# Anaxagoras

Anaxagoras (c. 500 BC – 428 BC) was a Pre-Socratic Greek philosopher from Clazomenae in Asia Minor. He introduced the concept of Nous (Mind), as an ordering force in the cosmos. He regarded material substance as an infinite multitude of imperishable primary elements, referring all generation and disappearance to mixture and separation respectively.

## Quotes

* Wrongly do the Greeks suppose that aught begins or ceases to be; for nothing comes into being or is destroyed; but all is an aggregation or secretion of pre-existent things: so that all-becoming might more correctly be called becoming-mixed, and all corruption, becoming-separate.
** quoted in Heinrich Ritter, Tr. from German by Alexander James William Morrison, The History of Ancient Philosophy, Vol.1 (1838)
* All things were together, infinite both in number and in smallness; for the small too was infinite.
** Frag. B 1, quoted in John Burnet's Early Greek Philosophy, (1920), Chapter 6.
* And since these things are so, we must suppose that there are contained many things and of all sorts in the things that are uniting, seeds of all things, with all sorts of shapes and colours and savours
** Frag. B 4, quoted in John Burnet's Early Greek Philosophy, (1920), Chapter 6.
* Mind is infinite and self-ruled, and is mixed with nothing, but is alone itself by itself.
** Frag. B 12, quoted in John Burnet's Early Greek Philosophy, (1920), Chapter 6.
* Thought is something limitless and independent, and has been mixed with no thing but is alone by itself. ... What was mingled with it would have prevented it from having power over anything in the way in which it does. ... For it is the finest of all things and the purest.
** Frag. B12, in Jonathan Barnes, Early Greek Philosophy (1984), p. 190.
* The Greeks follow a wrong usage in speaking of coming into being and passing away; for nothing comes into being or passes away, but there is mingling and separation of things that are. So they would be right to call coming into being mixture, and passing away separation.
** Frag. B 17, quoted in John Burnet's Early Greek Philosophy, (1920), Chapter 6.
* The sun provides the moon with its brightness.
** Fragment in Plutarch De facie in orbe lunae, 929b, as quoted in The Riverside Dictionary of Biography (2005), p. 23

## Quotes about Anaxagoras

* If one examines the reasons for the persecution of the best minds of different nations, and compares the reasons for the persecution and banishment of Pythagoras, Anaxagoras, Socrates, Plato, and others, one can observe that in each case the accusations and reasons for banishment were almost identical and unfounded. But in the following centuries full exoneration came, as if there had never been any defamation. It would be correct to conclude that such workers were too exalted for the consciousness of their contemporaries, and the sword of the executioner was ever ready to cut off a head held high.... A book should be written about the causes of the persecution of great individuals. By comparing the causes is it possible to trace the evil will.
** Agni Yoga, Supermundane, (1938), 222.
* In mathematics... the Greek attitude differed sharply from that of the earlier potamic cultures. The contrast was clear in... Thales and Pythagoras, and it continues to show... in Athens during the Heroic Age. ...while Anaxagoras was in prison he occupied himself with an attempt to square the circle... the first mention of a problem that was to fascinate mathematicians for more than 2000 years. ...Here we see a type of mathematics that is quite unlike that of the Egyptians and Babylonians. It is not the practical application of a science of number... but a theoretical question involving a... distinction between accuracy in approximation and exactitude in thought. ...no more the concern of the technologist than those he raised... concerning the ultimate structure of matter.
** Carl B. Boyer, A History of Mathematics (1968)
* The big bang and the steady state debate in some ways echoed that between the ideas of Anaximander and Anaxagoras from two and a half millennia earlier. Anaxagoras had envisaged that at one time "all things were together" and that the motive force for the universe originated at a single point... Anaximander on the other hand wanted a universe determined by "the infinite" and needed an "eternal motion" to explain the balancing process of things coming into being and passing away in an eternal universe... ancient philosophy was debating the alternatives of a creation event starting the universe from a single point versus a continuous creation in an eternal universe.
** David H. Clark & Matthew D. H. Clark, in Measuring the Cosmos: How Scientist Discovered the Dimensions of the Universe (2004)
* Anaxagoras of Clazomenae postulated another element called the aether, which was in constant rotation and carried with it the celestial bodies. He also believed that there was a directing intelligence in nature that he called Nous which gives order to what otherwise would be a chaotic universe. By Nous he meant literally "the Mind of the Cosmos"… Anaxagoras was the last of the Ionian physicists.
** John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2012)
* The endless sequence of explanation is explicit in Anaxagoras. Even the ingredients that go to make up something and account for its behaviour are themselves composed of ingredients which are themselves again composed of ingredients. [...] In every case, behaviour is a consequence of both the predominant features (which make it seem to be such and such) and also the hidden features (which can make it do otherwise inexplicable things). And this dual explanation will apply as much to the hidden ingredients as to the macroscopic items we encounter in daily life.But still it remains true for Anaxagoras that in principle the material composition (if we could know it in detail) would account for the current behaviour of each item in the world. Unless the thing is alive, that is. For living things, it looks as though the explanation must be supplemented by appeal to another principle, what Anaxagoras called ‘Mind’.
** Catherine Osborne, Presocratic Philosophy: A Very Short Introduction (2004), Ch. 4 : Reality and appearance: more adventures in metaphysics
* My dear Meletus, do you think you are prosecuting Anaxagoras? Are you so contemptuous of these men and think them so ignorant of letters as not to know that the books of Anaxagoras of Clazomenae are full of those theories, and further, that the young men learn from me what they can buy from time to time for a drachma, at most, in the bookshops, and ridicule Socrates if he pretends that these theories are his own, especially as they are so absurd? Is that, by Zeus, what you think of me, Meletus, that I do not believe that there are any gods?—That is what I say, that you do not believe in the gods at all.
** Plato, Apology, 26d-26e
* Anaxagoras held that everything is infinitely divisible, and that even the smallest portion of matter contains some of each element. Things appear to be that of which they contain the most. Thus, for example, everything contains some fire, but we only call it fire if that element preponderates. He argues against the void, saying that the clepsydra or an inflated skin shows that there is air where there seems to be nothing.
** Bertrand Russell, in A History of Western Philosophy (1945), Book One, Part I, Chapter VIII, Anaxagoras, p. 62
* In science [Anaxagoras] had great merit. It was he who first explained that the moon shines by reflected light... Anaxagoras gave the correct theory of eclipses, and knew that the moon was below the sun. The sun and stars, he said, are fiery stones, but we do not feel the heat of the stars because they are too distant. The sun is larger than the Peloponnesus. The moon has mountains, and (he thought) inhabitants.
** Bertrand Russell, Ibid., p. 63
* Anaxagoras was more inclined to the study of physics than of metaphysics, for which reason he is accused by Plato and by Aristotle of not having conceded enough to final causes, and of having converted God into a machine. Accordingly he explained on physical principles the formation of plants and animals, and even celestial phenomena; which drew upon him the charge of atheism. Nevertheless, he regarded the testimony of the senses as subjectively true; but as insufficient to attain to objective truth, which was the privilege of the reason.
** Wilhelm Gottlieb Tennemann, John Reynell Morell, A Manual of the History of Philosophy (1870)
* Anaxagoras says that perception is produced by opposites; for like things cannot be affected by like. ...It is in the same way that touch and taste discern their objects. That which is just as warm or just as cold as we are neither warms us nor cools us... [I]n the same way, we do not apprehend the sweet and the sour by means of themselves. We know cold by warm, fresh by salt, and sweet by sour, in virtue of our deficiency in each; for all these are in us to begin with. And we smell and hear in the same... And all sensation implies pain... for all unlike things produce pain by their contact. Brilliant colours and excessive noises produce pain... The larger animals are the more sensitive, and... sensation is proportionate to the size of the organs of sense. ...Rarefied air has more smell ... when air is heated and rarefied, it smells. ...[S]mell is better perceived when it is near than when it is far by reason of its being more condensed, while when dispersed it is weak.
** Theophrastos, De Sensu or On Sense Perception (c. 330 BC) 27 sqq. (Dox. p. 507) as quoted by John Burnet, Early Greek philosophy (1908) pp. 316-317.

### Early Greek Philosophy (1908)

    by John Burnet Quotes are from 2nd edition, Ch. VI. Anaxagoras of Klazomenai pp. 290-318.
* [W]e may assume [Anaxagoras] belonged to a family which had won distinction in the State. Nor need we reject the tradition that Anaxagoras neglected his possessions to follow science. ...[I]n the fourth century he was... regarded as the type of the man who leads the "theoretic life."
* One incident belonging to the early manhood of Anaxagoras is... his observation of the huge meteoric stone which fell into the Aigospotamos in 468-67 B.c. ...[I]t may have occasioned one of his most striking departures from the earlier cosmology, and led to ...the ...view for which he was condemned at Athens.
* Anaxagoras was the first philosopher to take up his abode at Athens.
* We are not to suppose... he was attracted... by... the character of the Athenians. ...Athens had ...become the political centre of the Hellenic world; but it had not yet produced a single scientific man. ...[T]he temper of the citizen body... remained hostile to free inquiry... Sokrates, Anaxagoras, and Aristotle fell victims... to the bigotry of the democracy, though... their offence was political rather than religious. They were condemned not as heretics, but as innovators in the state religion. ..[A] recent historian observes, "Athens... was far from... a place for free inquiry to thrive unchecked." ...T]his ...has been in the minds of ...writers who ...represented philosophy as ...un-Greek. It was in reality thoroughly Greek, though... thoroughly unAthenian.
* It seems... reasonable... that Perikles... brought Anaxagoras to Athens... Holm has shown... the aim... was... to Ionise his ...citizens, to impart ...flexibility and openness of mind which characterised their kinsmen across the sea. ...The close relation in which Anaxagoras stood to Perikles is placed ...by the testimony of Plato ...In the Phaedrus ...Sokrates say[s]: "For all arts that are great, there is need of talk and discussion on the parts of natural science that deal with things on high; for that seems to be the source which inspires high-mindedness and effectiveness in every direction. Perikles added this very acquirement to his original gifts. He fell in... with Anaxagoras, who was a scientific man; and, satiating himself with the theory of things on high, and having attained to a knowledge of the true nature of intellect and folly, which were... what the discourses of Anaxagoras were mainly about, he drew from that source... to further him in the art of speech."
* Alexander of Aitolia... referred to Euripides as the "nursling of brave Anaxagoras." ...The famous fragment on the blessedness of the scientific life might just as well refer to any other cosmologist as to Anaxagoras, and ...suggests ...a thinker ...more primitive ...[T]here is one fragment which distinctly expounds the central thought of Anaxagoras ...We may conclude ...that Euripides knew the philosopher and his views ...
* Shortly before the ...Peloponnesian War ...enemies of Perikles began ...attacks upon him through his friends. Pheidias was the first to suffer, and Anaxagoras... next. ...[H]e was an object of special hatred to the religious party ...even though the charge ...against him does not suggest ...he went out of his way to hurt their susceptibilities. The details of the trial are somewhat obscure... [F]irst ...was ...a psephism by Diopeithes—the same whom Aristophanes laughs at in The Birds—enacting that an impeachment should be brought against those who did not practise religion, and taught theories about "the things on high." ...[A]t the actual trial ... authorities give ... conflicting accounts. ...[F]rom Plato ...the accusation was ...that Anaxagoras taught the sun was a red-hot stone, and the moon earth; ...[H]e ...did hold these views ...[H]e was got out of prison and sent away by Perikles.
* Anaxagoras... went back to Ionia... settled at Lampsakos, and... founded a school there. Probably he did not live long after his exile. The Lampsakenes erected an altar to his memory in their market-place, dedicated to Mind and Truth; and the anniversary of his death was long kept as a holiday for school-children...
* Diogenes includes Anaxagoras in... philosophers who left... a single book, and... preserved the... criticism... that it was written "in a lofty and agreeable style." ...[F]rom the ...Apology ...the works of Anaxagoras could be bought at Athens for a single drachma; and ...was of some length ...[as] Plato ...speak[s] of it. ...Simplicius had ...a copy, ...and it is to him we owe the preservation of all our fragments, with ...[a few] doubtful exceptions. Unfortunately his quotations seem... confined to the First Book... dealing with general principles, so... we are... in the dark with regard to... details. This is... unfortunate, as... Anaxagoras... first gave the true theory of the moon’s light and... the true theory of eclipses.
** Footnote: Apol. 26 d-e
* The system of Anaxagoras, like that of Empedokles, aimed at reconciling the Eleatic doctrine that corporeal substance is unchangeable with... a world which... presents the appearance of coming into being and passing away. The conclusions of Parmenides are... accepted and restated. Nothing can be added to all things; for there cannot be more than all, and all is always equal (fr. 5). Nor can anything pass away. What men commonly call coming into being and passing away is... mixture and separation (fr. 17). This... reads almost like a prose paraphrase of Empedokles (fr. 9); and it is... probable... Anaxagoras derived his theory... from his younger contemporary, whose poem was most likely published before his own treatise.
* Empedokles sought to save the world of appearance by maintaining that the opposites—hot and cold, moist and dry—were things, each...real in the Parmenidean sense. Anaxagoras regarded this as inadequate. ...[T]hings of which the world is made are not "cut off with a hatchet" (fr. 8) ...the true formula must be: There is a portion of everything in everything (fr. 11).
* The statement... there is a portion of everything in everything, is not... referring simply to the original mixture of things before the formation of the worlds (fr. 1). ...[E]ven now “all things are together,” and everything... has an equal number of “portions” (fr. 6). A smaller particle... could only contain a smaller number of portions... [I]f anything is, in the... Parmenidean sense, it is impossible that mere division should make it cease to be (fr. 3). Matter is infinitely divisible... there is no least thing, any more than there is a greatest. But however great or small.., it contains... the same number of "portions,"... [i.e.,] a portion of everything.
* Aristotle says... if we suppose the first principles to be infinite, they may either be one in kind, as with Demokritos, or opposite. Simpliciuss, following Porphyry and Themistios, refers the latter view to Anaxagoras; and Aristotle... implies that the opposites of Anaxagoras had as much right to be... first principles as the "homoeomeries."
* It is of those opposites... that everything contains a portion. Every particle... large or... small, contains... [all] of those opposite qualities. ...Even snow, Anaxagoras affirmed, was black ...white contains a ...portion of the opposite quality. It is enough to indicate the connexion... with... Herakleitos...
** See Burnet, (§ 80) Herakleitos: Correlation of Opposites.
* Anaxagoras held that, however far you may divide... things—and they are infinitely divisible—you never come to a part so small that it does not contain portions of all the opposites. The smallest portion of bone is... bone. On the other hand, everything can pass into everything else... because the "seeds"... of each form of matter contain a portion of everything... [i.e.,] of all the opposites, though in different proportions. If we... use the word "element" at all, it is these seeds... [T]he "seeds"... he... substituted for the "roots" of Empedokles, were not the opposites in a state of separation, but each contained a portion of them all.
* Though everything has a portion of everything in it, things appear to be that of which there is most in them (fr. 12 sub fin.). ...Air is that in which there is most cold, Fire that in which there is most heat ... [etc.]
* [W]hen "all things were together," and when the different seeds... were mixed... in infinitely small particles (fr. 1), the appearance... would be that of one of... the primary substances. ...[T]hey did present the appearance of "air and aether"; for the qualities (things) which belong to these prevail in quantity... and everything is... that of which it has most... (fr. 12 sub fin.). Here... Anaxagoras attaches... to Anaximenes. The primary condition... before... formation of... worlds, is much the same in both; only, with Anaxagoras, the original mass is no longer the primary substance, but a mixture of innumerable seeds divided into infinitely small parts. This mass is infinite, like the air of Anaximenes, and... supports itself, since there is nothing surrounding it. ... [T]he "seeds" of all things which it contains are infinite in number (fr. 1). But... the... seeds may be divided into those in which the portions of cold, moist, dense, and dark prevail, and those which have most... warm, dry, rare, and light... the original mass was a mixture of infinite Air and... Fire. ...
* [T]here is no void in this mixture, an addition... made necessary by... arguments of Parmenides. Anaxagoras added an experimental proof of this to the purely dialectical one of the Eleatics. He used the klepsydra experiment ... as Empedokles had done... and... showed the corporeal nature of air by means of inflated skins.
* Like Empedokles, Anaxagoras required some external cause to produce motion in the mixture. Body, Parmenides had shown, would never move itself... Anaxagoras called the cause of motion... Nous. ...[T]his ...made Aristotle say that he "stood out like a sober man from the random talkers that had preceded him," and he has often been credited with the introduction of the spiritual into philosophy. ...[D]isappointment [was] expressed ...by Plato and Aristotle as to the way in which Anaxagoras worked out the theory ... Plato makes Sokrates say: "I once heard a man reading a book... of Anaxagoras... saying it was Mind that ordered the world and was the cause of all things. I was delighted... and... thought he... was right. ...But my extravagant expectations were all dashed... when I... found... the man made no use of Mind... He ascribed no causal power... to it in the ordering of things, but to airs, and aethers, and waters, and a host of other strange things." Aristotle... says: "Anaxagoras uses Mind as a deus ex machina to account for the formation of the world ; and whenever he is at a loss to explain why anything necessarily is, he drags it in. But in other cases he makes anything rather than Mind the cause." These utterances... suggest... Nous of Anaxagoras did not... stand on a higher level than... Love and Strife of Empedokles...
* Nous is unmixed (fr. 12), and does not... contain a portion of everything. This would hardly be worth saying of an immaterial mind... The result of its being unmixed is that it "has power over" everything... [i.e.,] it causes things to move. Herakleitos had said as much of Fire, and Empedokles of Strife. Further, it is the "thinnest" of all things, so that it can penetrate everywhere... Nous also "knows all things"... [P]robably... Anaxagoras substituted Nous for the Love and Strife of Empedokles... to retain the old Ionic doctrine of a substance that "knows" all things, and... identify this with the new... substance that "moves" all things. Perhaps... his increased interest in physiological as distinguished from purely cosmological matters... led him to... Mind rather than Soul. ...[T]he originality of Anaxagoras lies ...more in the theory of matter than ...of Nous.
* The formation of a world starts with a rotatory motion which Nous imparts to a portion of the mixed mass in which "all things are together" (fr. 13), and this... motion gradually extends over... wider space. Its rapidity (fr. 9) produced a separation of the rare and the dense, the cold and the hot, the dark and the light, the moist and the dry (fr. 15). This... produces two great masses, the one... of the rare, hot, light, and dry, called... "Aether"; the other... [of] the opposite qualities... called "Air" (fr. 1). ...the Aether or Fire took the outside while the Air occupied the centre (fr. 15).
* The next stage is the separation of the air into clouds, water, earth, and stones (fr. 16). In this Anaxagoras follows Anaximenes... In his account of the origin of the heavenly bodies... he... [was] more original. ...[A]t the end of fr. 16... stones "rush outwards more than water," and... from the doxographers... heavenly bodies were... stones torn from the earth by the rapidity of its revolution and made red-hot by the speed... Perhaps the fall of the meteoric stone at Aigospotamoi had something to do with... this theory. ...[W]hile in the earlier stages of the world-formation we are guided... by the analogy of water rotating with light and heavy bodies... in it, we are here reminded... of a sling.
* Anaxagoras adopted the ordinary Ionian theory of innumerable worlds... fr. 4... The words "that it was not only with us that things were separated off, but elsewhere too" can only mean... Nous... caused a rotatory movement in more parts of the boundless mixture than one.
* The cosmology of Anaxagoras is clearly based upon that of Anaximenes... Theophrastos... [states] that Anaxagoras had belonged to the school of Anaximenes. The flat earth floating on the air, the dark bodies below the moon, the explanation of the solstices and the "turnings" of the moon by the resistance of air, the explanations given of wind and of thunder and lightning, are all derived from the earlier inquirer.
* "There is a portion of everything in everything except Nous, and there are some things in which there is Nous also" (fr. 11). In these words Anaxagoras laid down the distinction between animate and inanimate things. ...[T]he same Nous ..."has power over," ...[i.e.,] sets in motion, all things that have life ...(fr. 12). ...The Nous was the same, but it had more opportunities in one body than another. Man was the wisest... not because he had... better... Nous, but... because he had hands. ...Parmenides ...had ...made the thought of men depend upon ...their limbs.
* As all Nous is the same... plants were regarded as living creatures. ...Plutarch says... [Anaxagoras] called plants "animals fixed in the earth." ...Plants first arose when the seeds... which the air contained were brought down by the rain-water, and animals originated in a similar way.
* It was a happy thought of Anaxagoras to make sensation depend upon irritation by opposites, and to connect it with pain. Many modern theories are based upon a similar idea.
* That Anaxagoras regarded the senses as incapable of reaching the truth... is shown by... fragments preserved by Sextus. But we must not... turn him into a sceptic. ... He did say (fr. 21) that "the weakness of our senses prevents our discerning the truth," but this meant... we do not see the "portions"... [e.g.,] the portions of black which are in the white. Our senses simply show us the portions that prevail. He also said... things which are seen give us the power of seeing the invisible, which is the... opposite of scepticism (fr. 21a).

## See also

* A History of Western Philosophy#Chapter VIII. Anaxagoras

## External links

* Anaxagoras entry by Patricia Curd in the Stanford Encyclopedia of Philosophy
* Translation and Commentary from John Burnet's Early Greek Philosophy.
Ancient Greek schools of philosophy :
| Pre-Socratic | Anaxagoras • Anaximander • Anaximenes • Democritus • Empedocles • Heraclitus • Leucippus • Melissus • Parmenides • Protagoras • Pythagoras • Thales • Zeno of Elea |
| Socratic | Antisthenes • Aristippus • Aristotle • Diogenes of Sinope • Euclid of Megara • Phaedo of Elis • Plato • Socrates |
| Hellenistic | Apollonius of Tyana • Augustine • Epictetus • Epicurus • John Philoponus • Lucretius • Plotinus • Proclus • Pyrrho • Sextus Empiricus • Zeno of Citium |
Mathematics :
| Mathematicians (by country) | Abel • Anaxagoras • Archimedes • Aristarchus of Samos • Averroes • Arnold • Banach • Cantor • Cartan • Chern • Cohen • Descartes • Diophantus • Erdős • Euclid • Euler • Fourier • Gauss • Gödel • Grassmann • Grothendieck • Hamilton • Hilbert • Hypatia • Lagrange • Laplace • Leibniz • Milnor • Newton • von Neumann • Noether • Penrose • Perelman • Poincaré • Pólya • Pythagoras • Riemann • Russell • Schwartz • Serre • Tao • Tarski • Thales • Turing • Weil • Weyl • Wiles • Witten |
| Numbers | 1 • 23 • 360 • e • π • Fibonacci numbers • Irrational number • Negative number • Number • Prime number • Quaternion • Octonion |
| Concepts | Abstraction • Algorithms • Axiomatic system • Completeness • Deductive reasoning • Differential equation • Dimension • Ellipse • Elliptic curve • Exponential growth • Infinity • Integration • Geodesic • Induction • Proof • Partial differential equation • Principle of least action • Prisoner's dilemma • Probability • Randomness • Theorem • Topological space • Wave equation |
| Results | Euler's identity • Fermat's Last Theorem |
| Pure math | Abstract algebra • Algebra • Analysis • Algebraic geometry (Sheaf theory) • Algebraic topology • Arithmetic • Calculus • Category theory • Combinatorics • Commutative algebra • Complex analysis • Differential calculus • Differential geometry • Differential topology • Ergodic theory • Foundations of mathematics • Functional analysis • Game theory • Geometry • Global analysis • Graph theory • Group theory • Harmonic analysis • Homological algebra • Invariant theory • Logic • Non-Euclidean geometry • Nonstandard analysis • Number theory • Numerical analysis • Operations research • Representation theory • Ring theory • Set theory • Sheaf theory • Statistics • Symplectic geometry • Topology |
| Applied math | Computational fluid dynamics • Econometrics • Fluid mechanics • Mathematical physics • Science |
| History of math | Ancient Greek mathematics • Euclid's Elements • History of algebra • History of calculus • History of logarithms • Indian mathematics • Principia Mathematica |
| Other | Mathematics and mysticism • Mathematics education • Mathematics, from the points of view of the Mathematician and of the Physicist • Philosophy of mathematics • Unification in science and mathematics |