Aristotle

How to use this course

Aristotle is usually taught as a philosopher. This course treats him as a natural scientist, which is how he spent most of his working life and how he was read for two thousand years. He wrote the first systematic treatises on motion, the cosmos, logic, animals and the weather. He was wrong about falling bodies, the void and the structure of the heavens, and his errors set the agenda of the Scientific Revolution. He was right, often strikingly, about animals, and his logic remained the only formal logic in use until the nineteenth century.

Part I tells the life from the ancient sources and says how far each can be trusted. Part II takes the natural philosophy topic by topic. Each lesson states Aristotle’s position precisely, with references to the standard Bekker page numbers (such as Physics 215a), then examines it with modern tools: fluid mechanics for his law of motion, limits for Zeno, set-theoretic semantics for the syllogism, and geometric optics for his rainbow.

Aristotle’s works on ethics, politics, poetics and metaphysics appear only where the natural philosophy needs them. Companion courses treat Eudoxus of Cnidus, whose planetary spheres Aristotle adopted, and Galileo Galilei, who took his theory of motion apart.

Timeline

Dates of Aristotle’s life rest mainly on Diogenes Laertius (3rd century AD) and on Dionysius of Halicarnassus (1st century BC), who dates events by Athenian archon years. Dates for the treatises are modern estimates.

Stagira and the sources

Aristotle was born in 384 BC at Stagira, a small Greek city on the Chalcidic peninsula in the north Aegean. His father, Nicomachus, belonged to a family that traced its descent to the healer Asclepius and served as physician to Amyntas III, king of Macedon and father of Philip II. His mother, Phaestis, came from Chalcis on Euboea, where Aristotle would die. Both parents died while he was young. A relative, Proxenus of Atarneus, became his guardian; Aristotle later provided in his will for Proxenus’s son Nicanor.

A medical family may explain his lifelong interest in anatomy and dissection, but this is an inference. Ancient reports that he was trained in medicine himself are not reliable.

The sources

• Diogenes Laertius, Lives of Eminent Philosophers Book V (3rd century AD), gives the fullest life, a list of works, and the text of Aristotle’s will. The will is generally accepted as authentic and is the best evidence for his household.
• Dionysius of Halicarnassus, First Letter to Ammaeus (1st century BC), gives a chronology by archon years, drawn from earlier Hellenistic scholarship.
• Late lives in Greek, Latin, Syriac and Arabic, from Neoplatonist schools, add anecdotes and praise. Historians treat them with caution.
• Hostile traditions from rival schools accused him of ingratitude to Plato and of flattering Macedon. These are polemic, not evidence.

The surviving treatises say little about their author. They are working texts, probably lecture notes revised over many years, and they are hard to date. Aristotle also wrote polished dialogues for a general audience, which Cicero admired for their style. Those are lost apart from fragments.

Twenty years in Plato’s Academy

In 367 BC, aged about seventeen, Aristotle went to Athens and entered Plato’s Academy. Plato was then away in Syracuse. Aristotle stayed until Plato’s death in 347 BC, first as a student and then as a teacher and researcher.

What the Academy offered

The Academy was the leading centre of mathematics in the Greek world. Eudoxus, who was there in these years, had developed the theory of proportion that became Book V of Euclid’s Elements, the method of exhaustion, and the model of the planets by nested rotating spheres. Theaetetus had classified irrational lines. Aristotle’s works are full of mathematical examples drawn from this milieu: the incommensurability of the diagonal of a square with its side, the sum of the angles of a triangle, and the theorem that alternate proportions hold for numbers, lines and times alike. Aristotle remarks that this last theorem was once proved separately for each kind, and later in general, a reference to Eudoxus’ theory.

Early writings

Aristotle’s first works included dialogues in the Platonic manner, such as the Eudemus on the soul and the Protrepticus, an exhortation to philosophy. He taught rhetoric in the Academy and began the logical investigations that became the Topics, a manual of dialectical argument, and the Categories. He also began to criticize Plato’s theory of Forms. In the Nicomachean Ethics he says that friends must be honoured, but truth more.

When Plato died, his nephew Speusippus became head of the school. Aristotle left Athens. Whether he left because he was passed over, because of disagreement with Speusippus, or because Philip’s capture of Olynthus in 348 BC had made Macedonians unwelcome in Athens is not known.

Assos, Lesbos and Macedon

The twelve years between Plato’s death and the founding of the Lyceum were Aristotle’s years of research in the field.

Assos and Lesbos, 347–343 BC

Hermias, ruler of Atarneus in the Troad and a friend of the Academy, invited Aristotle and his colleague Xenocrates to Assos on the coast opposite Lesbos. There Aristotle married Pythias, Hermias’s niece and adopted daughter. They had a daughter, also named Pythias. After about three years he moved to Mytilene on Lesbos, probably at the suggestion of Theophrastus, a native of Eresus on the island, who became his closest collaborator and eventual successor.

The biological works mention many places on and around Lesbos, especially the lagoon of Pyrrha, now the Gulf of Kalloni. The density of these references led D’Arcy Thompson and later scholars to conclude that much of Aristotle’s zoological fieldwork was done there. Lesson 09 examines the results.

Around 341 BC the Persians captured Hermias by treachery and executed him. Aristotle wrote a hymn in his honour, which survives, and an epigram for his statue at Delphi.

Macedon, 343–335 BC

In 343 or 342 BC Philip II invited Aristotle to Macedon to teach his son Alexander, then thirteen. Ancient writers, especially Plutarch, report that the lessons took place at Mieza, near the capital Pella. The tutorship is reported by several ancient authors, but almost nothing reliable is known of its content or length, and the influence of the teacher on the conqueror is a matter of speculation. Aristotle is said to have prepared an edition of the Iliad for him and to have written him a treatise on kingship, now lost. Alexander became regent in 340 BC and Aristotle probably returned to Stagira around then.

Nature, change and the four causes

For the general reader. Aristotle’s physics begins with a question that sounds philosophical: what is change? His answer, that change is the realization of a capacity, gave him a vocabulary of potential and actual, matter and form, and four kinds of explanation. Modern science dropped two of his causes and kept the other two, but the questions he asked still organize the way biologists explain organs and engineers explain machines.

Matter, form, potential

In Physics I Aristotle argues against Parmenides that change is possible. Every change involves a subject that persists and a pair of opposites, a lack and a form: an unmusical man becomes musical, bronze without shape becomes a statue. The persisting subject is matter, relative to that change.

The four causes

To know a thing is to grasp its why. In Physics II.3 Aristotle lists four kinds of answer:

• Material: that out of which, as bronze for a statue.
• Formal: the form or account of what it is to be the thing, as the shape of the statue, or the ratio 2:1 for the octave.
• Efficient: the primary source of change, as the sculptor, or the father of a child.
• Final: that for the sake of which, as health for walking.

In nature, Aristotle argues (Physics II.8), final causes operate without design: teeth grow sharp in front for cutting and broad behind for grinding because this serves the animal, and such regularity cannot be chance. He considers and rejects a view, attributed to Empedocles, that animals arose by chance combinations and only the fit survived. The passage was quoted by Charles Darwin in a footnote to later editions of the Origin of Species.

Everything moved is moved by something

Physics VII.1 and VIII.4–5 argue that whatever is in motion is moved by something, and that the chain of movers cannot go to infinity. The argument ends with a first unmoved mover (Physics VIII.6, Metaphysics Λ). For natural motion such as falling, the mover is whatever made the body heavy or removed an obstacle; for projectiles the problem is acute (Lesson 05).

Motion, resistance and the void

For the general reader. Aristotle held that a heavier body falls faster than a lighter one, that a body moves only while something keeps moving it, and that a vacuum is impossible. Galileo and Newton showed all three are false for motion in empty space. But Aristotle lived in a world of air and water, and in a viscous fluid his rules are close to the truth. This lesson states his rules carefully and finds the regime where they hold.

Natural and forced motion

Each of the four elements has a natural place: earth at the centre of the cosmos, water around it, then air, then fire (Lesson 07). A body moves naturally toward its place, up or down in a straight line, and rests there. Any other motion is forced, and needs an external mover in contact.

In modern notation, speed \(v\propto F/R\), where \(R\) is the resistance, with no motion when \(F\) is below a threshold. Aristotle never wrote an equation; the proportional form is due to his commentators, and a functional version was written by Thomas Bradwardine in 1328.

The argument against the void

Suppose the same body crosses equal distances in media of densities \(\rho_1>\rho_2\). By the proportion, the times are in the ratio \(t_1:t_2=\rho_1:\rho_2\). A void has density zero, which bears no ratio to any density. So a body would cross a void in no time, or rather in a time that bears no ratio to any time, which is absurd (Physics IV.8, 215b). Aristotle adds further arguments: in a void there is no reason for a body to move in one direction rather than another, or to stop anywhere.

Projectiles

A thrown stone keeps moving after it leaves the hand. Since every forced motion needs a mover in contact, Aristotle concludes that the thrower moves the air as well as the stone and gives the air a power of moving, which passes from layer to layer and weakens until the stone falls (Physics VIII.10, 266b–267a). He reports and rejects an alternative, “mutual replacement”, in which displaced air circles round and pushes from behind. John Philoponus in the sixth century replaced both with an impressed force inside the projectile, the ancestor of the medieval impetus theory.

When Aristotle is right

For a sphere of radius \(r\) in a fluid of viscosity \(\mu\) at small Reynolds number, Stokes’ law gives \(b=6\pi\mu r\). A heavier sphere of the same size falls faster, in direct proportion to its effective weight. The physicist Carlo Rovelli argued in 2015 that Aristotle’s physics is a correct approximation in this domain, much as Newton’s is an approximation to relativity. In air at everyday speeds, drag is quadratic and the transient is long, so for short falls bodies of different weight land almost together, which is what Galileo stressed.

The infinite, the continuum and Zeno

For the general reader. Zeno of Elea argued that motion is impossible: to cross a room you must first cross half of it, then half the rest, and so on forever. Aristotle preserved Zeno’s arguments and answered them by distinguishing an infinity that can be completed from one that can only be continued. His view of the infinite governed mathematics until Georg Cantor, and his account of the continuum is still the intuitive picture behind real analysis.

Potential infinity

Aristotle also argues that there is no actually infinite body, since the cosmos is a finite sphere (Lesson 07), and that the infinite by addition is the converse of the infinite by division.

The continuum

Argument. A point has no parts, so it has no extremity distinct from itself. Two points cannot be continuous, since that would require their extremities to be one, which makes them a single point. They cannot be in contact, since partless things in contact coincide completely. So points cannot even be successive in a way that builds a line, because between any two points there is always a line, and hence further points. By the same reasoning, time is not made of instants nor motion of indivisible jerks (VI.1–2). In modern terms, Aristotle asserts that a continuum is dense and that it is not the union of a sequence of indivisible pieces placed side by side. The real line satisfies both, though it does consist of points as a set; Cantor’s theory reconciles the two pictures by making the line an uncountable set whose measure is not the sum of the measures of its points.

Zeno’s paradoxes

Aristotle reports four arguments of Zeno against motion (Physics VI.9, 239b): the Dichotomy, the Achilles, the Arrow and the Stadium. His first reply to the Dichotomy (VI.2, 233a) is that time is divisible exactly as distance is, so infinitely many parts of distance are crossed in infinitely many parts of time. In VIII.8 (263a) he admits this does not meet the deeper worry and gives a second answer: the halves are only potential divisions; a runner who does not stop at each midpoint does not actualize them, and so does not complete an actual infinity.

The cosmos of On the Heavens

For the general reader. Aristotle’s universe is a finite sphere with the Earth motionless at its centre. Below the Moon everything is made of four elements that change into one another; above it the heavens are made of a fifth substance that only turns in circles and never changes. This picture lasted until Tycho Brahe’s comets and Galileo’s telescope. Inside it are some excellent arguments, including the first surviving proofs that the Earth is round.

Elements and qualities

In On Generation and Corruption II.3 the four elements are pairs of the primary qualities hot, cold, dry and moist: fire is hot and dry, air hot and moist, water cold and moist, earth cold and dry. Elements sharing a quality change into each other easily, by exchanging the other. Earth is absolutely heavy, fire absolutely light, water and air relatively so.

The fifth body

Simple motions are straight (up or down) and circular. Straight motions belong to the four elements. Circular motion, which has no contrary and can continue forever in a finite space, must belong to another simple body, neither heavy nor light, ungenerated and unchanging (On the Heavens I.2–3). Aristotle calls it the first body and connects the old name aithēr with “always running”. Later writers called it the fifth element, quintessence.

The spheres

For the planets Aristotle adopted the homocentric spheres of Eudoxus as corrected by Callippus (Metaphysics Λ.8, 1073b–1074a). Eudoxus had used 26 moving spheres, Callippus 33. To make the system mechanical, so that each planet’s spheres would not disturb the next planet’s, Aristotle inserted “counteracting” spheres that undo the motion of all but the outermost sphere of each planet above. He counts 55 spheres, or 47 if the Sun and Moon need no extra ones, and remarks that the count is the astronomers’ business. Each sphere has its own unmoved mover; the outermost is moved by the first mover, which moves as an object of love, as a final cause.

The Earth

On the Heavens II.13–14 argues that the Earth is at rest at the centre, because earth moves naturally toward the centre and heavy bodies fall at right angles to the surface, and that it is a sphere. The arguments for sphericity:

• Earth converging from all sides toward the centre settles into a sphere.
• In lunar eclipses the edge of the shadow is always curved.
• Short journeys north or south change the stars visible: some stars seen in Egypt and near Cyprus are not seen in more northern lands. So the Earth is a sphere, and not a large one.

He adds that mathematicians who try to calculate the circumference put it at 400,000 stades (298a). This is the earliest surviving estimate of the Earth’s size; who made it is unknown.

Syllogistic as the method of science

For the general reader. Aristotle invented formal logic. In the Prior Analytics he identified which arguments of a certain form are valid in virtue of form alone, and proved it, reducing them all to a few self-evident patterns. In the Posterior Analytics he described a science as a body of such deductions from first principles. Euclid’s Elements fits this ideal closely, and Aristotle meant his own natural philosophy to aim at it.

Categorical propositions

A premise says something of something, in one of four forms, traditionally labelled:

• A (universal affirmative): every \(S\) is \(P\), written \(SaP\);
• E (universal negative): no \(S\) is \(P\), \(SeP\);
• I (particular affirmative): some \(S\) is \(P\), \(SiP\);
• O (particular negative): some \(S\) is not \(P\), \(SoP\).

A syllogism has two premises sharing a middle term \(M\) and a conclusion linking the extremes. The position of \(M\) defines the figure: in the first it is subject of one premise and predicate of the other, in the second predicate of both, in the third subject of both.

The tools of reduction are the conversion rules of I.2: \(SeP\Rightarrow PeS\), \(SiP\Rightarrow PiS\), and \(SaP\Rightarrow PiS\) (conversion by limitation). Moods with O premises (Baroco, Bocardo) are reduced by reductio ad impossibile: assume the contradictory of the conclusion and derive a contradiction with a premise via Barbara. In I.7 Aristotle shows further that Darii and Ferio themselves reduce to Barbara and Celarent, so two moods suffice.

Example. Cesare: \(PeM,\ SaM\vdash SeP\). Convert the first premise to \(MeP\); then \(MeP,\ SaM\vdash SeP\) is Celarent.

Semantics and existential import

Read terms as non-empty sets: \(SaP\) is \(S\subseteq P\), \(SeP\) is \(S\cap P=\varnothing\), \(SiP\) is \(S\cap P\ne\varnothing\), and \(SoP\) is \(S\not\subseteq P\). All fourteen moods are then valid. Aristotle tacitly assumes non-empty terms; without that assumption, conversion by limitation fails, and so do Darapti and Felapton. Jan Łukasiewicz in 1951 axiomatized the system; John Corcoran and Timothy Smiley in the early 1970s showed that Aristotle’s own procedure is best read as a natural-deduction system, sound and complete for this semantics.

Demonstration

In the Posterior Analytics a demonstration is a syllogism from premises that are true, primary, immediate, better known than, prior to and causes of the conclusion. The middle term gives the cause. Aristotle’s example (I.13): the planets do not twinkle; what does not twinkle is near; so the planets are near. This proves the fact. Reversed, with nearness as the middle (what is near does not twinkle), it gives the reason why. Every science rests on indemonstrable first principles, grasped by induction from perception, as an army in rout is rallied when one soldier makes a stand and then another (II.19).

The biologist of Lesbos

For the general reader. About a quarter of Aristotle’s surviving writing is about animals. He describes some 500 kinds, dissected dozens, and asked how each part serves the life of the animal. Several of his observations were dismissed for two thousand years and then confirmed in the nineteenth century. Charles Darwin, reading a translation late in life, wrote that his own heroes Linnaeus and Cuvier were “mere schoolboys to old Aristotle”.

The works and the method

The History of Animals (Historia animalium) collects the facts: parts, ways of life, activities and characters. Parts of Animals, Generation of Animals, Movement of Animals and Progression of Animals give the causes. A lost work, Dissections, contained drawings to which the texts refer. On the Soul and the short treatises (Parva naturalia) treat life, sensation, sleep, respiration and ageing. Parts of Animals I.5 defends the study of humble animals: there is something marvellous in every natural thing, as Heraclitus told visitors who found him warming himself at the kitchen stove that there were gods there too.

Classification

Aristotle divides animals into blooded (roughly vertebrates) and bloodless (roughly invertebrates). Among the blooded he distinguishes viviparous quadrupeds, oviparous quadrupeds, birds, fish and cetaceans, and he places dolphins and whales with the animals that breathe air and suckle their young, not with fish. Among the bloodless he distinguishes cephalopods, crustaceans, testaceans (shelled molluscs) and insects. He arranges kinds by the degree of perfection of their offspring at birth, a series later called the ladder of nature, though he did not build a single linear classification.

Three observations

• The smooth shark (History of Animals VI.10, 565b). Aristotle reports that in the so-called smooth dogfish the embryo is attached by a cord to a placenta-like structure in the uterus, as in mammals. Johannes Müller confirmed this for the smooth hound Mustelus in a paper of 1842.
• The octopus arm (History of Animals V.6, 541b). Fishermen said the male uses one arm in mating. Aristotle records this but doubts that the arm contributes to generation. Nineteenth-century zoologists showed that the modified arm, the hectocotylus, transfers sperm.
• The chick embryo (History of Animals VI.3). Opening eggs at successive days, he saw the heart as a beating blood-red speck on about the third day. He concluded that the heart, not the brain, is the first organ and the seat of sensation, a correct observation leading to a wrong conclusion.

He also made errors: he held that males have more teeth than females in humans, sheep, goats and pigs, and that the brain cools the blood. In Generation of Animals he argued that the male contributes form and the source of movement, the female the matter, a view that shaped embryology until the eighteenth century.

Meteorology: exhalations and the rainbow

For the general reader. The Meteorology, probably written around 340 BC, is the oldest systematic book on the weather. It explains rain, wind, comets, earthquakes and the saltiness of the sea by two vapours that the Sun draws up from the Earth. Most of its explanations are wrong, but its account of the rainbow contains a genuine geometric theorem, and its description of the water cycle is essentially right.

The sublunary region

Between the Earth and the Moon, the Sun’s heat draws up two exhalations: a moist one, vapour, from water; and a dry, smoky one from the land (I.4, II.4). Vapour cools aloft and falls as rain; Aristotle describes the cycle of evaporation and precipitation as a river flowing in a circle, up and down, made of air and water (I.9). The dry exhalation, carried into the upper region and ignited by the motion of the heavens, produces shooting stars, comets and the Milky Way (I.4–8). Underground, trapped dry exhalation produces earthquakes; in the clouds, wind and thunder. The sea is salt because dry, earthy exhalation mixes with it.

Aristotle also describes the Earth as divided into five zones, with two habitable zones between the tropics and the arctic circles (II.5). He argued that the sea and land change places over long times, too slowly for human memory to record (I.14).

The rainbow

Aristotle explains haloes and rainbows as reflection of sight from small droplets acting as mirrors that show only colour, not shape (III.2–5). He then proves that the rainbow must be an arc of a circle, using an idea now attributed to Apollonius.

Proof. Put \(K=(0,0)\), \(H=(d,0)\) in the plane. The condition \(|M-H|^2=c^2|M-K|^2\) gives \((x-d)^2+y^2=c^2(x^2+y^2)\), that is \((1-c^2)(x^2+y^2)-2dx+d^2=0\). For \(c\ne1\) this is a circle with centre \(\big(d/(1-c^2),0\big)\) on the axis and radius \(cd/|1-c^2|\). Aristotle’s proof works with ratios of segments and finds the centre on the extension of \(HK\).

From the construction Aristotle concludes that the rainbow is a semicircle when the Sun is on the horizon, smaller when the Sun is higher, and that in summer it cannot appear around midday. The modern theory of René Descartes (1637) and Isaac Newton replaces reflection by refraction and internal reflection in raindrops. The bow is a cone of half-angle about \(42^\circ\) around the antisolar point, and Aristotle’s qualitative conclusions follow directly.

The Lyceum and the last years

In 335 BC, after Philip’s death and Alexander’s accession, Aristotle returned to Athens. As a resident alien he could not own land, and he taught in the Lyceum, a public gymnasium outside the city walls sacred to Apollo Lykeios. His followers were called Peripatetics, probably from the covered walk (peripatos) of the school, though a later story says from his habit of lecturing while walking.

The work of the school

The Lyceum was a research institution. Aristotle and his associates collected the constitutions of 158 Greek states, of which the Constitution of the Athenians was recovered on papyrus and published in 1891. They compiled lists of victors at the Pythian games, histories of earlier opinions in physics, mathematics and medicine, and a library. Theophrastus wrote the first systematic works on plants and on stones; Eudemus of Rhodes wrote histories of geometry, arithmetic and astronomy, through which much of our knowledge of early Greek mathematics survives. Most of the surviving treatises probably took their final form in these years.

Family and death

His wife Pythias died, and he lived with Herpyllis, whose status is uncertain; they had a son, Nicomachus. When Alexander died in Babylon in June 323 BC, the anti-Macedonian party in Athens revived and a charge of impiety was brought against Aristotle. He withdrew to his mother’s family house at Chalcis, reportedly saying he would not let Athens sin twice against philosophy, a reference to Socrates. The saying is an ancient tradition, not a documented quotation. He died at Chalcis in 322 BC, aged about 62, of an illness of the stomach.

His will, preserved by Diogenes, names Antipater, the Macedonian regent, as executor; provides for Herpyllis, his daughter Pythias and his son Nicomachus; frees several slaves; and asks that the bones of his wife Pythias be laid with his own, as she had wished. The school passed to Theophrastus, and after him to Strato of Lampsacus.

Two thousand years of Aristotle

Survival of the texts

Strabo and Plutarch tell how the library of Aristotle and Theophrastus passed to Neleus of Scepsis, whose heirs hid it in a cellar, until it was bought by Apellicon of Teos and taken to Rome by Sulla in 86 BC. Modern scholars accept the outline but doubt that the treatises were unknown in the meantime. In the first century BC Andronicus of Rhodes produced the edition and arrangement on which our corpus rests. The polished dialogues were lost; the working treatises survived.

Commentators and critics

• Late antiquity: Alexander of Aphrodisias, Simplicius and John Philoponus wrote commentaries. Philoponus rejected the law of fall, arguing that weights differing greatly fall in nearly equal times, and proposed impressed force for projectiles.
• Islamic world: the corpus was translated into Arabic in the eighth to tenth centuries. Ibn Sina (Avicenna) and Ibn Rushd (Averroes), whose commentaries earned him the Latin name “the Commentator”, made Aristotle central to philosophy and science.
• Latin West: translated from Greek and Arabic in the twelfth and thirteenth centuries, the natural works entered the universities; Thomas Aquinas combined Aristotle with Christian theology. Jean Buridan and Nicole Oresme in Paris, and the Oxford Calculators, criticized and quantified his physics in the fourteenth century.

The Scientific Revolution

Tycho Brahe’s comet of 1577, shown by parallax to lie beyond the Moon, refuted the unchanging heavens and the solid spheres. Galileo’s telescope found mountains on the Moon and spots on the Sun. Galileo’s law of fall and Newton’s first law replaced the dynamics of Lesson 05. Torricelli, Pascal and Boyle produced and studied the vacuum. The syllogistic held longer: George Boole’s algebra of logic (1847–54) and Gottlob Frege’s quantifiers (1879) finally superseded it, while keeping it as a fragment.

Assessment

• Physics and cosmology: wrong in its central laws, but the first unified theory of nature, and in the viscous domain a correct approximation.
• Mathematics: the clearest ancient analysis of the infinite and the continuum, and of the axiomatic structure of a science.
• Logic: the first formal system with proved metatheorems, dominant for two thousand years.
• Biology: the founding of comparative anatomy, embryology and systematic zoology, with observations confirmed only in the nineteenth century.

Sources and further reading

Biography and context

1. J. J. O’Connor and E. F. Robertson, Aristotle, MacTutor History of Mathematics.
2. C. Shields, Aristotle, Stanford Encyclopedia of Philosophy.
3. Aristotle, Wikipedia (with extensive references).
4. Diogenes Laertius, Lives of Eminent Philosophers, Book V, trans. R. D. Hicks, Loeb Classical Library.
5. I. Düring, Aristotle in the Ancient Biographical Tradition, Göteborg, 1957.
6. J. Barnes (ed.), The Complete Works of Aristotle: The Revised Oxford Translation, Princeton University Press, 1984.

Natural philosophy

1. C. Rovelli, Aristotle’s Physics: a physicist’s look, Journal of the American Philosophical Association 1 (2015); arXiv:1312.4057.
2. Aristotelian physics, Wikipedia.
3. T. L. Heath, Mathematics in Aristotle, Oxford, 1949.
4. R. Smith, Aristotle’s Logic, Stanford Encyclopedia of Philosophy.
5. J. Łukasiewicz, Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, Oxford, 1951.
6. J. Corcoran, Completeness of an ancient logic, Journal of Symbolic Logic 37 (1972).
7. Aristotle’s biology and Meteorology (Aristotle), Wikipedia.
8. A. M. Leroi, The Lagoon: How Aristotle Invented Science, Bloomsbury, 2014.
9. J. Müller, Über den glatten Hai des Aristoteles, Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin, 1842.
10. C. B. Boyer, The Rainbow: From Myth to Mathematics, Princeton University Press, 1987.