Democritus (//; Greek: Δημόκριτος, Dēmókritos, meaning "chosen of the people"; c. 460 – c. 370 BC) was an Ancient Greek pre-Socratic philosopher primarily remembered today for his formulation of an atomic theory of the universe.
|Died||c.370 BC (aged around 90)|
Democritus was born in Abdera, Thrace, around 460 BC, although there are disagreements about the exact year. His exact contributions are difficult to disentangle from those of his mentor Leucippus, as they are often mentioned together in texts. Their speculation on atoms, taken from Leucippus, bears a passing and partial resemblance to the 19th-century understanding of atomic structure that has led some to regard Democritus as more of a scientist than other Greek philosophers; however, their ideas rested on very different bases. Largely ignored in ancient Athens, Democritus is said to have been disliked so much by Plato that the latter wished all of his books burned. He was nevertheless well known to his fellow northern-born philosopher Aristotle. Many consider Democritus to be the "father of modern science". None of his writings have survived; only fragments are known from his vast body of work.
Democritus was said to be born in the city of Abdera in Thrace, an Ionian colony of Teos, although some called him a Milesian. He was born in the 80th Olympiad (460–457 BC) according to Apollodorus of Athens, and although Thrasyllus placed his birth in 470 BC, the later date is probably more likely. John Burnet has argued that the date of 460 is "too early" since, according to Diogenes Laërtius ix.41, Democritus said that he was a "young man (neos)" during Anaxagoras's old age (c.440–428). It was said that Democritus's father was from a noble family and so wealthy that he received Xerxes on his march through Abdera. Democritus spent the inheritance which his father left him on travels into distant countries, to satisfy his thirst for knowledge. He traveled to Asia, and was even said to have reached India and Ethiopia.
It is known that he wrote on Babylon and Meroe; he visited Egypt, and Diodorus Siculus states that he lived there for five years. He himself declared that among his contemporaries none had made greater journeys, seen more countries, and met more scholars than himself. He particularly mentions the Egyptian mathematicians, whose knowledge he praises. Theophrastus, too, spoke of him as a man who had seen many countries. During his travels, according to Diogenes Laërtius, he became acquainted with the Chaldean magi. "Ostanes", one of the magi accompanying Xerxes, was also said to have taught him.
After returning to his native land he occupied himself with natural philosophy. He traveled throughout Greece to acquire a better knowledge of its cultures. He mentions many Greek philosophers in his writings, and his wealth enabled him to purchase their writings. Leucippus, the founder of atomism, was the greatest influence upon him. He also praises Anaxagoras. Diogenes Laertius says that he was friends with Hippocrates, and he quotes Demetrius saying: "It would seem that he also went to Athens and was not anxious to be recognized, because he despised fame, and that while he knew of Socrates, he was not known to Socrates, his words being, `I came to Athens and no one knew me.'" Aristotle placed him among the pre-Socratic natural philosophers.
The many anecdotes about Democritus, especially in Diogenes Laërtius, attest to his disinterest, modesty, and simplicity, and show that he lived exclusively for his studies. One story has him deliberately blinding himself in order to be less disturbed in his pursuits; it may well be true that he lost his sight in old age. He was cheerful, and was always ready to see the comical side of life, which later writers took to mean that he always laughed at the foolishness of people.
He was highly esteemed by his fellow citizens, because as Diogenes Laërtius says, "he had foretold them some things which events proved to be true," which may refer to his knowledge of natural phenomena. According to Diodorus Siculus, Democritus died at the age of 90, which would put his death around 370 BC, but other writers have him living to 104, or even 109.
Popularly known as the Laughing Philosopher (for laughing at human follies), the terms Abderitan laughter, which means scoffing, incessant laughter, and Abderite, which means a scoffer, are derived from Democritus. To his fellow citizens he was also known as "The Mocker".
Philosophy and science
Most sources say that Democritus followed in the tradition of Leucippus and that they carried on the scientific rationalist philosophy associated with Miletus. Both were thoroughly materialist, believing everything to be the result of natural laws. Unlike Aristotle or Plato, the atomists attempted to explain the world without reasoning as to purpose, prime mover, or final cause. For the atomists questions of physics should be answered with a mechanistic explanation ("What earlier circumstances caused this event?"), while their opponents search for explanations which, in addition to the material and mechanistic, also included the formal and teleological ("What purpose did this event serve?").
Later Greek historians consider Democritus to have established aesthetics as a subject of investigation and study, as he wrote theoretically on poetry and fine art long before authors such as Aristotle. Specifically, Thrasyllus identified six works in the philosopher's oeuvre which had belonged to aesthetics as a discipline, but only fragments of the relevant works are extant; hence of all Democritus's writings on these matters, only a small percentage of his thoughts and ideas can be known.
The theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible; that between atoms, there lies empty space; that atoms are indestructible, and have always been and always will be in motion; that there is an infinite number of atoms and of kinds of atoms, which differ in shape and size. Of the mass of atoms, Democritus said, "The more any indivisible exceeds, the heavier it is". However, his exact position on atomic weight is disputed.
Leucippus is widely credited with having been the first to develop the theory of atomism, although Isaac Newton preferred to credit the obscure Mochus the Phoenician (whom he believed to be the biblical Moses) as the inventor of the idea on the authority of Posidonius and Strabo. The Stanford Encyclopedia of Philosophy notes, "This theologically motivated view does not seem to claim much historical evidence, however".
Democritus, along with Leucippus and Epicurus, proposed the earliest views on the shapes and connectivity of atoms. They reasoned that the solidness of the material corresponded to the shape of the atoms involved. Thus, iron atoms are solid and strong with hooks that lock them into a solid; water atoms are smooth and slippery; salt atoms, because of their taste, are sharp and pointed; and air atoms are light and whirling, pervading all other materials. Using analogies from humans' sense experiences, he gave a picture or an image of an atom that distinguished them from each other by their shape, their size, and the arrangement of their parts. Moreover, connections were explained by material links in which single atoms were supplied with attachments: some with hooks and eyes others with balls and sockets. The Democritean atom is an inert solid (merely excluding other bodies from its volume) that interacts with other atoms mechanically. In contrast, modern, quantum-mechanical atoms interact via electric and magnetic force fields and are far from inert.
The theory of the atomists appears to be more nearly aligned with that of modern science than any other theory of antiquity. However, the similarity with modern concepts of science can be confusing when trying to understand where the hypothesis came from. Classical atomists could not have had an empirical basis for modern concepts of atoms and molecules.
However, Lucretius, describing atomism in his De rerum natura, gives very clear and compelling empirical arguments for the original atomist theory. He observes that any material is subject to irreversible decay. Through time, even hard rocks are slowly worn down by drops of water. Things have the tendency to get mixed up: Mix water with soil and mud will result, seldom disintegrating by itself. Wood decays. However, there are mechanisms in nature and technology to recreate "pure" materials like water, air, and metals. The seed of an oak will grow out into an oak tree, made of similar wood as historical oak trees, the wood of which has already decayed. The conclusion is that many properties of materials must derive from something inside, that will itself never decay, something that stores for eternity the same inherent, indivisible properties. The basic question is: Why has everything in the world not yet decayed, and how can exactly some of the same materials, plants, and animals be recreated again and again? One obvious solution to explain how indivisible properties can be conveyed in a way not easily visible to human senses, is to hypothesize the existence of "atoms". These classical "atoms" are nearer to humans' modern concept of "molecule" than to the atoms of modern science. The other central point of classical atomism is that there must be considerable open space between these "atoms": the void. Lucretius gives reasonable arguments that the void is absolutely necessary to explain how gasses and liquids can flow and change shape, while metals can be molded without their basic material properties changing.
The atomistic void hypothesis was a response to the paradoxes of Parmenides and Zeno, the founders of metaphysical logic, who put forth difficult to answer arguments in favor of the idea that there can be no movement. They held that any movement would require a void—which is nothing—but a nothing cannot exist. The Parmenidean position was "You say there is a void; therefore the void is not nothing; therefore there is not the void". The position of Parmenides appeared validated by the observation that where there seems to be nothing there is air, and indeed even where there is not matter there is something, for instance light waves.
The atomists agreed that motion required a void, but simply ignored the argument of Parmenides on the grounds that motion was an observable fact. Therefore, they asserted, there must be a void. This idea survived in a refined version as Newton's theory of absolute space, which met the logical requirements of attributing reality to not-being. Einstein's theory of relativity provided a new answer to Parmenides and Zeno, with the insight that space by itself is relative and cannot be separated from time as part of a generally curved space-time manifold. Consequently, Newton's refinement is now considered superfluous.
The knowledge of truth, according to Democritus, is difficult, since the perception through the senses is subjective. As from the same senses derive different impressions for each individual, then through the sensual impressions we cannot judge the truth. We can interpret the senses' data and grasp the truth only through the intellect, because the truth is in an abyss:
And again, many of the other animals receive impressions contrary to ours; and even to the senses of each individual, things do not always seem the same. Which then, of these impressions are true and which are false is not obvious; for the one set is no more true than the other, but both are alike. And this is why Democritus, at any rate, says that either there is no truth or to us at least it is not evident.
Furthermore, they find Xenophanes, Zeno of Elea, and Democritus to be sceptics: … Democritus because he rejects qualities, saying,"Opinion says hot or cold, but the reality is atoms and empty space," and again, "Of a truth we know nothing, for truth is in a well."
There are two kinds of knowing, the one he calls "legitimate" (γνησίη, gnēsiē, "genuine") and the other "bastard" (σκοτίη, skotiē, "secret"). The "bastard" knowledge is concerned with the perception through the senses; therefore it is insufficient and subjective. The reason is that the sensual perception is due to the effluences of the atoms from the objects to the senses. When these different shapes of atoms come to us, they stimulate our senses according to their shape, and our sensual impressions arise from those stimulations.
The second sort of knowledge, the "legitimate" one, can be achieved through the intellect, in other words, all the sense data from the "bastard" must be elaborated through reasoning. In this way one can get away from the false perception of the "bastard" knowledge and grasp the truth through inductive reasoning. After taking into account the sense impressions, one can examine the causes of the appearances, draw conclusions about the laws that govern the appearances, and discover the causality (αἰτιολογία, aetiologia) by which they are related. This is the procedure of thought from the parts to the whole or else from the apparent to nonapparent (inductive reasoning). This is one example of why Democritus is considered to be an early scientific thinker. The process is reminiscent of that by which science gathers its conclusions:
But in the Canons Democritus says there are two kinds of knowing, one through the senses and the other through the intellect. Of these he calls the one through the intellect 'legitimate' attesting its trustworthiness for the judgment of truth, and through the senses he names 'bastard' denying its inerrancy in the discrimination of what is true. To quote his actual words: Of knowledge there are two forms, one legitimate, one bastard. To the bastard belong all this group: sight, hearing, smell, taste, touch. The other is legitimate and separate from that. Then, preferring the legitimate to the bastard, he continues: When the bastard can no longer see any smaller, or hear, or smell, or taste, or perceive by touch, but finer matters have to be examined, then comes the legitimate, since it has a finer organ of perception.
In the Confirmations ... he says: But we in actuality grasp nothing for certain, but what shifts in accordance with the condition of the body and of the things (atoms) which enter it and press upon it.
As well as:
Ethics and politics
The ethics and politics of Democritus come to us mostly in the form of maxims. As such, the Stanford Encyclopedia of Philosophy has gone as far as to say that: "despite the large number of ethical sayings, it is difficult to construct a coherent account of Democritus's ethical views," noting that there is a "difficulty of deciding which fragments are genuinely Democritean".
He says that "Equality is everywhere noble", but he is not encompassing enough to include women or slaves in this sentiment. Poverty in a democracy is better than prosperity under tyrants, for the same reason one is to prefer liberty over slavery. In his History of Western Philosophy, Bertrand Russell writes that Democritus was in love with "what the Greeks called democracy." Democritus said that "the wise man belongs to all countries, for the home of a great soul is the whole world." Democritus wrote that those in power should "take it upon themselves to lend to the poor and to aid them and to favor them, then is there pity and no isolation but companionship and mutual defense and concord among the citizens and other good things too many to catalogue". Money when used with sense leads to generosity and charity, while money used in folly leads to a common expense for the whole society—excessive hoarding of money for one's children is avarice. While making money is not useless, he says, doing so as a result of wrongdoing is the "worst of all things". He is on the whole ambivalent towards wealth, and values it much less than self-sufficiency. He disliked violence but was not a pacifist: he urged cities to be prepared for war, and believed that a society had the right to execute a criminal or enemy so long as this did not violate some law, treaty, or oath.
Goodness, he believed, came more from practice and discipline than from innate human nature. He believed that one should distance oneself from the wicked, stating that such association increases disposition to vice. Anger, while difficult to control, must be mastered in order for one to be rational. Those who take pleasure from the disasters of their neighbors fail to understand that their fortunes are tied to the society in which they live, and they rob themselves of any joy of their own. Democritus believed that happiness was a property of the soul. He advocated a life of contentment with as little grief as possible, which he said could not be achieved through either idleness or preoccupation with worldly pleasures. Contentment would be gained, he said, through moderation and a measured life; to be content one must set one's judgment on the possible and be satisfied with what one has—giving little thought to envy or admiration. Democritus approved of extravagance on occasion, as he held that feasts and celebrations were necessary for joy and relaxation. He considers education to be the noblest of pursuits, but cautioned that learning without sense leads to error.
Democritus was also a pioneer of mathematics and geometry in particular. We only know this through citations of his works (titled On Numbers, On Geometrics, On Tangencies, On Mapping, and On Irrationals) in other writings, since most of Democritus's body of work did not survive the Middle Ages. Democritus was among the first to observe that a cone and pyramid with the same base and height has one-third the volume of a cylinder or prism respectively .
Anthropology, biology, and cosmology
His work on nature is known through citations of his books on the subjects, On the Nature of Man, On Flesh (two books), On Mind, On the Senses, On Flavors, On Colors, Causes concerned with Seeds and Plants and Fruits, and Causes concerned with Animals (three books). He spent much of his life experimenting with and examining plants and minerals, and wrote at length on many scientific topics. Democritus thought that the first humans lived an anarchic and animal sort of life, going out to forage individually and living off the most palatable herbs and the fruit which grew wild on the trees. They were driven together into societies for fear of wild animals, he said. He believed that these early people had no language, but that they gradually began to articulate their expressions, establishing symbols for every sort of object, and in this manner came to understand each other. He says that the earliest men lived laboriously, having none of the utilities of life; clothing, houses, fire, domestication, and farming were unknown to them. Democritus presents the early period of mankind as one of learning by trial and error, and says that each step slowly led to more discoveries; they took refuge in the caves in winter, stored fruits that could be preserved, and through reason and keenness of mind came to build upon each new idea.
Democritus held that originally the universe was composed of nothing but tiny atoms churning in chaos, until they collided together to form larger units—including the earth and everything on it. He surmised that there are many worlds, some growing, some decaying; some with no sun or moon, some with several. He held that every world has a beginning and an end and that a world could be destroyed by collision with another world. To epitomize Democritus's cosmology, Russell calls on Shelley: "Worlds on worlds are rolling ever / From creation to decay, / Like the bubbles on a river / Sparkling, bursting, borne away".
According to Bertrand Russell, the point of view of Leucippus and Democritus "was remarkably like that of modern science, and avoided most of the faults to which Greek speculation was prone."
Karl R. Popper admired Democritus's rationalism, humanism, and love of freedom and writes that Democritus, along with fellow countryman Protagoras, "formulated the doctrine that human institutions of language, custom, and law are not taboos but man-made, not natural but conventional, insisting, at the same time, that we are responsible for them."
- On the Disposition of the Wise Man
- On the Things in Hades
- On Manliness or On Virtue
- The Horn of Amaltheia
- On Contentment
- Ethical Commentaries
- Natural science
- The Great World-ordering (may have been written by Leucippus)
- On the Planets
- On Nature
- On the Nature of Man or On Flesh (two books)
- On the Mind
- On the Senses
- On Flavours
- On Colours
- On Different Shapes
- On Changing Shape
- On Images
- On Logic (three books)
- Heavenly Causes
- Atmospheric Causes
- Terrestrial Causes
- Causes Concerned with Fire and Things in Fire
- Causes Concerned with Sounds
- Causes Concerned with Seeds and Plants and Fruits
- Causes Concerned with Animals (three books)
- Miscellaneous Causes
- On Magnets
- On Different Angles or On contact of Circles and Spheres
- On Geometry
- On Irrational Lines and Solids (two books)
- On the Great Year or Astronomy (a calendar)
- Contest of the Waterclock
- Description of the Heavens
- Description of the Poles
- Description of Rays of Light
- On the Rhythms and Harmony
- On Poetry
- On the Beauty of Verses
- On Euphonious and Harsh-sounding Letters
- On Homer
- On Song
- On Verbs
- Technical works
- On Diet
- Medical Judgment
- Causes Concerning Appropriate and Inappropriate Occasions
- On Farming
- On Painting
- Fighting in Armor
Democritus was depicted on the following contemporary coins/banknotes:
- DK 68 B118.
- DK 59 A80: Aristotle, Meteorologica 342b.
- Barnes (1987).
- Russell, pp. 64–65.
- Stephen Toulmin and June Goodfield, The Architecture of Matter (Chicago: University of Chicago Press, 1962), 56.
- Diogenes Laërtius, Lives and Opinions of Eminent Philosophers, ix. 40: "Aristoxenus in his Historical Notes affirms that Plato wished to burn all the writings of Democritus that he could collect".
- Pamela Gossin, Encyclopedia of Literature and Science, 2002.
- Democritus at Stanford Encyclopedia of Philosophy
- Aristotle, De Coel. iii.4, Meteor. ii.7
- Diogenes Laërtius, ix. 34, etc.
- Diogenes Laërtius, ix. 41.
- "The latter date [460 BC] is perhaps somewhat preferable, especially given the evident temptation to classify Democritus as older than Socrates on generic grounds, i.e. that Democritus was the last 'scientific' philosopher, Socrates the first 'ethical' one". Cynthia Farrar, 1989, The Origins of Democratic Thinking: The Invention of Politics in Classical Athens, page 195. Cambridge University Press
- John Burnet (1955). Greek Philosophy: Thales to Plato, London: Macmillan, p. 194.
- Cicero, de Finibus, v.19; Strabo, xvi.
- Diodorus, i.98.
- Clement of Alexandria, Stromata, i.
- Aelian, Varia Historia, iv. 20; Diogenes Laërtius, ix. 35.
- Tatian, Orat. cont. Graec. 17. "However, this Democritus, whom Tatian identified with the philosopher, was a certain Bolus of Mendes who, under the name of Democritus, wrote a book on sympathies and antipathies" – Owsei Temkin (1991), Hippocrates in a World of Pagans and Christians, p. 120. JHU Press.
- Diogenes Laërtius, ii.14; Sextus vii.140.
- Diogenes Laërtius, ix.42.
- Diogenes Laertius 9.36. See also Cicero Tusculanae Quaestiones 5.36.104.
- Aristotle, Metaph. xiii.4; Phys. ii.2, de Partib. Anim. i.1
- Cicero, de Finibus v.29; Aulus Gellius, x.17; Diogenes Laërtius, ix.36; Cicero, Tusculanae Quaestiones v.39.
- Seneca, de Ira, ii.10; Aelian, Varia Historia, iv.20.
- Diodorus, xiv.11.5.
- Lucian, Macrobii 18
- Hipparchus ap. Diogenes Laërtius, ix.43.
- Brewer, E. Cobham (1978) [reprint of 1894 version]. The Dictionary of Phrase and Fable. Edwinstowe, England: Avenel Books. p. 3. ISBN 0-517-25921-4.
- Tatarkiewicz, Wladyslaw (1 April 2006). J. Harrell; C. Barrett; D. Petsch (eds.). History of Aesthetics. A&C Black. p. 89. ISBN 0826488552. Retrieved 6 May 2015.
- Derek Gjertsen (1986), The Newton Handbook, p. 468.
- Sylvia Berryman (2005). "Ancient Atomism", Stanford Encyclopedia of Philosophy. – Retrieved on 15 July 2009.
- Pfeffer, Jeremy, I.; Nir, Shlomo (2001). Modern Physics: An Introduction Text. World Scientific Publishing Company. p. 183. ISBN 1-86094-250-4.
- See testimonia DK 68 A 80, DK 68 A 37 and DK 68 A 43. See also Cassirer, Ernst (1953). An Essay on Man: an Introduction to the Philosophy of Human Culture. Doubleday & Co. p. 214. ASIN B0007EK5MM.
- "Periodo presocrático". Ministerio de Educación, Cultura y Deporte. Archived from the original on 21 June 2013. Retrieved 28 June 2018.
- Russell, p. 69.
- Aristotle, Phys. iv.6
- Russell, pp. 69–71.
- Aristotle, Metaphysics iv.1009 b 7.
- Diogenes Laërtius (tr. Hicks, 1925), ix.72. See also Bakalis (2005, p. 86)
- Fr. 135 (Bakalis (2005)): Theophrastus 12, De Sensu [On the Senses], 49–83.
- Fr. 11 (Bakalis (2005)): Sextus vii.138.
- Fr. 9 (Bakalis (2005)): Sextus vii.136.
- Fr. 118 (Bakalis (2005))
- "Democritus (Stanford Encyclopedia of Philosophy)". Plato.stanford.edu. Retrieved 15 October 2012.
- Popper, Karl R. (1945). The Open Society and its Enemies. Vol I.: The Spell of Plato. London: George Routledge & Sons.
- Petronius ch. 88.
- Diodorus I.viii.1–7.
- Russell, pp. 71–72.
- Russell (1972, p.85).
- Barnes (1987), pp. 245–246
- "Drachma Banknotes & Coins". Bank of Greece. Archived from the original on 1 January 2009. Retrieved 27 March 2009.
- J. Bourjaily. Banknotes featuring Scientists and Mathematicians. – Retrieved on 7 December 2009.
- Bailey, C. (1928). The Greek Atomists and Epicurus. Oxford.
- Bakalis, Nikolaos (2005). Handbook of Greek Philosophy: From Thales to the Stoics: Analysis and Fragments, Trafford Publishing, ISBN 1-4120-4843-5.
- Barnes, Jonathan (1982). The Presocratic Philosophers, Routledge Revised Edition.
- _____ (1987). Early Greek Philosophy, Penguin.
- Burnet, J. (2003). Early Greek Philosophy, Kessinger Publishing
- Diodorus Siculus (1st century BC). Bibliotheca historica.
- Diogenes Laërtius (3rd century AD). Lives and Opinions of Eminent Philosophers.
- Freeman, Kathleen (2008). Ancilla to the Pre-Socratic Philosophers: A Complete Translation of the Fragments in Diels, Forgotten Books, ISBN 978-1-60680-256-4.
- Guthrie, W. K. (1979) A History of Greek Philosophy—The Presocratic tradition from Parmenides to Democritus, Cambridge University Press.
- Kirk, G. S., J. E. Raven and M. Schofield (1983). The Presocratic Philosophers, Cambridge University Press, 2nd edition.
Laërtius, Diogenes (1925). . Lives of the Eminent Philosophers. 2:9. Translated by Hicks, Robert Drew (Two volume ed.). Loeb Classical Library.
- Melchert, Norman (2002). The Great Conversation: A Historical Introduction to Philosophy. McGraw Hill. ISBN 0-19-517510-7.
- Pyle, C. M. (1997). 'Democritus and Heracleitus: An Excursus on the Cover of this Book,' Milan and Lombardy in the Renaissance. Essays in Cultural History. Rome, La Fenice. (Istituto di Filologia Moderna, Università di Parma: Testi e Studi, Nuova Serie: Studi 1.) (Fortuna of the Laughing and Weeping Philosophers topos)
- Petronius (late 1st century AD). Satyricon. Trans. William Arrowsmith. New York: A Meridian Book, 1987.
- Russell, Bertrand (1972). A History of Western Philosophy, Simon & Schuster.
- Sextus Empiricus (c. 200 AD). Adversus Mathematicos.
- Brumbaugh, Robert S. (1964). The Philosophers of Greece. New York: Crowell.
- Burnet, John (1914). Greek Philosophy: Thales to Plato. London: Macmillan.
- Lee, Mi-Kyoung (2005). Epistemology after Protagoras: responses to relativism in Plato, Aristotle, and Democritus. Oxford University Press. ISBN 978-01-99-26222-9. Retrieved 22 September 2016.
- Sandywell, Barry (1996). Presocratic Reflexivity: The Construction of Philosophical Discourse c. 600 - 450 BC. London: Routledge. ISBN 0-415-10170-0.
- Vlastos, Gregory (1945–1946). "Ethics and Physics in Democritus". Philosophical Review. 54-55: 578–592, 53–64.
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- Berryman, Sylvia. "Democritus". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
- "Democritus". Internet Encyclopedia of Philosophy.
- O'Connor, John J.; Robertson, Edmund F., "Democritus", MacTutor History of Mathematics archive, University of St Andrews.