus, On Aristotle Physics, various translators, Ancient Commentators on Aristotle series, Duckworth / Bloomsbury.
2. Philoponus, Corollaries on Place and Void, trans. D. Furley, with Simplicius, Against Philoponus on the Eternity of the World, trans. C. Wildberg, Duckworth, 1991.
3. Philoponus, Against Aristotle on the Eternity of the World, trans. C. Wildberg, Duckworth, 1987.
4. Philoponus, Against Proclus on the Eternity of the World, trans. M. Share and J. Wilberding, Ancient Commentators on Aristotle, 2004–2006.
5. M. R. Cohen and I. E. Drabkin, A Source Book in Greek Science, Harvard University Press, 1948 (the falling-bodies passage).
6. S. Sambursky, The Physical World of Late Antiquity, Routledge, 1962.
7. R. Sorabji, Time, Creation and the Continuum, Duckworth, 1983.
8. Theory of impetus, Wikipedia.
9. H. A. Davidson, John Philoponus as a source of medieval Islamic and Jewish proofs of creation, Journal of the American Oriental Society 89 (1969).
10. Philoponus, On the Use and Construction of the Astrolabe, ed. H. Hase (1839); English trans. in R. T. Gunther, The Astrolabes of the World, Oxford, 1932.