Aristotle: Philosopher and Philosophies

Aristotle was not primarily a mathematician but made important contributions by systematising deductive logic. He wrote on physical subjects: some parts of his Analytica posteriora show an unusual grasp of the mathematical method.

There is little doubt that Nicomachus would have wished Aristotle to become a doctor, for the tradition was that medical skills were kept secret and handed down from father to son. It was not a society where people visited a doctor but rather it was the doctors who travelled round the country tending to the sick. Although Aristotle's early years are less known, it is highly likely that he would have accompanied his father in his travels. We do know that Nicomachus found the conditions in Chalcidice less satisfactory than in the neighboring state of Macedonia and he began to work there with so much success that he was soon appointed as the personal physician to Amyntas III, king of Macedonia.

There is no record to indicate whether Aristotle lived with his father in Pella, the capital of Macedonia, while Nicomachus attended to king Amyntas at the court there. However, Aristotle was certainly friendly with Philip, king Amyntas's son, some years later and it seems reasonable to assume that the two, who were almost exactly the same age, had become friendly in Pella as young children.

When Aristotle was about ten years old his father died. This certainly meant that Aristotle could not now follow in his father's profession of doctor and, since his mother seems also to have died young, Aristotle was brought up by a guardian, Proxenus of Atarneus, who was his uncle (or possibly a family friend as is suggested by some authors). Proxenus taught Aristotle Greek, rhetoric, and poetry which complemented the biological teachings that Nicomachus had given Aristotle as part of training his son in medicine. Since in latter life Aristotle wrote fine Greek prose, this too must have been part of his early education.

In 367 BC Aristotle, at the age of seventeen, became a student at Plato's Academy in Athens. At the time that Aristotle joined the Academy it had been operating for twenty years. Plato was not in Athens, but rather he was on his first visit to Syracuse. We should not think of Plato's Academy as a non-political organization only interested in abstract ideas. The Academy was highly involved in the politics of the time, in fact Plato's visit to Sicily was for political reasons, and the politics of the Academy and of the whole region would play a major role in influencing the course of Aristotle's life.

He stayed at Plato's Academy until about 347). Though a brilliant pupil, Aristotle opposed some of Plato's teachings, and when Plato died, Aristotle was not appointed head of the Academy. After leaving Athens, Aristotle spent some time traveling, and possibly studying biology, in Asia Minor (now Turkey) and its islands. He returned to Macedonia in 338 to tutor Alexander the Great; after Alexander conquered Athens, Aristotle returned to Athens and set up a school of his own, known as the Lyceum. After Alexander's death, Athens rebelled against Macedonian rule, and Aristotle's political situation became precarious. To avoid being put to death, he fled to the island of Euboea, where he died soon after.

Aristotle is said to have written 150 philosophical treatises. The 30 that survive touch on an enormous range of philosophical problems, from biology and physics to morals to aesthetics to politics. Many, however, are thought to be "lecture notes" instead of complete, polished treatises, and a few may not be the work of Aristotle but of members of his school.

Whereas Aristotle's teacher Plato had located ultimate reality in Ideas or eternal forms, knowable only through reflection and reason, Aristotle saw ultimate reality in physical objects, knowable through experience. Objects, including organisms, were composed of a potential, their matter, and of a reality, their form; thus, a block of marble -- matter -- has the potential to assume whatever form a sculptor gives it, and a seed or embryo has the potential to grow into a living plant or animal form.

In living creatures, the form was identified with the soul; plants had the lowest kinds of souls, animals had higher souls which could feel, and humans alone had rational, reasoning souls. In turn, animals could be classified by their way of life, their actions, or, most importantly, by their parts.

Though Aristotle's work in zoology was not without errors, it was the grandest biological synthesis of the time, and remained the ultimate authority for many centuries after his death. His observations on the anatomy of octopus, cuttlefish, crustaceans, and many other marine invertebrates are remarkably accurate, and could only have been made from first-hand experience with dissection. Aristotle described the embryological development of a chick; he distinguished whales and dolphins from fish; he described the chambered stomachs of ruminants and the social organization of bees; he noticed that some sharks give birth to live young -- his books on animals are filled with such observations, some of which were not confirmed until many centuries later.

Aristotle's classification of animals grouped together animals with similar characters into genera (used in a much broader sense than present-day biologists use the term) and then distinguished the species within the genera. He divided the animals into two types: those with blood, and those without blood (or at least without red blood). These distinctions correspond closely to our distinction between vertebrates and invertebrates.

The blooded animals, corresponding to the vertebrates, included five genera: viviparous quadrupeds (mammals), birds, oviparous quadrupeds (reptiles and amphibians), fishes, and whales (which Aristotle did not realize were mammals). The bloodless animals were classified as cephalopods (such as the octopus); crustaceans; insects (which included the spiders, scorpions, and centipedes, in addition to what we now define as insects); shelled animals (such as most molluscs and echinoderms); and "zoophytes," or "plant-animals," which supposedly resembled plants in their form -- such as most cnidarians.

Aristotle's thoughts on earth sciences can be found in his treatise Meteorology -- the word today means the study of weather, but Aristotle used the word in a much broader sense, covering, as he put it, "all the affections we may call common to air and water, and the kinds and parts of the earth and the affections of its parts." Here he discusses the nature of the earth and the oceans.

He worked out the hydrologic cycle: "Now the sun, moving as it does, sets up processes of change and becoming and decay, and by its agency the finest and sweetest water is every day carried up and is dissolved into vapor and rises to the upper region, where it is condensed again by the cold and so returns to the earth."

He discusses winds, earthquakes (which he thought were caused by underground winds), thunder, lightning, rainbows, and meteors, comets, and the Milky Way (which he thought were atmospheric phenomena). His model of Earth history contains some remarkably modern-sounding ideas:

The same parts of the earth are not always moist or dry, but they change according as rivers come into existence and dry up. And so the relation of land to sea changes too and a place does not always remain land or sea throughout all time, but where there was dry land there comes to be sea, and where there is now sea, there one day comes to be dry land. But we must suppose these changes to follow some order and cycle. The principle and cause of these changes is that the interior of the earth grows and decays, like the bodies of plants and animals. . . .

But the whole vital process of the earth takes place so gradually and in periods of time which are so immense compared with the length of our life, that these changes are not observed, and before their course can be recorded from beginning to end whole nations perish and are destroyed.

Where Aristotle differed most sharply from medieval and modern thinkers was in his belief that the universe had never had a beginning and would never end; it was eternal. Change, to Aristotle, was cyclical: water, for instance, might evaporate from the sea and rain down again, and rivers might come into existence and then perish, but overall conditions would never change.

In the later Middle Ages, Aristotle's work was rediscovered and enthusiastically adopted by medieval scholars. His followers called him Ille Philosophus (The Philosopher), or "the master of them that know," and many accepted every word of his writings -- or at least every word that did not contradict the Bible -- as eternal truth. Fused and reconciled with Christian doctrine into a philosophical system known as Scholasticism, Aristotelian philosophy became the official philosophy of the Roman Catholic Church. As a result, some scientific discoveries in the Middle Ages and Renaissance were criticized simply because they were not found in Aristotle. It is one of the ironies of the history of science that Aristotle's writings, which in many cases were based on first-hand observation, were used to impede observational science.

Some quotes by Aristotle:-

1) A flatterer is a friend who is your inferior, or pretends to be so.

2) A friend is a second self.

3) All human actions have one or more of these seven causes: chance, nature, compulsion, habit, reason, passion, and desire.

4) All paid jobs absorb and degrade the mind.

5) All virtue is summed up in dealing justly.

6) Dignity consists not in possessing honors, but in the consciousness that we deserve them.

7) Education is the best provision for the journey to old age.

8) Happiness depends upon ourselves.

9) Humor is the only test of gravity, and gravity of humor; for a subject which will not bear raillery is suspicious, and a jest which will not bear serious examination is false wit.

10) In the arena of human life the honors and rewards fall to those who show their good qualities.

11) It is in justice that the ordering of society is centered.

12) It is the mark of an educated mind to be able to entertain a thought without accepting it.

13) It is unbecoming for young men to utter maxims.

14) Law is mind without reason.

15) Man perfected by society is the best of all animals; he is the most terrible of all when he lives without law, and without justice.

16) Men acquire a particular quality by constantly acting a particular way...you become just by performing just actions, temperate by performing temperate actions, brave by performing brave actions.

17) Pleasure in the job puts perfection in the work.

18) Poverty is the parent of revolution and crime.

19) The Gods too are fond of a joke.

20) The only stable state is the one in which all men are equal before the law.

21) To give a satisfactory decision as to the truth it is necessary to be rather an arbitrator than a party to the dispute.

22) To perceive is to suffer.

23) We are what we repeatedly do.

24) Young people are in a condition like permanent intoxication, because youth is sweet and they are growing.

25) It is not always the same thing to be a good man and a good citizen.

26) Misfortune shows those who are not really friends.

27) Education is the best provision for old age.

References and further reading for Aristotle

Biography in Dictionary of Scientific Biography (New York 1970-1990).

Biography in Encyclopaedia Britannica. [available on the Web]

Books:

J L Ackrill, Aristotle the philosopher (Oxford, 1981).

D J Allan, The Philosophy of Aristotle (1978).

H G Apostle, Aristotle's philosophy of mathematics (Chicago, 1952).

J Barnes, Aristotle (Oxford, 1982).

J Barnes, M Schofield and R Sorabji (eds.), Articles on Aristotle (4 vols.) (London, 1975-79).

Z Bechler, Aristotle's theory of actuality (Albany, NY, 1995).

J J Cleary, Aristotle on the many senses of priority (Carbondale, IL, 1988).

Diogenes Laertius, Lives of eminent philosophers (New York, 1925).

I Düring, Aristotle in the Ancient Biographical Tradition (Göteborg, 1957).

F Grayeff, Aristotle and his school (London, 1974).

W K C Guthrie, A history of Greek philosophy Volume 6, Aristotle : An encounter (Cambridge, 1981).

T L Heath, Mathematics in Aristotle (Oxford, 1949).

T L Heath, A history of Greek mathematics 1 (Oxford, 1931).

W W Jaeger, Aristotle (Oxford, 1948).

J Lear, Aristotle and logical theory (Cambridge-New York, 1980).

J Lukasiewicz, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic (1967).

J P Lynch, Aristotle's school : A Study of a Greek Educational Institution (Berkeley, 1972).

R Sorabji, Necessity, Cause, and Blame: Perspectives on Aristotle's Theory (1980).

R Sorabji, Time, Creation, and the Continuum: Theories in Antiquity and the Early Middle Ages (1983).

H B Veatch, Aristotle, a contemporary appreciation (Bloomington, 1974).

S Waterlow, Nature, Change, and Agency in Aristotle's "Physics" (1982).

J Wiesner (ed.), Aristoteles : Werk und Wirkung. Band 1. (Berlin-New York, 1985).

J Wiesner (ed.), Aristoteles : Werk und Wirkung. Band 2. (Berlin-New York, 1987).

Articles:

J Annas, Die Gegenstände der Mathematik bei Aristoteles, in Mathematik und Metaphysik bei Aristoteles (Bern, 1987), 131-147.

A Back, Syllogisms with reduplication in Aristotle, Notre Dame J. Formal Logic 23 (4) (1982), 453-458.

H Barreau, La physique du continu chez Aristote, sa réponse à Zénon, in Le labyrinthe du continu (Paris, 1992), 3-15.

Z Bechler, Aristotle corrects Eudoxus, Centaurus 15 (2) (1970/71), 113-123.

M Caveing, La proportionnalité des grandeurs dans la doctrine de la nature d'Aristote, Rev. Histoire Sci. 47 (2) (1994), 163-188.

E Filloy, Geometry and the axiomatic method. III. The era of Plato and Aristotle (Spanish), Mat. Ense nanza 7-8 (1976), 39-63.

G Fine, Forms as causes : Plato and Aristotle, in Mathematik und Metaphysik bei Aristoteles (Bern, 1987), 69-112.

C La Greca and A Pisani, Two assertions of Aristotle (Italian), Atti Accad. Pontaniana (N.S.) 41 (1992), 219-243.

J Hintikka, The varieties of being in Aristotle, in The logic of being (Dordrecht, 1986), 81-114.

V P Hjutt, Aristotle's physical doctrine, and the Copernican revolution (Russian), Tartu Riikl. Ul. Toimetised Vih. 360 (1975), 29-40.

E Hussey, Aristotle on mathematical objects, in On mathematics (Edmonton, AB, 1992), 105-133.

C V Jones, The influence of Aristotle in the foundation of Euclid's 'Elements' (Spanish), Mathesis. Mathesis 3 (4) (1987), 375-387.

W Knorr, Aristotle and incommensurability : some further reflections, Arch. Hist. Exact Sci. 24 (1) (1981), 1-9.

T Krischer, Mathematische Unendlichkeit und Induktion bei Platon und Aristoteles, in Aristoteles : Werk und Wirkung Band 1 (Berlin-New York, 1985), 518-542.

P K Machamer, Aristotle on natural place and natural motion, Isis 69 (248) (1978), 377-387.

S Maracchia, Aristotle and incommensurability (Italian), Arch. Hist. Exact Sci. 21 (3) (1979/80), 201-228.

R D McKirahan, Aristotle's subordinate sciences, British J. Hist. Sci. 11 (39, 3) (1978), 197-220.

M Mignucci, Aristotle's arithmetic, in Mathematik und Metaphysik bei Aristoteles (Bern, 1987), 175-211.

I Mueller, On the notion of a mathematical starting point in Plato, Aristotle, and Euclid, in Science and philosophy in classical Greece (New York, 1991), 59-97.

J D North, Finite and otherwise : Aristotle and some seventeenth century views, in Nature mathematized I (Dordrecht-Boston, Mass., 1983), 113-148.

F J Pelletier, Sameness and referential opacity in Aristotle, Nous 13 (3) (1979), 283-311.

A R Perreiah, Aristotle's axiomatic science : peripatetic notation or pedagogical plan?, Hist. Philos. Logic 14 (1) (1993), 87-99.

T De Praetere, Thomas The demonstration by refutation of the principle of non-contradiction in Aristotle's 'Metaphysics', Book IV, Logique et Anal. (N.S.) 36 (143-144) (1993), 343-358.

E Rudolph, Zum Verhältnis von Zeit und erstem Beweger bei Aristoteles, Philos. Natur. 20 (1) (1983), 96-107.

B Russell, History of Western Philosophy (London, 1961), 173-217.

V Sainati, Aristotle : From the 'Topics' to the 'Analytics' (Italian), Teoria (N.S.) 13 (2) (1993), 1-117.

M Scanlan, On finding compactness in Aristotle, Hist. Philos. Logic 4 (1) (1983), 1-8.

B H Slater, Aristotle's propositional logic, Philos. Stud. 36 (1) (1979), 35-49.

R Smith, Predication and deduction in Aristotle : aspirations to completeness, Topoi 10 (1) (1991), 43-52.

R Smith, Aristotle as proof theorist, Philos. Natur. 21 (2-4) (1984), 590-597.

R Smith, The mathematical origins of Aristotle's syllogistic, Arch. Hist. Exact Sci. 19 (3) (1978/79), 201-209.

T A Szlezak, Die Lückenhaftigkeit der akademischen Prinzipientheorien nach Aristoteles' Darstellung in 'Metaphysik' M und N, in Mathematik und Metaphysik bei Aristoteles (Bern, 1987), 45-67.

R Thom, Mathématique et réalité : faut-il croire Aristote?, in Logik, Wissenschaftstheorie und Erkenntnistheorie (Vienna, 1987), 115-121.

V Vita, Mathematical infinity in Aristotle and his time (Italian), Boll. Storia Sci. Mat. 6 (2) (1986), 109-132.

V Vita, Two geometric loci in Aristotle's 'Meteorologica' (Italian), Boll. Storia Sci. Mat. 3 (1) (1983), 3-18.

V Vita, On a geometric locus studied by Aristotle (Italian), Archimede 31 (3) (1979), 172-177.

P G J Vredenduin, Aristotle's analysis of the continuum (Dutch), Euclides (Groningen) 36 (1960/1961), 1-6.

M V Wedin, Negation and quantification in Aristotle, Hist. Philos. Logic 11 (2) (1990), 131-150.

M J White, On continuity : Aristotle versus topology?, Hist. Philos. Logic 9 (1) (1988), 1-12.

E T Whittaker, Aristotle, Newton, Einstein, Philos. Mag. (7) 34 (1943), 266-280.

E T Whittaker, Aristotle, Newton, Einstein, Proc. Roy. Soc. Edinburgh, Sect. A 61 (1942), 231-246.

M Yrjönsuuri, Aristotle's 'Topics' and medieval obligational disputations, Synthese 96 (1) (1993), 59-82.