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Stanford Encyclopedia of Philosophy

Presocratic Philosophy

First published Sat Mar 10, 2007; substantive revision Mon Jun 22, 2020

The Presocratics were 6th and 5th century BCEGreek thinkers who introduced a new way of inquiring into the worldand the place of human beings in it. They were recognized in antiquityas the first philosophers and scientists of the Western tradition.This article is a general introduction to the most importantPresocratic philosophers and the main themes of Presocratic thought.More detailed discussions can be found by consulting the articles onthese philosophers (and related topics) in the SEP (listed below).

For over a century, the standard collection of texts for thePresocratics has been that by H. Diels revised by W. Kranz(abbreviated as DK). DK provides the original language of the texts,usually Greek or Latin, with translation in German. In 2016, a newcollection was published by A. Laks and G. Most with original textsand translation into English (abbreviated as LM; a version with Frenchtranslations was also published in 2016). In DK, each thinker isassigned an identifying chapter number (e.g., Heraclitus is 22,Anaxagoras 59); then the reports from ancient authors about thatthinker’s life and thought are collected in a section of“testimonies” (A) and numbered in order, while thepassages the editors take to be direct quotations are collected andnumbered in a section of “fragments” (B). Allegedimitations in later authors are sometimes added in a section labeledC. Thus, each piece of text can be uniquely identified: DK59B12.3identifies line 3 of Anaxagoras fragment 12; DK22A1 identifiestestimonium 1 on Heraclitus.

A similar system is adopted in LM. (LM provide helpful concordances toDK.) Section P contains passages dealing with the life and works ofthe author (overlapping in some ways with DK’s A section);section D includes passages covering doctrine with direct quotationsin boldface font (thus overlapping with DKB and somewhat with DKA);and a section R includes reaction to the author (Reception) and textsthe editors deem to be ancient forgeries or imitations. Like DK, LMassign an identifying number to each thinker and numbers to each pieceof text: LM25D27 picks out Anaxagoras (25) doctrine number 27 (=DK59B12), LM25P37 is the same text as DK59A30, and LM25D94 is DK59A117.

1. Who Were the Presocratic Philosophers?

Fragmentary evidence complicates our understanding of thePresocratics. Most of them wrote at least one “book”(short pieces of prose writing, or, in some cases, poems), but nocomplete work survives. Instead, we depend on later philosophers,historians, and compilers of collections of ancient wisdom fordisconnected quotations (fragments) and reports about their views(testimonia). In some cases, these sources were themselvesable to consult the works of the Presocratics directly. In manyothers, the line is indirect and often depends on the work of Hippias,Aristotle, Theophrastus, Simplicius, and other ancient philosopherswho did have direct access. All of the sources for the fragments andtestimonia made selective use of the material available to them, inaccordance with their own special, and varied, interests in the earlythinkers. (For analyses of the doxographic tradition, and theinfluence of Aristotle and Theophrastus on later sources, see Mansfeld1999; Runia 2008; Mansfeld and Runia 1997, 2009a, and 2009b; Laks andMost, 2016.) Despite (or perhaps because of) the fragmentary nature ofthe evidence, new material occasionally comes to light. In 1962“The Derveni Papyrus,” probably dating from the secondpart of the fourth century B.C.E., was discovered in Greece (Betegh2004, Janko 2001, Kotwick 2017). It is primarily concerned with Orphicreligion, including a commentary on a poem attributed toOrpheus. Through the work of scholars to reconstruct and interpret it(see Kouremenos, Pássoglou, & Tantsanaglou 2006) it hasbecome clear that the author of the commentary was familiar with thephilosophical theories of the time, and the papyrus has provedvaluable to the study of early Greek Philosophy (see, for instanceBetegh 2014a and 2014b, and Betegh & Piano 2019). Further newPresocratic material was found in a papyrus from Upper Egypt, now inStrasbourg, that contains texts from Empedocles, some already includedin DK, but also previously unknown lines which have complicated ourunderstanding of Empedocles’ thought. (See Martin &Primavesi 1999, and Janko 2001, 2005.) Although any account ofPresocratic thinkers has to be a reconstruction, we should not beoverly pessimistic about the possibility of reaching a historicallyresponsible understanding of them.

Calling this groupPresocratic raises certain difficulties.The term, coined in the eighteenth century, was made current byHermann Diels in the nineteenth, and was meant to mark a contrastbetween Socrates who was interested in moral problems, and hispredecessors, who were supposed to be primarily concerned withcosmological and physical speculation. “Presocratic,” iftaken strictly as a chronological term, is not accurate, for the lastof them were contemporaneous with Socrates and even Plato. Moreover,several of the early Greek thinkers explored questions about ethicsand the best way to live a human life. The term may also suggest thatthese thinkers are somehow inferior to Socrates and Plato, of interestonly as their predecessors, and its suggestion of archaism may implythat philosophy only becomes interesting when we arrive at theclassical period of Plato and Aristotle. Some scholars nowdeliberately avoid the term, but if we take it to refer to the earlyGreek thinkers who were not influenced by the views of Socrates,whether his predecessors or contemporaries, there is probably no harmin using it. (For discussions of the notion of Presocratic philosophy,see Long’s introduction in Long (ed.) 1999, Laks 2006, the articles inLaks and Louguet 2002, and Laks 2018.)

A second problem lies in referring to these thinkers asphilosophers. That is almost certainly not how they couldhave described themselves. While it is true that Heraclitus says that“those who are lovers of wisdom must be inquirers into manythings” (DK22B35/LM9D40), the word he uses,philosophos, does not have the special sense that it acquiresin the works of Plato and Aristotle, when the philosopher iscontrasted with both the ordinary person and other experts, includingthe sophist (particularly in Plato), or in the resulting modern sensein which we can distinguish philosophy from physics or psychology. Yetthe Presocratics certainly saw themselves as set apart from ordinarypeople and also from others (certain of the poets and historicalwriters, for example, as we can see from Xenophanes and Heraclitus)who were their predecessors and contemporaries. As the fragment fromHeraclitus shows, the early Greek philosophers thought of themselvesas inquirers into many things, and the range of their inquiry wasvast. They had views about the nature of the world, and these viewsencompass what we today call physics, chemistry, geology, meteorology,astronomy, embryology, and psychology (and other areas of naturalinquiry), as well as theology, metaphysics, epistemology, and ethics.In the earliest of the Presocratics, the Milesians, it can indeed bedifficult to discern the strictly philosophical aspects of the viewsin the evidence available to us. Nevertheless, despite the danger ofmisunderstanding and thus underestimating these thinkers because ofanachronism, there is an important sense in which it is quitereasonable to refer to them as philosophers. That sense is inherent inAristotle’s view (see, e.g.,Metaphysics I,Physics I,De Anima I,On Generation andCorruption I): these thinkers were his predecessors in aparticular sort of inquiry, and even though Aristotle thinks that theywere all, for one reason or another, unsuccessful and even amateurish,he sees in them a similarity such that he can trace a line ofcontinuity of both subject and method from their work to his own. Thequestions that the early Greek philosophers asked, the sorts ofanswers that they gave, and the views that they had of their owninquiries were the foundation for the development of philosophy as itcame to be defined in the work of Plato and Aristotle and theirsuccessors. Perhaps the fundamental characteristic is the commitmentto explain the world naturalistically, in terms of its own inherentprinciples. (For discussions, see Sassi, 2006, 2018.)

By contrast, consider the 7th century BCE poem of Hesiod,hisTheogony (genealogy of the gods). Hesiod tells thetraditional story of the Olympian gods, beginning with Chaos, a vaguedivine primordial entity or condition. From Chaos, a sequence of godsis generated, often by sexual congress, but sometimes no cause fortheir coming to be is given. The divine figures that thus arise areoften connected with a part of the physical universe, or with someaspect of human experience, so his theogony is also a cosmogony (anaccount of the generation of the world). The divinities (and theassociated parts of the world) come to be and struggle violently amongthemselves; finally Zeus triumphs and establishes and maintains anorder of power among the others. Hesiod’s world is one in whichthe major divinities are individuals who behave like super-humanbeings (Gaia or earth, Ouranos or sky, Cronos — an unlocatedregal power, Zeus); some of the others are personified characteristics(e.g., Momus, blame; and Dusnomia, lawlessness). For the Greeks, thefundamental properties of divinity are immortality (they are notsubject to death) and great power (as part of the cosmos or inmanaging events), and each of Hesiod’s characters has theseproperties (even though in the story some are defeated, and seem to bedestroyed). Hesiod’s story is like a vast Hollywood-style familyhistory, with envy, rage, love, and lust all playing important partsin the coming-to-be of the world as we know it. The earliest rulers ofthe universe are violently overthrown by their offspring (Ouranos isoverthrown by Cronos, Cronos by Zeus). Zeus insures his continuedpower by swallowing his first consort Metis (counsel or wisdom); bythis he prevents the predicted birth of rivals and acquires herattribute of wisdom (Theogony 886–900). In a secondpoem,Works and Days, Hesiod pays more attention to humanbeings, telling the story of earlier, greater creatures who died outor were destroyed by themselves or Zeus. Humans were created by Zeus,are under his power, and are subject to his judgment and to divineintervention for either good or ill. Hesiod’s world, likeHomer’s, is one that is god-saturated, where the gods mayintervene in all aspects of the world, from the weather to mundaneparticulars of human life, acting on the ordinary world order, in away that humans, limited as they are by time, location, and narrowpowers of perception, must accept but cannot ultimately understand.The Presocratics reject this account, instead seeing the world as akosmos, an ordered natural arrangement that is inherentlyintelligible and not subject to supra-natural intervention. A strikingexample is Xenophanes DK21B32/LM8D9: “And she whom they callIris, this too is by nature cloud / purple, red, and greeny yellow tobehold.” Iris, the rainbow, traditional messenger of the gods,is after all, not supra-natural, not a sign from the gods on Olympuswho are outside of and immune from the usual world order; rather itis, in its essence, colored cloud. (A good discussion of the Hesiodicmyths in relation to Presocratic philosophy can be found in McKirahan2011. Burkert 2008 surveys influence from the east on the developmentof Presocratic philosophy, especially the myths, astronomy, andcosmogony of the Babylonians, Persians, and Egyptians.)

Calling the Presocraticsphilosophers also suggests that theyshare a certain outlook; an outlook that can be contrasted with thatof other early Greeks (see Moore 2020). Although scholars disagreeabout the extent of the divergence between the early Greekphilosophers and their non-philosophical predecessors andcontemporaries, it is evident that Presocratic thought exhibits adifference not only in its understanding of the nature of the world,but also in its view of the sort of explanation of it that ispossible. This is clear in Heraclitus. Although Heraclitus assertsthat those who love wisdom must be inquirers into many things, inquiryalone is not sufficient. At DK22B40/LMD20 he rebukes four of hispredecessors: “Much learning does not teach understanding; elseit would have taught Hesiod and Pythagoras, and again Xenophanes andHecataeus.” Heraclitus’ implicit contrast is with himself;in DK 22B1/LM D9 and D110 he suggests that he alone truly understandsall things, because he grasps the account that enables him to“distinguish each thing in accordance with its nature” andsay how it is. For Heraclitus there is an underlying principle thatunites and explains everything. It is this that others have failed tosee and understand. According to Heraclitus, the four have amassed agreat deal of information — Hesiod was a traditional source ofinformation about the gods, Pythagoras was renowned for his learningand especially views about how one ought to live, Xenophanes taughtabout the proper view of the gods and the natural world, Hecataeus wasan early historian — but because they have failed to grasp thedeeper significance of the facts available to them, their unconnectedbits of knowledge do not constitute understanding. Just as the worldis akosmos, an ordered arrangement, so too, human knowledgeof that world must be ordered in a corresponding way.

2. The Milesians

In his account of his predecessors’ searches for “causesand principles” of the natural world and natural phenomena,Aristotle says that Thales of Miletus (a city in Ionia, on the westcoast of what is now Turkey) was the first to engage in such inquiry.He seems to have lived around the beginning of the 6th c.BCE. Aristotle mentions that some people, before Thales, placed greatimportance on water, but he credits Thales with declaring water to bethe first cause (Metaphysics 983b27–33), and he thenlater raises the question of whether perhaps Hesiod was the first tolook for a cause of motion and change (984b23ff.). These suggestionsare rhetorical: Aristotle does not seriously imply that those hementions are engaged in the same sort of inquiry as he thinks Thaleswas. Two other Greek thinkers from this very early period, Anaximanderand Anaximenes, were also from Miletus, and although the ancienttradition that the three were related as master and pupil may not becorrect, there are enough fundamental similarities in their views tojustify treating them together.

The tradition claims that Thales predicted a solar eclipse in 585 BC(DK 11A5/LM 5P9, P10), introduced geometry into Greece from Egypt (DK11A11/LM 5P4, P5, R11), and produced some engineering marvels.Anaximander is reported to have invented the gnomon (the raised pieceof a sundial whose shadow marks time); to have created a sphere of theheavens serving as an astronomical and cosmological model (DK 12A1/LM6P2, P4, P11); and to have been the first to draw a map of theinhabited world (DK 12A6/LM 6P6, D4). Regardless of whether thesereports are correct (and in the case of Thales’ prediction theyalmost certainly are not), they indicate something important about theMilesians: their interests in measuring and explaining celestial andterrestrial phenomena were as strong as their concern with the moreabstract inquiries into the causes and principles of substance andchange attributed to them by Aristotle (Algra 1999, White 2002 and2008). They did not see so-called “scientific” and“philosophical” questions as belonging to separatedisciplines, requiring distinct methods of inquiry. The assumptionsand principles that we (along with Aristotle) see as constituting thephilosophical foundations of their theories are, for the most part,implicit in the claims that they make. Nevertheless, it is legitimateto treat the Milesians as having philosophical views, even though noclear statements of these views or specific arguments for them can befound in the surviving fragments and testimonia.

Aristotle’s comments do not sound as if they were based onfirst-hand knowledge of Thales’ views, and the doxographicalreports say that Thales did not write a book. Yet Aristotle isconfident that Thales belongs, even if honorifically, to that group ofthinkers that he calls “inquirers into nature” anddistinguishes him from earlier poetical “myth-makers.” InBook I ofMetaphysics, Aristotle claims that the earliestof these, among whom he places the Milesians, explained things only interms of their matter (Met. I.3 983b6–18). This claimis anachronistic in that it presupposes Aristotle’s own novelview that a complete explanation must encompass four factors: what hecalled the material, efficient, formal, and final causes. Yet there issomething in what Aristotle says. Aristotle links Thales’ claimthat the world rests on water with the view that water was thearchē, or fundamental principle, and he adds that“that from which they come to be is a principle of allthings” (983b24–25; DK 11A12/LM 5D3, R9). He suggests thatThales chose water because of its fundamental role in coming-to-be,nutrition, and growth, and claims that water is the origin of thenature of moist things.

Aristotle’s general assertion about the first thinkers who gaveaccounts of nature (and his specific discussion of Thales’reliance on water as a first principle) brings out a difficulty ininterpreting the early Presocratics. According to Aristotle’sgeneral account, the Presocratics claimed that there was a singleenduring material stuff that is both the origin of all things andtheir continuing nature. Thus, on this view, when Thales says that thefirst principle is water, he should be understood as claiming boththat the original state of things was water and that even now (despiteappearances), everything is really water in some state or another. Thechange from the original state to the present one involves changes inthe material stuff such that although it may not now appear to bewater everywhere (but seems to be airier or earthier than water in itsusual state, or its original one), there is no transformation of waterinto a different kind of stuff (air or earth, for instance). Yet, whenAristotle comes to give what details he can of Thales’ view, hesuggests only that for Thales, water was the first principle becauseeverything comes from water. Water, then, was perhaps the originalstate of things for Thales, and water is a necessary condition foreverything that is generated naturally, but Aristotle’s summaryof Thales’ view does not imply that Thales claimed that waterendures through whatever changes have occurred since the originalstate, and now just has some new or additional properties. Thales maywell have thought that certain characteristics of the original waterpersisted: in particular its capacity for motion (which must have beeninnate in order to generate the changes from the original state). Thisis suggested by Thales’ reported claims that the lodestone (withits magnetic properties) and amber (which when rubbed exhibits powersof attraction through static electricity) have souls and that allthings are full of gods. Aristotle surmises that Thales identifiedsoul (that which makes a thing alive and thus capable of motion) withsomething in the whole universe, and so supposed that everything wasfull of gods (DK11A22/LM5D10, D11a )—water, or soul, being adivine natural principle. Certainly the claim that the lodestone hassoul suggests this account. Given that the analysis of change (bothqualitative and substantial) in terms of a substratum that gains andloses properties is Aristotelian (although perhaps foreshadowed inPlato), it is not surprising that the earlier views were unclear onthis issue, and it is probable that the Milesian view did not clearlydistinguish the notions of an original matter and an enduringunderlying stuff (Graham 2006).

The reports about Thales show him employing a certain kind ofexplanation: ultimately the explanation of why things are as they areis grounded in water as the basic stuff of the universe and thechanges that it undergoes through its own inherent nature. In this,Thales marks a radical change from all other previous sorts ofaccounts of the world (both Greek and non-Greek). Like the otherPresocratics, Thales sees nature as a complete and self-orderingsystem, and sees no reason to call on divine intervention from outsidethe natural world to supplement his account—water itself may bedivine, but it is not something that intervenes in the natural worldfrom outside (Gregory, 2013). While the evidence for Thales’naturalistic account is circumstantial, this attitude can be directlyverified for Anaximander.

In the one fragment that can be securely attributed to Anaximander(although the extent of the implied quotation is uncertain), heemphasizes the orderly nature of the universe, and indicates that theorder is internal rather than imposed from outside. Simplicius, a6th c. CE commentator on Aristotle’sPhysics, writes:

Of those who say that [the first principle] is one and moving andindefinite, Anaximander, son of Praxiades, a Milesian who becamesuccessor and pupil to Thales, said that the indefinite (toapeiron) is both principle (archē) and element(stoicheion) of the things that are, and he was the first tointroduce this name of the principle. He says that it is neither waternor any other of the so-called elements, but some other indefinite(apeiron) nature, from which come to be all the heavens andthe worlds in them; and those things, from which there is coming-to-befor the things that are, are also those into which is theirpassing-away, in accordance with what must be. For they give penalty(dikê) and recompense to one another for theirinjustice (adikia) in accordance with the ordering oftime—speaking of them in rather poetical terms. It is clear thathaving seen the change of the four elements into each other, he didnot think it fit to make some one of these underlying subject, butsomething else, apart from these. (Simplicius,Commentary onAristotle’s Physics 24, lines 13ff. = DK12A9/LM6P5, D6, D12and DKB1/LM6D6)[1]

Thus, there is an original (and originating) indefinite stuff, fromwhich all the heavens and the worlds in them come to be. This claimprobably means that the original state of the universe was anindefinitely large mass of stuff that was also indefinite in its character.[2] This stuff then gave rise through its own inherent power to theingredients that themselves constitute the world as we perceive it.

A testimony about Anaximander from Pseudo-Plutarch (DK12A10/LM6P6, D4)says that “Something productive of hot and cold was separatedoff from the eternal at the genesis of this world and from this asphere of flame grew around the air around the earth like the barkaround a tree.” Neither the cause nor the precise process ofseparation is explained, but it is probable that Anaximander wouldhave thought of motion as innate and so that the original source ofchange was part of the character of the indefinite itself. The passagefrom Simplicius shows that Anaximander does not think that the eternalindefinite stuff gives rise directly to the cosmos as we know it.Rather, relying on a semi-biological model, Anaximander claims thattheapeiron somehow generates the opposites hot and cold. Hotand cold are themselves stuffs with powers; and it is the actions ofthese stuffs/powers that produce the things that come to be in ourworld. The opposites act on, dominate, and contain each other,producing a regulated structure; thus things pass away into thosethings from which they came to be. It is this structured arrangementthat Anaximander refers to when he speaks of justice and reparation.Over the course of time, the cycles of the seasons, the rotations ofthe heavens, and other sorts of cyclical change (includingcoming-to-be and passing-away) are regulated and thus form a system.This system, ruled by the justice of the ordering of time is in sharpcontrast with the chaotic and capricious world of the personifiedGreek gods who interfere in the workings of the heavens and in theaffairs of human beings (Kahn 1985a, Vlastos 1947, Guthrie 1962).

The pattern that can be seen in Thales and Anaximander of an originalstuff giving rise to the phenomena of the cosmos continues in theviews of the third of the Milesians, Anaximenes. He replacesAnaximander’sapeiron with air, thus eliminating thefirst stage of the coming-to-be of the cosmos (the somethingproductive of hot and cold). Rather, he returns to an originatingstuff more like Thales’ water. In DK13A5/LM7D1 and D7Aristotle’s associate Theophrastus, quoted by Simplicius,speculates that Anaximenes chose air because he agreed that a basicprinciple must be neutral (as Anaximander’sapeiron is)but not so lacking in properties that it seems to be nothing at all.Air can apparently take on various properties of color, temperature,humidity, motion, taste, and smell. Moreover, according toTheophrastus, Anaximenes explicitly states the natural mechanism forchange; it is the condensation and rarefaction of air that naturallydetermine the particular characters of the things produced from theoriginating stuff. Rarified, air becomes fire; more and morecondensed, it becomes progressively wind, cloud, water, earth, andfinally stones. “The rest,” says Theophrastus, “cometo be from these.” Plutarch says that condensation andrarefaction are connected with cooling and heating, and he gives theexample of breath (DK13B1/LM7D8,R4). Releasing air from the mouth withcompressed lips produces cool air (as in cooling soup by blowing onit), but relaxed lips produce warm air (as when one blows on coldhands to warm them up).

Does the originating stuff persist through the changes that itundergoes in the generating processes? Aristotle’s accountsuggests that it does, that Anaximenes, for instance, would havethought that stone was really air, although in an altered state, justas we might say that ice is really water, cooled to a point where itgoes from a liquid to a solid state. Because the water does not ceaseto be water when it is cooled and becomes ice, it can return to aliquid when heated and then become a gas when more heat is applied. Onthis view, the Milesians were material monists, committed to thereality of a single material stuff that undergoes many alterations butpersists through the changes (Barnes 1979, Guthrie 1962, Sedley 2007and 2009). Yet there are reasons to doubt that this was actually theMilesian view. It presumes that the early Greek thinkers anticipatedAristotle’s general theory that change requires enduringunderlying substances that gain and lose properties. The earliestGreeks thought more in terms of powers (Vlastos 1947, Heidel 1906),and the metaphysical problem of what it is to be a substance was yetto be formulated. Clearly the Milesians were interested in theoriginating stuff from which the world developed (Anaximander andAnaximenes are explicit about transformations of such an eternaloriginating stuff), but the view that this endured as a singlesubstratum may not have been theirs. Rather, it has been suggested byGraham (1997 and 2006; Mourelatos 2008) that the Milesians were not,in Aristotle’s sense, material monists. On this view, theoriginal/originating stuff is transformed into other substances.Anaximenes, for instance, may have thought that the change from air towater does not involve the persistence of air as any sort ofsubstratum. There is no special role that air plays in the theoryexcept that it is the originating stuff and so first in an analysis ofthe law-like cyclical changes that produce various stuffs as thecosmos develops (Graham 2006, ch. 4). Such an interpretation suggestshow different the Milesian conception of the world is fromAristotle’s.

3. Xenophanes of Colophon and Heraclitus of Ephesus

Living in the last years of the 6th c. and the beginning ofthe 5th, Xenophanes and Heraclitus continue the Milesianinterest in the nature of the physical world, and both offercosmological accounts; yet they go further than the Milesians not onlythrough their focus on the human subject and the expanded range oftheir physical explanations, but by investigating the nature ofinquiry itself. Both explore the possibility of human understandingand question its limits. Recent work on Xenophanes’ epistemologyand his cosmology has made much of his scientific work clearer andmore impressive (Lesher 1992, Mourelatos 2008). He has, to a greatextent, been rescued from his traditional status as a minor travelingpoet-sage who railed against the glorification of athletes and madesome interesting comments about the relativity of human conceptions ofthe gods. Instead, he has come to be seen as an original thinker inhis own right who influenced later philosophers trying to characterizethe realms of the human and the divine, and exploring the possibilitythat human beings can gain genuine knowledge and wisdom, i.e., areable to have a god’s eye view of things and understand them(Curd 2013, Mogyoródi 2002 and 2006).

Xenophanes claims that all meteorological phenomena are clouds,colored, moving, incandescent: rainbow, St. Elmo’s Fire, thesun, the moon. Clouds are fed by exhalations from the land and sea(mixtures of earth and water). The motions of earth and water, andhence of clouds, account for all the things we find around us. Hisexplanations of meteorological and heavenly phenomena lead to anaturalistic science:

She whom they call Iris, this too is by nature (pephuke)cloud
purple, and red, and greeny-yellow to behold. (DK21B32/LM8D39)

Xenophanes says that the star-like phenomena seen when aboard ship,which some call the Dioscuri, are cloudlets, glimmering because oftheir kind of motion. (DkA39/LM8D38)

In the 1980’s Alexander Mourelatos argued that Xenophanesemploys an important new pattern of explanation:X is reallyY, whereY reveals the true character ofX.Xenophanes signals this by the use ofpephuke inDK21B32/LM8D39, and no doubt it (or some word like it) was there inthe original of DKA39/LMD36 as well. Xenophanes thus provides anaccount of a phenomenon often taken to be a sign from thedivine—Iris as the messenger; the Dioscuri (St. Elmo’sfire) as comfort for sailors—that reduces it to a naturaloccurrence.

That meteorological phenomena are not divine is not all thatXenophanes has to say about the gods. He notes anthropomorphictendencies in conceptions of the gods (DKB14/LMD12: “Mortalssuppose that the gods are born, and have their own dress, voice, andbody;” DKB16/LMD13: “Ethiopians say that their gods aresnub-nosed and dark, Thracians, that theirs are grey-eyed andred-haired”). He also famously suggests that horses, oxen, andlions would have equine, bovine, and leonine gods (DKB15/LM14). YetXenophanes also makes positive claims about the nature of the divine,including the claim that there is a single greatest god:

One god greatest among gods and men,
Resembling mortals neither in body nor in thought.
… whole [he] sees, whole [he] thinks, and whole [he] hears,
but completely without toil he agitates all things by the
   thought of his mind.
… always he remains in the same (state), agitated not at all,
nor is it fitting that he come and go to different places at differenttimes. (DK B23, B24, B25, B26 / LM D16, 17, 18, 19)

While indifferent to the affairs of human beings, Xenophanes’divine being comprehends and controls a cosmos that is infused withthinking: it is understood, organized, and managed by divineintellection. Having removed the gods as bearers of knowledge tohumans, and denied that the divine takes an active interest in whatmortals can or cannot know, Xenophanes asserts the conclusion to bedrawn from his naturalistic interpretation of phenomena: the gods arenot going to reveal anything to us; we are epistemologicallyautonomous and must rely on our own capacity for inquiry. That way, we“discover better,” as he says in DKB18/LMD53, a fragmentthat is optimistic about the capacities of human intelligence (seeLesher 1991):

Indeed not even from the beginning did the gods indicate all things tomortals, but, in time, inquiring, they discover better.

This suggests that human thought can mimic divine understanding, atleast to some degree. Xenophanes’ own practice seems consistentwith the claims of DKB18/LMD53; his own inquiries and explanations ledhim to unified explanations of terrestrial and celestial phenomena.Yet DKB34/LMD49 suggests skepticism:

And of course the clear and certain truth no man has seen,
nor will there be anyone who knows about the gods and what I say aboutall things;
for even if, in the best case, he should chance to speak what is thecase,
all the same, he himself does not know; but opinion is found over all.

Whether this is global or limited skepticism is controversial (Lesher1992 and 1994 argues for a limited interpretation). Xenophanesstresses the difficulty of coming to certainty, particularly aboutthings beyond our direct experience. Nonetheless, in DKB35/LMD50 (atantalizingly short fragment), Xenophanes says, “Let these thingbe accepted to be like the truth” (see Bryan 2012 for a fulldiscussion).

Famously obscure, accused by Plato of incoherence and by Aristotle ofdenying the law of non-contradiction, Heraclitus writes in anaphoristic style. His apparently paradoxical claims presentdifficulties to any interpreter. Nevertheless, he raises importantquestions about knowledge and the nature of the world. The opening ofHeraclitus’ book refers to a “logos which holds forever.”[3] There is disagreement about exactly what Heraclitus meant by usingthe termlogos, but it is clear from DK22B1/LM9D1, D110, andR86 and DKB2/LM9D2 as well as DKB50/LMD46 and other fragments that herefers to an objective law-like principle that governs the cosmos, andwhich it is possible (but difficult) for humans to come to understand.There is a single order that directs all things (“all things areone” DKB50/LMD46); this order is divine, and is sometimesconnected by humans with the traditional gods (it is “bothunwilling and willing to be called by the name of Zeus”DKB32/LMD45). Just as Zeus, in the traditional view, controlseverything from Olympus with a thunderbolt, so this single orderedsystem also steers and controls the whole cosmos, but from within. Thesign of the unchanging order of the eternal system is fire—justas fire is always changing and always the same, thelogos,itself permanent, contains the unchanging account that explains thealterations and transformations of the cosmos.

This plan or order that steers the cosmos is, itself, a rationalorder. This means not only that it is non-capricious and sointelligible (in the sense that humans can, at least in principle,come to understand it), it is also an intelligent system: there is anintelligent plan at work, if only in the sense of the cosmos workingitself out in accordance with rational principles.[4] Consider DKB114/LMD105:

Those who would speak with understanding must ground themselves firmlyin that which is common to all, just as a city does in its law, andeven more firmly! For all human laws are nourished by one law, thedivine; for it rules as far at it wishes and suffices for all, and isstill more than enough.

Heraclitus is not only claiming that human prescriptive law mustharmonize with divine law, but he is also asserting that divine lawencompasses both the universal laws of the cosmos itself and theparticular laws of humans. The cosmos itself is an intelligent,eternal (and hence divine) system that orders and regulates itself inan intelligent way: thelogos is the account of thisself-regulation. We can come to grasp and understand at least part ofthis divine system. This is not merely because we ourselves are partof (contained in) the system, but because we have, through ourcapacity for intelligent thinking, the power to grasp the system as awhole, through knowing thelogos. How this grasping issupposed to work is tantalizingly obscure.

Heraclitus regards the cosmos as an ordered system like a languagethat can be read or heard and understood by those who are attuned toit. That language is not just the physical evidence around us(“Eyes and ears are bad witnesses to those with barbariansouls” DKB107/LMD33); the sheer accumulation of information isnot the same as wisdom (see the rebuke in DK22B40/LMD20, quotedabove). Although the evidence of the senses is important (seeDKB55/LMD31),careful and thoughtful inquiry is also necessary. Those who are loversof wisdom must be good inquirers into many things (DKB35/LMD40; alsoDKB101/LM36: “I enquired into myself”) and must be able tograsp how the phenomena are signs or evidence of the larger order; asHeraclitus notes in DKB123/LMD35, “nature is accustomed to hideitself,” and the evidence must be interpreted carefully. Thatevidence is the interplay of opposing states and forces, whichHeraclitus points to by claims about the unity of opposites and theroles of strife in human life as well as in the cosmos. There arefragments that proclaim the unity or identity of opposites: the roadup and down are one and the same (DKB60/LMD51), the path of writing isboth straight and crooked (DKB59/LMD52), sea water is very pure andvery foul (DKB61/LMD78). The famous river fragments (DKB49a/LMR9;DKB12/LMD65a, D102; DKB91a not in LM) question the identity of thingsover time, while a number of fragments point to the relativity ofvalue judgments (DKB9, B82, B102 / LM D79, D81, D73).Anaximander’s orderly arrangement of just reciprocity governedby time is replaced by a system ruled by what Heraclitus calls war:“It is right to know that war is common and justice strife, andthat all things come to be through strife and are so ordained”(DKB80/LMD63). This strife or war is the set of changes andalterations that constitute the processes of the cosmos. These changesare regular and capable of being understood by one who can speak thelanguage of thelogos and thus interpret it properly (seeLong 2009). Although the evidence is confusing, it points to thedeeper regularities that constitute the cosmos, just asHeraclitus’ own remarks can seem obscure yet point to the truth.Heraclitus surely has his own message (and his delivery of it) in mindin DKB93/LM41, “The lord whose oracle is at Delphi neitherspeaks nor conceals, but gives a sign.”

One of the earliest of the Greek philosophers to discuss the humansoul, Heraclitus’ claims about it, like his other views, areexpressed enigmatically. Yet it seems fairly clear that he treats soulas the seat of emotion, movement, and intellect. DKB107/LMD33 (quotedabove) indicates that understanding is a function of soul, and inDKB117/LMD104, the drunken man who must be led by a boy because he haslost control of his legs, and does not know where he goes or what hedoes. Drunkenness is the cause of all this: because his soul hasbecome wet its powers are dampened down and become ineffective.DKB118/LMD103 asserts “gleam of light: dry soul, wisest andbest” (there is some uncertainty about the text). This suggeststhat for Heraclitus, soul is a stuff that is affected by changes alongthe hot/cold and wet/dry continua and that the a fiery, i.e., hottersoul is best. Indeed in DKB36/LMD100, soul is listed as one of thestages of transformation of the cosmic stuffs: “it is death tosouls to become water, and to water death to become earth; from earthwater comes to be, from from water, soul.” Although Heraclitussays that it is only divine nature that has complete understanding(DKB78/LMD74), his linking of fire with thelogos and thedivine, along with his view that the best and wisest soul is hot anddry, suggests that humans who care for their souls and search for thetruth contained in thelogos can overcome human ignorance and approach theunderstanding that Heraclitus himself has obtained. (Betegh 2007,2009, 2013b and Dilcher 1995 discuss the nature and importance of soulfor Heraclitus; see also Granger 2000 and Kahn 1979.)

4. Parmenides of Elea

Parmenides, born ca. 510 BCE in the Greek colony of Elea in southernItaly (south of Naples, and now known as Velia), explores the natureof philosophical inquiry, concentrating less on the contents of knowledge orunderstanding (although he has views about these) than on what sort of thing can beunderstood. Xenophanes identified genuine knowledge with the graspingof the sure and certain truth and claimed that “no man hasseen” it, at least with respect to some topics (DK21B34/LM8D49);Heraclitus had asserted that divine nature, not human, has rightunderstanding (DK22B78/LM9D74), although he implies that some humanscan acquire divine-like understanding. Parmenides argues that humanthought can reach genuine knowledge or understanding, and that thereare certain marks or signs that act as guarantees that the goal ofknowledge has been reached. A fundamental part of Parmenides’claim is that whatmust be (cannot not-be, as Parmenides putsit) is more knowable than what is merely contingent (what may or maynot be), which can be the object only of belief.

Parmenides gives us a poem in Homeric hexameters, narrating thejourney of a young man (akouros, in Greek) who is taken tomeet a goddess who promises to teach him “all things”(DK28B1/LM19D4). The content of the story the goddess tells is not theknowledge that will allow humans, by having it, to know. Rather, thegoddess gives thekouros the tools to acquire that knowledgehimself:

It is right that you learn all things,
Both the unshaking heart of well-persuasive truth,
and the beliefs of mortals, in which there is no true trust.
But nevertheless, you shall learn these things too, how it were rightthat the things that seem be reliably, being indeed the whole ofthings. (DKB1.28–32/LMD4.28–32; the last two lines text are uncertain.)

The goddess does not provide thekouros with a list of truepropositions, as a body of knowledge for him to acquire, and falseones to be avoided. Rather, in teaching him how to evaluate claimsabout what-is, the goddess unleashes thekouros’ owncognitive powers to know everything, by testing and evaluation,accepting or rejecting claims about the ultimate nature ofthings— for that alone is capable of being known. ForParmenides, the mark of what is known is that it is something thatgenuinely is, with no taint of what-is-not. That is why, for him,what-is not only is, but must be and cannot not-be. He sets this outin the key passages of DKB2 and B3/LM19D6:[5]

Come now, and I will tell you, and you, hearing, preserve the story,
the only routes of inquiry there are for thinking;
the one that it is and that it cannot not be
is the path of Persuasion (for it attends upon truth)
the other, that it is not and that it is right that it not be,
this I point out to you is a path wholly inscrutable
for you could not know what is not (for it is not to be accomplished)
nor could you point it out… For the same thing is for thinkingand for being.

The routes are methods of inquiry: keeping on the correct route willbring one to what-is, the real object of thought and understanding.Although what the goddess tells thekouros has divinesanction (hers), that is not why he should accept it. Rather, thetruth she tells reveals a mark of its own truth: it is testable byreason or thought itself. In DKB7/LMD8 the goddess warns that we mustcontrol our thought in the face of the ever-present seductions ofsense-experience:

For never shall this be forced through: that things that are not are;
but restrain your thought from this route of inquiry,
nor let much-experienced habit force you along this path,
to ply an aimless eye and resounding ear
and tongue, but judge by reasoning (logos) the much-battledtesting
spoken by me.

Thekouros himself can reach a decision or determination ofthe truth solely through use of hislogos.Logoshere means thinking or reasoning (Parmenides probably means the humancapacity for thought in general). The test (restated atB8.15–16/LMD8.20–21, is “is or is not?” Thisis not just a question of non-contradiction (which would give uscoherence), but an inquiry whether or not the supposition thatsomething is would entail, on further examination, the reality ofwhat-is-not (which is impossible).

The arguments of DKB8/LMD8 demonstratehow what-is must be.In applying these arguments as tests against any suggested basicentity in the Presocratic search for ultimate causes or principles,thekouros can determine whether or not a proposed theory isacceptable. For Parmenidesnoos is not itself an infalliblecapacity. One can think well or badly; correct thinking is that whichtakes the correct route and so reaches what-is. The mortals on theincorrect route are thinking, but their thoughts have no real object(none that is real in the appropriate way), and so cannot be completedor perfected by reaching the truth. In B8 Parmenides sets out thecriteria for the being of what-is, and then the arguments for thosecriteria:

… a single account still
remains of the route that it is; and on this route there are
very many signs, that what-is is ungenerable and imperishable,
a whole of a single kind, and unshaking and complete;
nor was it nor will it be, since it is now all together
one, cohesive. (DKB8.1–6/LMD8.6–11)

Any thing that genuinely is cannot be subject to coming-to-be orpassing-away, must be of a single nature, and must be complete, in thesense of being unchangeably and unalterably what it is. These aresigns for what any ultimate cause or principle must be like, if it isto be satisfactory as a principle, as something that can be known. Thesigns are adverbial, showing how what-is is (Mourelatos 2008). Only anentity which is in the complete way can be grasped and understood inits entirety by thought. McKirahan (2008) provides a thorough analysisof the arguments of DKB8/LMD8, as do Palmer (2009) and Graham(2010).

After laying out the arguments about what-is, the goddess turns to theroute of mortals, in an account which she calls“deceptive.” Although Parmenides has been read as thusrejecting any possibility of cosmological inquiry (Barnes 1979, Owen1960), there are forceful interpretations that allow for justifiedbelief about the contingent world, a world that may or may not be, andis not such that it must be (Nehamas 2002, Curd 2004, Palmer 2009).The problem of mortals is that they mistake what they perceive forwhat there is (and must be). As long as one realizes that the world ofperception is not genuinely real, and cannot therefore be the objectof knowledge, it may be possible for there to be justified beliefabout the cosmos. Some details of Parmenides’ own cosmology aregiven, arguably as justified belief, in theDoxa section ofthe poem, and more in the testimonia from later authors. Parmenidesseems to have been the first Presocratic to claim that the moon getsits light from from the sun and that the earth is spherical. Recentlyscholars have focused on these claims about the natural world, andhave argued that Parmenides should be understood as offering anaccount of appearances that can and should be deemed acceptable(Palmer 2009, Cordero 2010, Graham 2013, Mourelatos 2013, Bryan 2012,Johansen 2016). Nevertheless, Parmenides marks a sharp distinctionbetween being (what-is and must be) and becoming, and betweenknowledge and perception-based belief or opinion.

5. The Pythagorean Tradition

In the last quarter of the sixth century, before Parmenides’birth, Pythagoras of Samos (an Aegean island) arrived in Croton, insouthern Italy. He established a community of followers who adoptedhis political views, which favored rule by the “betterpeople,” and also the way of life he recommended on what seem tohave been more or less philosophical bases. The traditional view hasbeen that the aristocracy, the “better people,” generallymeant the rich. But Burkert notes that as early as the 4thc. BCE there were two traditions about Pythagoras, one that mesheswith the traditional view and associates Pythagoras with politicaltyrants, and another that credits him with rejecting tyrannies foraristocracies that might not have been grounded in wealth (Burkert1972, 119). The Pythagorean Archytas (born late 5thcentury) lived in a democracy (Tarentum in southern Italy), and seemsto have argued for fair and proportionate dealings between rich andpoor (Huffman 2005). The Pythagorean way of life included adherence tocertain prescriptions including religious rites and dietaryrestrictions (there is a general discussion in Kahn 2001). Detailedtreatment of Pythagoras and Pythagoreanism can be found in Zhmud (2012and 2013); an excellent collection of articles on Pythagoreanism is inHuffman (ed.) 2014.

Like Socrates, Pythagoras wrote nothing himself, but had a greatinfluence on those who followed him. He had a reputation for greatlearning and wisdom (see Empedocles DKD31B129/LM22.D38, R43), althoughhe was treated satirically by both Xenophanes (DK21B7/LM8.D64) andHeraclitus (DK22B40/LM9D20, DKB129/LMD26). We do not know to whatextent this included knowledge of mathematics, as would be suggestedby the attribution to him of the famous Pythagorean theorem ofgeometry (Rowett 2013). The details of Pythagoras’ views areunclear, but he seems to have advocated the reincarnation of the soul(a novel idea among the Greeks, also developed in Orphic religion) andthe possibility of the transmigration of the human soul after deathinto other animal forms. Pythagorean writers after his own timestressed the mathematical structure and order of the universe. This isoften attributed directly to Pythagoras, but recent scholarship hasshown that the evidence for attributing this mathematically-basedcosmology to Pythagoras himself is convoluted and doubtful (Burkert1972, Huffman 1993 and 2005; but see Zhmud 1997).

What seems clear is that the early Pythagoreans conceived of nature asa structured system ordered by number (see the entry onPythagoras), and that such post-Parmenidean Pythagoreans as Philolaus(last half of the 5th century, more than a generation afterPythagoras’ death) and Archytas (late 5th to early4th century) held more complicated views about the relationbetween mathematics and cosmology than it is reasonable to supposePythagoras himself could have advanced. The Pythagorean tradition thusincludes two strains. There are reports of a split in the period afterPythagoras’ death between what we would term the morephilosophically inclined Pythagoreans and others who primarily adoptedthe Pythagorean ethical, religious and political attitudes. Thelatter, called theacusmatici, followed the Pythagoreanprecepts, oracusmata (which means “thingsheard”). The former, the philosophical Pythagoreans (includingPhilolaus and Archytas), were the so-calledmathematici, andwhile they recognized that theacusmatici were indeedPythagoreans by virtue of accepting Pythagorean precepts, they claimedthat they themselves were the true followers of Pythagoras.

Philolaus of Croton seems to have blended the Pythagorean life with anawareness of and appreciation for the arguments of Parmenides (Huffman1993). According to Philolaus, “Nature in the cosmos was fittedtogether out of unlimiteds and limiters” (DK44B1/LM12D2). Theselimiters and unlimiteds play the role of Parmenidean basicrealities—they are and unchangingly must be what they are, andso can be known; they are joined together in a harmonia (literally, acarpenter’s joint; metaphorically, a harmony), and “it wasnot possible for any of the things that are and are known by us tocome to be, without the existence of the being of things from whichthe cosmos was put together” (DK44B6/LM12D5, D14). Theunlimiteds are unstructured stuffs and continua; the limiters imposestructure (shape, form, mathematical structure) on the unlimiteds.Things become knowable because they are structured in this way; thestructure can apparently be expressed in a numerical ratio that allowsfor understanding: “All things that are known have number; forwithout this nothing whatever could possibly be thought of orknown” (DK44B4/LMD7). Philolaus also developed a theory of thecosmos that displaced the earth from the center, replaced by what hecalled Hestia, the central fire (Graham 2013, 2014), and offered novelaccounts of eclipses.

6. Other Eleatics: Zeno and Melissus

Parmenides had argued that there were strict metaphysical requirementson any object of knowledge; the later Eleatics (named for followingParmenidean doctrines rather than for strictly geographical reasons),Zeno of Elea (born ca. 490) and Melissus of Samos (fl. ca. 440),extended and explored the consequences of his arguments. Zeno paidparticular attention to the contrast between the requirements oflogical argument and the evidence of the senses (Vlastos 1967 is amasterly treatment of Zeno; see also McKirahan 1999 and 2005). Thefour famous paradoxes of motion, for which he is now and in antiquitybest known, purported to show that, despite the evidence all aroundus, the ordinary motion of everyday experience is impossible. Theparadoxes claim that motions can never be begun (the Achilles) or becompleted (the Dichotomy), entail contradictions (the Moving Blocks),or are altogether impossible (the Arrow).[6] Recent philosophers of space and time (see Grünbaum 1967,articles in Salmon 2001, Huggett 1999, and the entry onZeno’s Paradoxes) hold that the arguments are reductios of the theses thatspace and time are continuous (the Achilles and the Dichotomy) ordiscrete (the Moving Blocks and the Arrow). Consider the Dichotomy: arunner can never complete a run from point A to point B. First, therunner must move from A to a point halfway between A and B (call itC). But between A and C there is yet another halfway point (D), andthe runner must first reach D. But between A and D there is yetanother halfway point … and so on, ad infinitum. So the runner,starting at A, can never reach B. The argument assumes that it isimpossible to pass an infinite number of points in a finite time.Similarly, Zeno produced paradoxes showing that plurality isimpossible: if things are many, contradictions follow (Plato’sParmenides 127e1ff.; Zeno in DK29B1/LM20D5, D6;DK29B2/LM20D7, R6; and DK29B3/LM20D11); there were also purportedproofs that place is impossible (DK29A24/LM20D13a, R22, R23) and thatthings cannot have parts (the Millet Seed, DK29A29/LM20D12a, D12b,R16).

Melissus, dismissed as a simple-minded thinker by Aristotle (and bysome contemporary scholars as well but see Makin 2005), expandsParmenides’ arguments about the nature of what-is (Palmer 2004).It is Melissus who explicitly claims that only one thing can be: ifwhat-is is unlimited (as he thinks it is), it must be one and allalike (if there were two [in number or in character] they would be“limited against each other” DK30B6/LM21D6). Melissusspecifically argues against the empty (the void), and rejects thepossibility of rearrangement (which would allow for the appearance ofcoming-to-be and passing-away, and of movement)—all thesecharacteristics are incompatible with the unity of what-is (i.e., theOne). Melissus thus claims that what is real is completely unlike theworld that we experience: the split between appearance and reality iscomplete and unbridgeable.

7. The Pluralists: Anaxagoras of Clazomenae and Empedocles of Acragas

While Zeno and Melissus reinforced Parmenides’ distinctionbetween what-is (i.e., what must be) and what appears, otherpost-Parmenidean thinkers accepted Parmenides’ arguments againstcoming-to-be and passing-away (as characterizing what-is), and aboutthe stable nature of what is ultimately real, and argued that thesearguments did not rule out the possibility of metaphysically-based (orrational) cosmology. Both Anaxagoras and Empedocles worked within theParmenidean pattern while developing distinct cosmological systemsthat addressed their own particular concerns (especially in the caseof Empedocles, concerns about the proper way to live).

Anaxagoras (writing in the mid-5th c.) claims, “TheGreeks [i.e., ordinary people] do not think correctly aboutcoming-to-be and passing-away; for no thing comes to be or passesaway, but is mixed together and dissociated from the things that are.And thus they would be correct to call coming-to-be mixing-togetherand passing-away dissociating” (DK59B17/LM25D15). What seem tobe generated objects (human beings, plants, animals, the moon, thestars) are instead temporary mixtures of ingredients (such as earth,air, fire, water, hair, flesh, blood, dense, dark, rare, bright, andso on). Recent treatments of Anaxagoras (Marmodoro 2015, 2017) havesuggested that the ingredients are primarily powers that manifestthemselves in the mixtures produced.[7] The original state was universal mixture: “All things weretogether, unlimited both in amount and in smallness, for the small,too, was unlimited. And because all things were together, nothing wasevident” (DK59B1/LM25D9). This mixture is set into rotary motionby the operation of Mind (Nous – DK59B12/LM25D27,DKB13/LM25DD29b, DK59B14/LM25D28; see discussions in Laks 1993, Lesher1995, Menn 1995, Curd 2007), a separate cosmic entity that does notshare in such mixture. As the rotation spreads out through theunlimited mass of indistinguishably intermingled ingredients, therotation causes a winnowing or separating effect, and the cosmos as weknow it emerges from the mixture. Moreover, not onlywere allthings together, they areeven now all together, in adifferent way, despite the differentiations now achieved. Everythingis in everything (DK59B5, B6, B11/LM25D16, D25, D26), in some proportions, however smallor great – this is a move to prevent even the appearance ofcoming-to-be from what-is-not.

Anaxagoras marks an important theoretical step in attributing themotion of his ingredients to an independent, intelligent force(although both Plato and Aristotle were disappointed that his theorywas not properly—from their point of view—teleological; onthis see Sedley 2007, Curd 2018). The rotation begun by Mind iscausally responsible for the formation of the heavens and theactivities of the great masses of the earth and the water on theearth, as well as all meteorological phenomena. Insofar as the causesof the operations of the heavens and the phenomena apparent to us fromday to day are the same at both the macro- and micro-level (therotations that cause the apparent motions of the stars are the same asthose that govern the cycles of weather and life and death on earth),we can infer the nature of what is real from what is apparent(Anaxagoras’ scientific views are treated in Graham 2006 and2013). Although we do not perceive all things as being together, andthe move to the ultimate explanations is an inference, it is alegitimate one (“owing to their [the senses’] feebleness,we are not able to determine the truth” yet “appearancesare a sight of the unseen” DK59B21/LM25D5 andDK59B21a/LM25D6).

A younger contemporary of Anaxagoras, Empedocles, who lived in Sicily,also recognized the force of Parmenides’ arguments againstcoming-to-be and passing-away. (Empedocles also adoptsParmenides’ poetic meter in order to tell his story.) Empedoclesproposes a cosmos formed of the four roots (as he calls them), earth,water, air, and fire along with the motive forces of Love and Strife.It is often claimed that, for Empedocles, Love simply produces mixtureand Strife only causes separation. Empedocles’ view is morecomplicated, for both forces mix and separate. Love unites opposed(unlike) things by pulling apart and then mixing these unlikes, whileStrife sets unlikes in opposition and segregates them, hence Strifemixes like with like. Just as painters can produce fantasticallylifelike scenes just by mixing colors, so the operations of Love andStrife, using just the four roots can produce “trees and men andwomen, and beasts and birds and water-nourished fish, and long-livedgods best in honors” (31B17). These are the things thatEmpedocles calls “mortal,” and he even provides recipes.DK31B73/LM22D73 tells how Kypris (the goddess Aphrodite, i.e. love)fashions shapes (or kinds): “she moistened earth in rain, andgave it to quick fire to harden.” DK31B96/LM44D192 gives arecipe for bones; flesh and blood both have the same recipe (earth,water, air, and fire in equal proportions), but differ in therefinement of the mixture (DK31B98/LM44D58a and D190).

Like the other Presocratics, Empedocles has a cosmological theory, inhis case, an unending cycle involving the competition between Love andStrife. Love overcomes the separating influence of Strife, bringingtogether unlikes and so preventing the clinging together of likes. Thetriumph of Love results in the Sphere, which is a complete mixturebecause the four unlike roots are as mixed (integrated) as possible.Strife breaks up the sphere by beginning to attract like to like andso pulling the mixture apart, until, when it triumphs, there iscomplete segregation of the roots. Love resists the separation ofunlikes and the clinging together of likes, by trying to keep unlikethings mixed. The cosmos as we know it is a result of intermediatephases between the two extremes of the triumph of one of the forces.[8]

Although Empedocles gives an account of the cosmos, cosmology is nothis sole interest. Both fragments and testimonia show his keenattention to questions about perception and its role in knowledge, theworkings of the body, and psychology. Like the Pythagoreans,Empedocles thought that how one lived was as important as one’stheoretical commitments (and that the two were intimately connected).The ancient evidence seems to suggest that Empedocles was the authorof two works, commonly called in modern scholarship thePhysics and thePurifications, one cosmological andthe other ethico-religious. The relation between the two works hasbeen a matter of some controversy. In the 1990s important new evidencefrom the Strasbourg Papyrus showed unequivocally that the cosmologicaland ethico-religious aspects of Empedocles’ thought areinextricably intertwined (Martin and Primavesi 1999, Primavesi 2008,Kingsley 1995), although commentators still disagree about whetherthis new evidence supports the conclusion that there was a single poemcombining both.[9] The correct philosophical understanding of the physical world and thecorrect way to live cannot be separated from one another inEmpedocles’ thought (a similar attitude appears in Heraclitus);one cannot fully understand the world without living correctly.[10] Like the Pythagorean, the Empedoclean way of life included dietaryrestrictions and a story of transmigratingdaimōns whoseem to have some kind of personal identity. (Marmodoro 2016 is acollection of recent work on Empedocles.)

8. Presocratic Atomism

The pluralism of Anaxagoras and Empedocles maintained the Eleaticstrictures on metaphysically acceptable basic entities (things thatare and must be just what they are) by adopting an irreduciblepluralism of stuffs meeting these standards that could pass on theirqualities to items constructed from them. Ancient atomism respondedmore radically: what is real is an infinite number of solid,uncuttable (atomon) units of matter. All atoms are made ofthe same stuff (solid matter, in itself otherwise indeterminate),differing from one another (according to Aristotle inMetaphysics 985b4-20=DK67A6/LM27D31 and R38) only in shape,position, arrangement. Later sources say that atoms differ in weight;some scholars have argued that, while this is certainly true forpost-Aristotelian atomism, it is less likely for Presocratic atomism.Recent scholarship has questioned this view, and find no reason todeny weight to Presocratic atomism (Augustin 2015). In addition to thereality of atoms, the Presocratic atomists, Leucippus and Democritus(Democritus was born in about 460 BCE in Abdera in Northern Greece,shortly after Socrates was born in Athens), enthusiastically endorsedthe reality of the empty (or void).[11] The void is what separates atoms and allows for the differences notedabove (except weight, which could not be accounted for by void, sincevoid in an atom would make it divisible and, hence, not an atom)(Sedley 1982; see also Sedley 2008).

Like Anaxagoras, the atomists consider all phenomenal objects andcharacteristics as emerging from the background mixture; in the caseof atomism, the mix of atoms and void (Wardy 1988). Everything isconstructed of atoms and void: the shapes of the atoms and theirarrangement with respect to each other (and the intervening void) givephysical objects their apparent characteristics. As Democritus says:“By convention sweet and by convention bitter, by conventionhot, by convention cold, by convention color: in reality atoms andvoid” (DK68B125/LM27D14, D13a = DK68B9/LM27D4, D14, D15, D23a,R108). For example, Theophrastus says that the flavors differaccording to the shapes of the atoms that compose various objects;thus “Democritus makes sweet that which is round and quitelarge, astringent that which large, rough, polygonal and notrounded” ( Caus. Plant. 6.1.6 = 68A129/LM27D60).Simplicius reports that things composed of sharp and very fine atomsin similar positions are hot and fiery; those composed of atoms withthe opposite character come to be cold and watery (in Phys.36.3–6 = 67A14). Moreover, Theophrastus reports that theatomists explain why iron is harder than lead but lighter; it isharder because of the uneven arrangements of the atoms that make itup, lighter because it contains more void than lead. Lead, on theother hand, has less void than iron, but the even arrangement of theatoms makes lead easier to cut or to bend (de Sens. 61–63 =68A135/LM27D64, D65, D66, D67, D69, D134, D147, D157, D158, D159a).

Adopting a strong distinction between appearance and reality, anddenying the accuracy of appearances, as we see him do in the abovequotation, Democritus was seen by some ancient sources (especiallySextus Empiricus) as a sort of skeptic, yet the evidence is unclear.It is true that Democritus is quoted as saying, “In truth weknow nothing; for truth is in the depths” (DK68B117/LM27D24). Sofor him, the truth is not given in the appearances. Yet, even Sextusseems to agree that Democritus allows for knowledge:

But in theRules [Democritus] says that there are two kindsof knowing, one through the senses and the other through theunderstanding. The one through the understanding he calls genuine,witnessing to its trustworthiness in deciding truth; the one throughthe senses he names bastard, denying it steadfastness in thediscernment of what is true. He says in these words, “There aretwo forms of knowing, one genuine and the other bastard. To thebastard belong all these: sight, hearing, smell, taste, touch. Theother, the genuine, has been separated from this”[DK68B11/LM27D6, D20, D21, R108]. Then preferring the genuine to thebastard, he continues, saying, “Whenever the bastard is nolonger able to see more finely nor hear nor smell nor taste norperceive by touch, but something finer…”

Thus Sextus suggests that the evidence of the senses, when properlyinterpreted by reason, can be taken as a guide to reality (the claimthat “appearances are a sight of the unseen” is attributedto Democritus as well as to Anaxagoras). We just need to know how tofollow this guide, through proper reasoning, so as to reach thetruth—i.e., the theory of atoms and void (Lee 2005).

In addition to fragments advancing these metaphysical and physicaldoctrines, there are a number of ethical fragments attributed toDemocritus (but the question of authenticity looms large here);although a passage reported in John Stobaeus seems to link moderationand cheerfulness with small measured movements in the soul and saysthat excess and deficiencies give rise to large movements(DK68B191/LMD226), it is unclear whether or how these claims arerelated to the metaphysical aspects of atomism (Vlastos 1945 and 1946,Kahn 1985b). Democritus was identified in antiquity with the idea of“good cheer” (euthumiē) as the properguiding objective in living one’s life. In this, as in otheraspects of his philosophy, he may have had some influence on theformation of Epicurus’ philosophy a century later.

9. Diogenes of Apollonia and the Sophists

In the last part of the 5th century, Diogenes of Apollonia(active after 440 BCE) revived and revised the Milesian system ofcosmology, claiming that “all the things that are arealterations from the same thing and are the same thing”(64B2/LM28D3); he identified this single basic substance with air,like Anaximenes more than a century before (Graham 2006, Laks 2008,2008a). Diogenes takes care to give arguments for the reality andproperties of his basic principle. In DK64B2/LM28D3 he says that onlythings that are alike can affect one another. If there were aplurality of basic substances, each differing in what Diogenes callstheir “own proper nature,” there could be no interactionbetween them. Yet the evidence of the senses is clear: things mix andseparate and interact with one another. Thus, all things must be formsof some one single thing. Like Anaxagoras, Diogenes claims that thecosmic system is ordered by intelligence, and he argues that that“which possesses intelligence (noēsis) is whathuman beings call air” (DK64B5/LM28D10). Humans and animals liveby breathing air, and are governed by it —in them air is bothsoul and intelligence, or mind (DK64B4/LM28D2). Moreover, Diogenesargues, air governs and rules all things and is god (DK64B5/LM28D10).Thus, like Anaxagoras, Diogenes has a theory grounded in intelligence,although Diogenes is more fully committed to teleologicalexplanations, insofar as he states explicitly that intelligence(noēsis) orders things in a good way (DK64B3/LM28D56).In presenting his arguments, Diogenes fulfills his own requirement fora philosophical claim. In DK64B1/LM28D2 he says, “In my opinion,anyone beginning alogos (account) ought to present astarting principle (archē) that is indisputable and astyle that is simple and stately.” He notes that his theory thatair is soul and intelligence “will have been made clearlyevident in this book” (DK64B4/LMD9).

Theophrastus says that Diogenes was the last of the physicalphilosophers, thephysiologoi, or “inquirers intonature,” as Aristotle called them; Diogenes Laertius(Lives II.16–17) gives that title to Archelaus, saying thathe was the teacher of Socrates (see Betegh 2013a). There was alsoanother group of thinkers active about this time: the Sophists. Manyof our views about this group have been shaped by Plato’saggressively negative assessment of them: in his dialogues Platoexpressly contrasts the genuine philosopher, i.e., Socrates, with theSophists, especially in their role as teachers of young men growinginto their maturity (youths at the age when Socrates, too, engagedwith them in his discussions). Modern scholarship (Woodruff andGagarin 2008, Kerferd 1981, Guthrie 1969) has shown the diversity oftheir views. They were not completely uninterested in the theoreticalproblems that concerned others of the Presocratics. Gorgias ofLeontini questioned the possibility of the certainty that Parmenidessought. In hisOn Nature, orOn what-is-not, Gorgiasclaims that nothing satisfies (or can satisfy) Parmenides’requirements for what-is (Mansfeld 1985, Mourelatos 1987b, Palmer1999, Caston 2002, Curd 2006). Protagoras, too, doubted thepossibility of the strong theoretical knowledge that the Presocraticschampioned. The Sophists raised ethical and political questions: Doeslaw or convention ground what is right, or is it a matter of nature?They traveled widely, sometimes serving as diplomats, and they wereboth entertainers and teachers. They gave public displays of rhetoric(this contrasts with Diogenes of Apollonia’s comments about hisbook, which seems to imply a more private enterprise)[12] and took on students, teaching both the art of rhetoric and theskills necessary for succeeding in Greek political life. With theSophists, as with Socrates, interest in ethics and political thoughtbecomes a more prominent aspect of Greek philosophy.

10. The Presocratic Legacy

The range of Presocratic thought shows that the first philosopherswere not merely physicists (although they were certainly that). Theirinterests extended to religious and ethical thought, the nature ofperception and understanding, mathematics, meteorology, the nature ofexplanation, and the roles of matter, form, causal mechanisms, andstructure in the world. Almost all the Presocratics seemed to havesomething to say about embryology, and fragments of Diogenes andEmpedocles show a keen interest in the structures of the body; theoverlap between ancient philosophy and ancient medicine is of growinginterest to scholars of early Greek thought (Longrigg 1963, van derEijk 2008). Recent discoveries, such as the Derveni Papyrus, show thatinterest in and knowledge of the early philosophers was notnecessarily limited to a small audience of rationalisticintellectuals. They passed on many of what later became the basicconcerns of philosophy to Plato and Aristotle, and ultimately to thewhole tradition of Western philosophical thought.

Bibliography

Primary Sources: Texts and Translations

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Secondary Literature

Note: In order to be useful to readers, this bibliography includesboth general accounts of and introductions to Presocratic philosophy,as well as more specialized material. Edited volumes containcollections of articles, not all of which are listed individually inthis bibliography.

  • Augustin, M. 2015, “Weight in Greek Atomism,”Philosophia, 45: 76–99.
  • Algra, K., 1995,Concepts of Space in Greek Thought,Leiden: E.J. Brill.
  • ––– 1999, “The Beginnings ofCosmology,” in Long (ed.) 1999: 45–65.
  • Austin, S., 1986,Parmenides: Being, Bounds, and Logic,New Haven: Yale University Press.
  • –––, 2007,Parmenides and the History ofDialectic: Three Essays, Las Vegas: Parmenides Publishing.
  • Baltussen, H., 2000,Theophrastus against the Presocratics andPlato: Peripatetic Dialectic in the De Sensibus, Leiden andBoston: Brill.
  • Barnes, J., 1982,The Presocratic Philosophers,2nd edition, London: Routledge and Kegan Paul.
  • Betegh, G., 2004,The Derveni Papyrus: Cosmology, Theology andInterpretation, Cambridge: Cambridge University Press.
  • –––, 2007, “On the Physical Aspect ofHeraclitus’ Psychology,”Phronesis, 52:3–32.
  • –––, 2009, “The Limits of Soul: HeraclitusB45 DK. Its Text and Interpretation,” in Hülz Piccone 2009:391–414.
  • ––– (ed.), 2013aThe Divine and the Human inthe Presocratic Age, special issue,Rhizomata,1(2).
  • –––, 2013b, “On the Physical Aspect ofHeraclitus’ Psychology: With New Appendices,” in Sider andObbink 2013: 225–261.
  • –––, 2013c, “Socrate et Archélaos dansLes Nuées,” in A. Laks and R. Saeta Cottone (eds.),Comédie et Philosophie: Socrate etles“présocratiques” dans les Nuéesd’Aristophane, Paris: Rue d'Ulm, 391–414.
  • –––, 2014a, “Pythagoreanism, Orphism, andGreek Religion,” in C. Huffman 2014, 149–166.
  • –––, 2014b, “Pythagoreans and the DerveniPapyrus,” in Sheffield and J Warren 2014, 79–93.
  • –––, 2017, “Archelaus on Cosmogony and theOrigins of Social Institutions,”Oxford Studies in AncientPhilosophy, 51: 1–40.
  • –––, 2020, “The Motive Force of Fire andHeat in Early Greek Philosophy and Medicine,” in H. Bartos andC. G. King (eds.),Heat, Pneuma, and Soul in Ancient Philosophyand Science, Cambridge: Cambridge University Press, 35–60.
  • Betegh, G. and V. Piano, 2019, “Column IV of the DerveniPapyrus: A New Analysis of the Text and the Quotation ofHeraclitus,” in C. Vassalo (ed.),Presocratics andPapyrological Tradition, Berlin and Boston: De Gruyter,179–220.
  • Brancacci, A. and P.-M. Morel (eds.), 2007,Democritus:Science, the Arts, and the Care of the Soul: Proceedings of theInternational Colloquium on Democritus, Berlin and Boston: DeGruyter.
  • Brown, L. 1994, “The verb ‘to be’ in GreekPhilosophy: Some Remarks,” in S. Everson, ed.,Language.Companions to Ancient Thought 3, Cambridge: Cambridge UniversityPress.
  • Brunschwig, J. and G.E.R. Lloyd, 2000,Greek Thought: A Guideto Classical Knowledge, Cambridge, Mass.: The Belknap Press ofHarvard University Press.
  • Bryan, J., 2012,Likeness and Likelihood in the Presocraticsand Plato, Cambridge: Cambridge University Press.
  • Burkert, W., 1972,Lore and Science in AncientPythagoreanism, E. L. Minar, Jr. (trans.), Cambridge, Mass.:Harvard University Press.
  • –––, 2008, “Prehistory of PresocraticPhilosophy in an Orientalizing Context,” in Curd and Graham2008: 55–85.
  • Burnet, J., 1930,Early Greek Philosophy, 4th edn.,London: Adam and Charles Black.
  • Cartledge, P., 1999,Democritus, New York:Routledge.
  • Cassertano, G., 2007,Empedocle tra Poesia, Medicina,Filosofia, e Politica, Naples: Loffredo.
  • Caston, V., 2002, “Gorgias on Thought and itsObjects,” in Caston and Graham 2002: 205–232.
  • Caston, V. and D. Graham (eds.), 2002,Presocratic Philosophy:Essays in Honor of A. P. D. Mourelatos, Aldershot: AshgatePublishing Co.
  • Cherniss, H., 1935,Aristotle’s Criticism of PresocraticPhilosophy, Baltimore: Johns Hopkins Press.
  • Cordero, N., 2004a,By Being, It Is, Las Vegas:Parmenides Publishing.
  • –––, 2004b, “La pensee s’exprime‘grace’ à l’etre,”RevuePhilosophique de la France et de l’Etranger, 129(1):5–13.
  • –––, 2010, “The ‘Doxa ofParmenides’ Dismantled,”Ancient Philosophy,30(2): 231–246.
  • –––, 2019, “There is, evidently, a‘Parmenides Physikos’ but …,”Archai, 25: 1–29.
  • Cornelli, G, 2013,In Search of Pythagoreanism: Pythagoreanismas an Historiographical Category, Berlin: De Gruyter.
  • –––, 2016, “A review of Aristotle’sClaim Regarding Pythagoreans Fundamental Beliefs: All isNumber?,”Prometeus: Filosofia Unisinos, 17(1):50–57.
  • Cornelli, G., R. McKirahan, and C. Macris, (eds.), 2013,OnPythagoreanism, Berlin: De Gruyter.
  • Curd, P., 2004,The Legacy of Parmenides: Eleatic Monism andLater Presocratic Thought, Princeton: Princeton University Press,1998, rev. edn. Las Vegas: Parmenides Press.
  • –––, 2006, “Gorgias and theEleatics,” in Sassi 2006, 183–200.
  • –––, 2011, “New Work on thePresocratics,”Journal of the History of Philosophy,49: 1–37.
  • –––, 2013, “The Divine and the Thinkable:Toward an Account of the Intelligible Cosmos,”Rhizomata, 1: 217–247.
  • –––, 2015, “Thinking, Supposing, andPhysis in Parmenides,”Etudes Platoniciennes,12: 1 –17.
  • –––, 2016a, “Empedocles on Sensation,Perception, and Thought,”Logical Analysis and History ofPhilosophy, special issue on Ancient Epistemology, K.Ierodiakonou and P. S. Hasper (eds.), 38–57.
  • –––, 2016b, “Powers, Structures, andThought in Empedocles”Rhizomata, 4(1): 55–79.
  • –––, 2018, “Presocratic Accounts ofPerception and Cognition,” in J. Sisko (ed.),Philosophy ofMind in Antiquity (Volume I), London and New York: Routledge,44–63.
  • –––, 2020, “Presocratic NaturalPhilosophy,” in L. Taub (ed.),The Cambridge Companion toAncient Greek and Roman Science, Cambridge: Cambridge UniversityPress, 15–38.
  • Curd, P. and D. H. Graham (eds.), 2008,The Oxford Handbook ofPresocratic Philosophy, New York: Oxford University Press.
  • De Lay, H. (1980), “Pangenesis Versus Panspermia:Democritean Notes on Aristotle’s Generation of Animals,”Hermes, 108(2): 129–153.
  • Dilcher, R., 1995,Studies in Heraclitus, Hildesheim:Georg Olms.
  • –––, 2006, “Parmenides on the Place ofMind,” in King 2006, 31–48.
  • –––, 2013, “How Not to ConceiveHeraclitean Harmony,” in Sider and Obbink 2013,263–280.
  • van der Eijk, P., 2008, “The Role of Hippocratic Medicine inthe Formation of Early Greek Thought,” in Curd and Graham 2008:385–412.
  • Frede, D. and B. Reis, (eds.), 2009,Body and Soul in AncientPhilosophy, Berlin: de Gruyter.
  • von Fritz, K., 1943, “NOOS and NOEIN in the HomericPoems,”Classical Philology, 38: 79–93.
  • –––, 1945 and 1946, “NOOS, NOEIN, andtheir Derivatives in Presocratic Philosophy (excluding Anaxagoras)I,”Classical Philology, 40: 223–242; and II“The Post-Parmenidean Period,”ClassicalPhilology, 41: 12–34.
  • Furley, D., 1967,Two Studies in the Greek Atomists,Princeton: Princeton University Press.
  • –––, 1983, “Weight and Motion inDemocritus’ Theory,”Oxford Studies in AncientPhilosophy, 1: 193–209.
  • –––, 1987,The Greek Cosmologists, Vol. I:The Formation of the Atomic Theory and its Earliest Critics,Cambridge: Cambridge University Press.
  • –––, 1989,Cosmic Problems: Essays on Greekand Roman Philosophy of Nature, Cambridge: Cambridge UniversityPress.
  • Furley, D. J. and R.E. Allen (eds.) 1970 and 1975,Studies inPresocratic Philosophy, 2 vols., London: Routledge and KeganPaul.
  • Furth, M., 1991, “A ‘Philosophical Hero?’Anaxagoras and the Eleatics,”Oxford Studies in,Ancient Philosophy, 9: 95–129.
  • ––– 1993, “Elements of EleaticOntology,” in A. P. D. Mourelatos 1993, 241–270.
  • Gemelli Marciano, M. L., 2002, “Le contexe culturel desPrésocratiques: adversaires et destinataires,” in Laksand Louguet 2002: 83–114.
  • –––, 2008, “Images and Experience: at theRoot of Parmenides’Aletheia,”AncientPhilosophy, 28: 83–114.
  • Gill, M. L. and P. Pellegrin (eds.), 2006,A Companion toAncient Philosophy, Oxford: Blackwell.
  • Graham, D. W., 1994, “The Postulates of Anaxagoras,”Apeiron, 27(2): 77–121.
  • –––, 1997, “Heraclitus’ Criticism ofIonian Philosophy,”Oxford Studies in AncientPhilosophy, 15: 1–50.
  • –––, 2004, “Was Anaxagoras aReductionist?”Ancient Philosophy, 24: 1–18.
  • –––, 2006,Explaining the Cosmos: The IonianTradition of Scientific Philosophy, Princeton: PrincetonUniversity Press.
  • –––, 2013,Science Before Socrates:Parmenides, Anaxagoras, and the New Astronomy, Oxford: OxfordUniversity Press.
  • Graham, D.W. and E. Hintz, 2007, “Anaxagoras and the SolarEclipse of 478 B.C.,”Apeiron, 40(4): 319–344.
  • Granger, H., 2000, “Death’s Other Kingdom: Heraclituson the Life of the Foolish and the Wise,”ClassicalPhilology, 95: 260–81.
  • –––, 2010a, “The Proem ofParmenides’ Poem,”Ancient Philosophy, 28:1–20.
  • –––, 2010b, “Parmenides of Elea:Rationalist or Dogmatist?”Ancient Philosophy, 30(1):15–38.
  • –––, 2013a, “Early Natural Theology: ThePurification of the Divine Nature,” in Sider and Obbink 2013:163–200.
  • –––, 2013b, “Xenophanes’ PositiveTheology and his Criticism of Greek Popular Religion,”Ancient Philosophy, 33(2): 235–271.
  • Gregory, A., 2007,Ancient Greek Cosmogony, London:Duckworth.
  • –––, 2013a, “Leucippus and Democritus onLike to Like and ou mallon,”Apeiron, 46(4):446–468.
  • –––, 2013b, “Parmenides, Cosmology, andSufficient Reason,”Apeiron, 1: 1–32.
  • –––, 2013c,The Presocratics and theSupernatural: Magic, Philosophy, and Science in Early Greece,London: Bloomsbury.
  • –––, 2016a,Anaximander: AReassessment, London: Bloomsbury.
  • –––, 2016b, “The Pythagoreans: Number andNumerology” in S. Lawrence and M. McCartney, (eds.),Mathematicians and their Gods: Interactions Between Mathematicsand Religious Beliefs, Oxford: Oxford University Press,21–50.
  • Grünbaum, A., 1967,Modern Science and Zeno’sParadoxes, Middletown: Connecticut Wesleyan UniversityPress.
  • Guthrie, W. K. C., 1962, 1965, 1969,A History of GreekPhilosophy, Vols. I, II, and III, Cambridge: Cambridge UniversityPress, 1965.
  • Hankinson, R. J., 2008, “Reason, Cause, and Explanation inPresocratic Philosophy,” in Curd and Graham, 2008:434–57.
  • Hasper, P. S. 1999, “The Foundations of PresocraticAtomism,”Oxford Studies in Ancient Philosophy, 27,1–14.
  • –––, 2006a, “Aristotle’s Diagnosisof Atomism,”Apeiron, 38(2): 121–156.
  • –––, 2006b, “Zeno Unlimited,”Oxford Studies in Ancient Philosophy, 30: 49–85.
  • –––, 2013, “Leucippus andDemocritus,” in Sheffield and Warren 2013: 65–78.
  • Heidel, W. A., 1906, “Qualitative Change in Pre-SocraticPhilosophy,”Archiv für Geschichte der Philosophie(New Series), 19(12): 333–379.
  • –––, 1913, “On Certain Fragments of thePre-Socratics: Critical Notes and Elucidations,”Proceedingsof the American Academy of Arts and Sciences, 48:681–734.
  • Hermann, A., 2004,To Think Like God. Pythagoras andParmenides: The Origins of Philosophy, Las Vegas: ParmenidesPublishing.
  • Hölscher, U., 1970, “Anaximander and the Beginnings ofGreek Philosophy,” in Furley and Allen 1975, 281–322.
  • Huffman, C. A., 1999, “The Pythagorean Tradition,” inLong (ed.) 1999, 66–87.
  • –––, 2009, “The Pythagorean Conception ofthe Soul from Pythagoras to Philolaus,” in Frede and Reis 2009:21–43.
  • –––, (ed.), 2014,A History ofPythagoreanism, Cambridge: Cambridge University Press.
  • Huggett, N. (ed.), 1999,Space from Zeno to Einstein: ClassicReadings with a Contemporary Commentary, Cambridge, MA: MITPress.
  • Hülz Piccone, E., (ed.), 2009,Nuevos Ensayos sobreHeráclito: Actas del Symposium Heracliteum Secundum,Mexico City: UNAM.
  • –––, 2013a, “Heraclitus onLogos:Language, Rationality, and the Real,” in Sider and Obbink 2013:281–302.
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