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Anaxagoras' ParmenideanCosmology: Worlds within Worldswithin the OneJohn E. Sisko

The aim of this paper is to suggest a limited solution to a long-standingpuzzle regarding the history of Pre-Socratic philosophical cosmology.The puzzle concerns the development of post-Parmenidean pluralism.Specifically, it concerns the relationship between Parmenides' accountof existence and the physical theories advanced by Democritus, Empe-docles and Anaxagoras.

Parmenides argues that all that is is one, an ungenerable, imperish-able, and unchangeable whole (DK 28 B 8.3, 8.6 & 8.38). Further, heasserts that all that is is continuous, lacking in nothing, and full of whatis (DK 28 B 8.6 & 8.24). Debate over the precise nature of Parmenides'theory continues, but it is widely accepted that he advances a thesis of'real monism': numerical monism.1 According to Parmenides, there is,

This view is endorsed in Montgomery Furth, 'Elements of Eleatic Ontology', inA.P.D. Mourelatos, ed., The Presocratics (Princeton, NJ: Princeton University Press1974), 241-70; G.E.L. Owen, 'Eleatic Questions' 1986 (/1960); rev. ed. reprinted inOwen, Logic, Science and Dialectic (Ithaca, NY: Cornell University Press 1986), 3-26;D.J. Furley, 'Melissus of Samos', in K. Boudouns, ed., Ionian Philosophy (Athens:International Association for Greek Philosophy 1989), 114-22; David Gallop, Par-memdes ofElea: Fragments (Toronto: University of Toronto Press 1984), esp. 40 n 81;David Sedley, 'Parmenides and Melissus' in A.A. Long, ed., The Cambridge Compan-ion to Early Greek Philosophy (Cambndge: Cambridge University Press 1999), 113-33;Aryeh Finkleberg, 'Parmenides: Material and Logical Monism', Archiv für Geschichteder Philosophie 70 (1988), 1-14; Theo Sinnige, Matter and Infinity m the PresocraticSchools and Plato (Assen: Van Gorcum 1971), esp. 45; John Malcolm, 'On Avoiding

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88 John E. Sisko

within physical reality, numerically one thing and what this one thing isit has always been and shall always be. It is an immobile, unalterable,and homogeneous whole. At first blush, this theory seems paradoxical;for, when we look to the world of appearance, we see that there is morethan just one thing, we see that objects are created and destroyed, andwe see that various items move and undergo qualitative change. How-ever, according to the widely accepted view, this seeming paradox failsto give Parmenides pause. For he is an arch-rationalist: he is willing tofollow what he understands to be the requirements of reason no matterwhere they might lead. Consequently, Parmenides considers the worldof appearance to be an illusion and he thinks that those who trust in sucha world amount to nothing more than a dazed, ignorant, horde of meremortals (DK 28 B 6.4-9).

Parmenides advances persuasive arguments in support of his theory.His initial argument centers on the unintelligibility of negation. Heargues that no thing can be nothing and no thing can be fruitfullydescribed as not-a-thing (DK 28 B 2). From his critique of negation,Parmenides advances the thesis of 'No Becoming'. He argues that thereis no thing which comes-to-be, for such a thing would have to come-to-beout of what is not (or out of what it is not) and 'not' is unintelligible (DK28 B 8.19-21). Further, he holds, that there is no thing which ceases-to-be,for, presumably, such a thing would have to perish into what is not (orinto what it is not) and, again, 'not' is unintelligible. In addition, Par-menides utilizes his own critique of negation in order to advance thethesis of 'real monism'. He argues that what exists is both one andcontinuous, for what is cannot be spatially contiguous with or hindered

the Void', Oxford Studies m Ancient Philosophy 9 (1991), 75-94; G.S. Kirk, J E. Raven& M. Schofield, The Presocratic Philosophers. (Second edition). (Cambridge. Cam-bridge University Press 1983), 250-4; R. McKirahan, Philosophy Before Socrates (Indi-anapolis: Hackett Publishing Company 1994), esp. 175. Some argue that Parmenidesdoes not advance a thesis of 'real monism'. See Jonathan Barnes, Tarmenides andthe Eleatic One', Archiv fur Geschichte der Philosophie 61 (1979a), 1-21; A.P.D. Moure-latos, The Route of Parmenides (New Haven, CT: Yale University Press 1971), esp130-3; Patricia Curd, Tarmenidean Monism', Phronesis, 35 (1991), 241-64, and P.Curd, The Legacy of Parmenides: Eleatic Monism and Later Presocratic Thought (Prince-ton, NJ: Princeton University Press 1998). I concur with the widely accepted viewBut, for the purpose of this paper, it need only be supposed that Anaxagorasunderstood Parmenides to be a numerical monist.



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by what is not (or by what it is not), since, once again, 'not' is unintelli-gible (DK 28 B 8.22-25 & 8.46-48).

Several philosophers from the generation subsequent to Parmenides'own incorporate the thesis of 'No Becoming' into their own cosmologicaltheories. While these philosophers, unlike Parmenides, are pluralists,each thinks that the basic constituents of the cosmos are imbued withwhat has now come to be called 'Parmenidean Being'. That is, each holdsthat there are basic material stuffs which are eternal and unchanging intheir essential nature. For Democritus the basic constituents of the cos-mos are atoms and void (DK 68 A 37); for Empedocles these are the fourelements: earth, air, fire, and water (DK 31 B 17); and for Anaxagorasthese are many, indeed, quite many things. Among those mentioned inthe surviving fragments are the wet and the dry, the hot and the cold,the bright and the dark, colours, flavours, earth, flesh and seeds (DK 59B 4a.l-4,4b.3-6 and 10.1-2).2

These philosophers embrace the thesis of 'No Becoming', but they alsoassert plurality, and this brings us to the long-standing puzzle. For, whenwe look to the surviving fragments of the pluralists, we find, in each case,that something is conspicuously absent. What is absent is an argumentthat is meant to justify pluralism. The pluralists accept the thesis of 'NoBecoming', which Parmenides derives from his own critique of negation.Yet, they seem to simply posit their own pluralism, even though Par-menides rejects pluralism in light of his critique of negation. The plural-ists appear to beg the question against Parmenides. So, the relationshipbetween Parmenides and the pluralists presents historians of philosophywith an interesting puzzle: Why do the pluralists so readily reject mo-nism, while endorsing key features of the account which leads Par-menides to embrace monism?

There is a substantial body of literature on Anaxagoras' understanding of seeds. Ifollow Jonathan Barnes and Malcolm Schofield in supposing that the account ofseeds is nothing more than an elaboration on Anaxagoras' Principle of UniversalMixture (discussed below). On this interpretation the claim that a seed of X is in Υmeans that Υ may grow from X (as any type of substance may emerge from anyother type of substance on Anaxagoras' account). See Jonathan Barnes, ThePresocrattc Philosophers, v.2 (London 1979b), 21 and Malcolm Schofield, An Essay onAnaxagoras (Cambridge: Cambridge University Press 1980), 130-1. For a recentcriticism of this view see Eric Lewis, 'Anaxagoras and the Seeds of a PhysicalTheory', Apeiron 33 (2000), 1-24.



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I wish to propose a limited solution to this puzzle. My solutionconcerns only the relationship between Anaxagoras' physical theory andParmenides' arguments. I suggest that Anaxagoras has little need toargue against Parmenides, because Anaxagoras' own cosmology beginsright where Parmenides' cosmology leaves off. Anaxagoras accepts thebasic tenets that Parmenides draws from the critique of negation, but hethen proceeds to show how a specific sort of plurality might be broughtto light within Parmenides' One.3 That is, Anaxagoras develops a plu-ralistic cosmology which is consistent with Parmenides' foundationalclaims about the One.

Now, even the more charitable reader shall not, at first, find this thesisto be especially plausible. Such a reader is likely to judge the thesis to beat most half right. For, it is well known that Anaxagoras ostensiblydivides the history of the cosmos into two periods, an initial staue periodand a subsequent dynamic period. And, while the initial period — theperiod of the Primordial Chaos — has features that are taken to suggesta possible kinship with Parmenides' One, the latter period — the periodof the Whirl — is, universally, held to be overtly and objectively dissimi-lar to the One.4 In this paper, I hope to correct certain broadly heldmisconceptions about Anaxagoras' cosmology. I shall argue thatAnaxagoras' cosmos, in each of its purported periods, conforms with thebasic definitional requirements for Parmenides' One: the PrimordialChaos is Parmenides' One under an alternate description, and the Whirl— the dynamic period of the cosmos in which the world, as we know it,has come to be formed — meets the fundamental requirements forParmenides' One. Anaxagoras provides a substantially Parmenidean

3 In this paper, I follow the practice of calling the numerical unity, which constitutesall that exists on Parmenides' account, 'the One'. However, it should be noted that,while Parmenides attributes unity to that which exists (see DK 28 B 8.6), he does notexplicitly call this unitary being 'the One'

4 Some scholars accept the view that Anaxagoras' Primordial Chaos is meant to beequivalent to Parmenides' One. See C.D.C. Reeve, 'Anaxagorean Panspermism',Ancient Philosophy 1 (1981), 89-108, esp. 102, n 56; and D. Graham, 'Empedocles andAnaxagoras: Responses to Parmenides', in A.A. Long, ed., 1999,159-80. Others rejectthis view. See, for example, Jonathan Barnes, 1979b, 38. Yet, even those scholars whoaccept that the Primordial Chaos meets the definitional requirements for the One,tend to argue that the cosmos of the dynamic period violates basic Parmenideanprinciples. See C.D C. Reeve, 1981,104 and D. Graham, 1999,173.




account of the existence of our world within the heavens. Yet, he does agreat deal more. Anaxagoras not only argues for a world of pluralitywithin a Parmenidean framework, he argues for a plurality of worldswithin this selfsame framework. Anaxagoras maintains that our worldis one among many, possibly infinitely many, worlds nested within theheavens and, interestingly, the existence of such a plurality of worldsdoes nothing to violate the basic definitional requirements for Par-menides' One. So, all in all, I shall show that Anaxagoras' cosmology isuniquely Parmenidean: it is a cosmology of worlds within worlds withinthe One.5

Parmenides

Let us agree that, for Parmenides, there is numerically one thing inexistence: the One. This unity possesses a number of salient features andcertain of these features are basic insofar as they issue directly fromParmenides' reflections on negation. In order to avoid positing either athat-which-is-not simpliciter or a that-which-is-not-the-One, Parmenidesmaintains that the One cannot fail to be complete in respect to time orspace, or even quality. He argues that the One is (1) eternal, (2) spatiallyunbounded (as a material plenum), and (3) predicationally saturated (itpossesses all predicates, of a given sort, everywhere throughout itself).In addition, Parmenides maintains that the One is (4) immobile, (5)unalterable and (6) phenomenally homogeneous. These latter featuresof the One are non-basic insofar as they do not issue directly fromParmenides' reflections on negation. Since a firm grasp of the salientfeatures of the One is crucial to the project of discerning Anaxagoras'Parmenidean commitments, let us consider each feature in rum.

(1) The One is eternal. The One is without generation or destruction.Parmenides advances a pair of arguments against generation (but heleaves it to the reader to supply analogous arguments against destruc-tion). First, he appeals to the thesis of 'No Becoming', which is derived

I borrow the phrase 'worlds within worlds' from D. Graham, 'The Postulates ofAnaxagoras', Apeiron 27 (1994), 77-121, esp. 105. Graham compares the infiniteregress of ingredients in Anaxagorean substances to Leibniz' account of worldswithin worlds in the Monadology. Graham does not suggest that, for Anaxagoras,our world is one among a plurality of worlds within the cosmos.



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from his own critique of negation. He argues that no thing can come-to-be out of what is not (or out of what it is not), since 'not' is unintelligible(see DK 28 B 8.3-9). Second, he argues against the possibility of a firstevent. Parmenides asks, if what-is is to be generated, 'what could havemade it grow later rather than sooner?' (DK 28 B 8.9-10). His argumentrests on a particular application of the Principle of Sufficient Reason.Admitting the possibility of time distinctions, Parmenides suggests thatif there had been a first event (the generation of what-is) at some time f,then there must be a sufficient reason for this event having occurred atf and not at some earlier time f-n.6 Since there is no such reason, therecould not have been a first event at t, nor, for that matter, could there havebeen such an event at any other time. Thus, having shown that a firstevent is impossible (and having supposed that a last event is similarlyimpossible), Parmenides concludes that the One is complete insofar asit has neither a temporal beginning nor a temporal end.

(2) The One is an infinitely extended material plenum. Parmenides arguesthat the One is spatially complete. He states,

... [it] is completed,From every direction like the bulk of a well-rounded sphere,Equally balanced in every way from the center; for [it] must not

be any largerOr any smaller here or there;For there is not what-is-not, which could stop it from reaching[its] like ... (DK 28 B 8.42-7, Trans. Gallop with slight changes)

Here I take up a line of interpretation that was introduced in G.E.L. Owen, 1974(/1966), 'Plato and Parmenides on the Timeless Present', reprinted in A.P.D. Moure-latos, ed., 1974,279-82. Owen ultimately rejects this line and instead maintains thatParmenides attacks the very notion of temporal distinctions. According to Owen,Parmenides does not think that the One is eternal, rather he thinks that it exists ina 'timeless present'. One reason why Owen rejects the view that Parmenides admitstime-distinctions is that Anaxagoras, in responding to Parmenides' challenge, notonly theorizes about a first event in an otherwise static cosmos, but also'... <takes>. . no care to meet the query why it should have happened when it did.' (Owen,ibid., 282). I shall argue (below) that Anaxagoras, together with Empedocles,circumvents the problem of a first event. Thus, I see no reason to reject the notionthat Parmenides admits time-distinctions.




Parmenides' use of spatial language in this passage is unmistakeable. Hemaintains that the One is physically extended in a manner that lacksboth variation and any sign of imperfection. There is, however, an initiallack of clarity about the precise nature of the One's spatial perfection. Onthe one hand, Parmenides compares the One to the bulk of a sphere(8.43) and this might be taken to suggest that the One is spherical.7 Onthe other hand, he claims that the One is not hindered by what-is-not(8.46) and this might be taken to suggest that the one is without spatiallimit and is infinitely extended.8 A moment's reflection shows that, forParmenides, the One is infinitely extended in space. First, the Onecannot be spherical, since it would then be bordered by what-is-not, and'not' (as we have learned) is unintelligible. Second, and more impor-tantly, Parmenides does not actually claim that the One is spherical.Instead, he claims that the One is akin to the bulk of a sphere insofar asit exhibits equal balance. Yet, such balance is not exhibited about someone center. Instead, it is exhibited about each and every location withinthe One. For, in elucidating the character of this balance, Parmenidesclaims that the One 'must not be any larger or any smaller here or there'(8.44-45) and this suggests that any location within the One must itselfstand as a point of equal balance (or equilibrium). Now, while only asingle location within a sphere (i.e., the center) will stand as a point ofbalance, any location within an infinitely extended plenum will stand assuch a point. So, Parmenides' One is an infinitely extended materialplenum. It is spatially complete, existing with neither a physical begin-ning nor a physical end.9

(3) The One is predicationally saturated. It is qualitatively complete:every predicate, of the sort with which Parmenides is concerned, isinstantiated both within the One as a whole and within every region of

7 David Sedley maintains that Parmenides' One is literally spherical. See his 1999,117and 125.

8 Many scholars hold that the One is infinitely extended. See, for example, D. Gallop,1984,20; G.E.L. Owen, 1986 (/1960), 20; and R. McKirahan, 1994,172-3.

9 Parmenides does claim that the One has a limit (πείρας; DK 28 B 8.26, 8.31 & 8.49)and this might, at first, be taken to mean that it has a spatial limit. But, as G.E.L.Owen has persuasively argued, Parmenides uses πείρας to mark the fixity oruniformity of what-is. He does not use this term to mark a spatial boundary. SeeOwen, 1986 (/1960), 20.



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the One.10 The demand for predicational saturation issues from Par-menides' reflections on negation. He contends that no negative predicate— no predicate of the form not-F — can be instantiated within physicalreality, while all positive predicates — predicates of the form F — areinstantiated (see DK 28 B 8,33 & b.37-38). On the face of it, this contentionis highly problematic; for it would seem that if we were to attribute twonon-synonymous positive predicates to the One, we would violate Par-menides' prohibition against negative predication. Consider, for exam-ple, the attribution of both hot and cold to the One (although, we neednot focus only on contraries). Once we acknowledge that hot is not-coldand cold is not-hot, such attribution brings negative predicates in itstrain.11 However, this is not a problem that confronts Parmenides; for heapproaches issues of predication from the perspective of the naive meta-physics of things.12 His predicational concerns range over, what we nowcall, mass-terms (like earth and fire) and quality-powers, or quality-things (like dry and black, taken as independent things). Parmenides isneither concerned with relational predicates (like ίο the left of) nor is heconcerned with other ancillary predicates (like of this quantity, taken asdependent upon more basic things). Further, the predicates that interestParmenides are considered to mark 'things' that are conceptually inde-pendent of one another. So, for Parmenides, hot fails to be not-cold andcold fails to be not-hot.13 From his perspective, the attribution of multiplenon-synonymous predicates to the One fails to be problematic. For if theOne were both hot and cold (and each throughout itself), then we couldnot say that what-is is not-hot and we could not say that it is not-cold

10 This view is endorsed in Furth, 1974, 267-8 and in McKirahan, 1994,166 and 169.

11 This particular worry has caused some to suggest that Parmenides is a predicationalmonist. On this view, Parmenides holds that, regarding what-is, we can say no morethan that it is: only a single predicate, being, can be attributed to the One. See Curd,1991,242 η 7. Curd, herself, does not endorse this view.

12 See A.P.D. Mourelatos, 'Heraclitus, Parmenides, and the Naive Metaphysics ofThings', in Exegesis and Argument, E.N. Lee, A.P.D. Mourelatos and R. Rorty, eds.(Assen: Van Gorcum 1973), 16-48.

13 The core difficulty within the admittedly false cosmology that is introduced in thesecond part of Parmenides' poem (at DK 28 B 8.55-61) is that fundamental objects(like aetherial fire) are defined as being conceptually dependent on their opposites:each is what its opposite is not. If this is the source of difficulty in the falsecosmology, then it cannot be a part of Parmenides' positive ontology.




(further, we could not say that any part of what-is is not-hot or not-cold);for in being both hot and cold it would neither be not-hot nor not-cold. So,from Parmenides' perspective, there is no difficulty with attributing allpositive predicates to the One. The One is predicationally saturated: it isqualitatively complete.

(4) The One is immobile. Beyond the basic features of being complete inrespect to time, space and quality, the One has a number of non-basicfeatures. Chief among these is immobility. Parmenides maintains thatthe One is infinitely extended and lacking any sort of empty space withinitself. It is full and complete in every direction and, so, it is entirely'chained up' (cf. DK 28 B 8.14). Thus, Parmenides contends that the Onecannot locomote as a whole, having no external space into which it mightmove. Further, he contends that there cannot be locomotion within theOne, since there are no empty spaces within it into which some part ofit might move.14 Parmenides' explicit argument against such internallocomotion issues from his concern over whether the putative physicallaws of the plenum might allow for a separation of the One into aplurality. He states,

Look upon things which, though far off, are yet firmly presentto the mind;

For you shall not split off (άποτμήζει) what-is from holding fastto what-is,

neither being dispersed (σκιδνάμενον) itself in every wayeverywhere in order,

Nor being gathered together (συνιστάμενον).(DK 28 B 4, trans. Gallop, with slight changes).

Parmenides contends that any process of dispersal and gathering (whichmight fracture the One into many), requires a splitting, or cutting, withinthe One. Such splitting is not possible, insofar as it would require theemergence of empty space (or void), i.e., the emergence of that-which-

14 See P.J. Bicknell, Tarmenides Refutation of Motion and an Implication', Phronesis12 (1967), 1-5; W.K.C. Guthrie, A History of Greek Philosophy, v.2, (Cambridge:Cambridge University Press 1965), 36; Owen, 1986 (/1960), 22-3, and John Malcolm,1991, esp. 85-7 and 91-4.



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is-not simpliciter, within the One and this is unintelligible.15 Thus, the Oneis completely immobile.

(5) The One is unalterable. Second among the non-basic features of theOne is its inability to undergo qualitative change. Parmenides contendsthat alteration within the One would require a mode of change that isindependent of locomotion and, consequently, alteration would requirethat some attribute, at a given location within the One, should perish,while another is generated in its place (DK 28 B 8.29-31). Since bothgeneration and perishing are prohibited on the grounds that they intro-duce negation and are, thus, unintelligible (DK 28 B 8.6-21), Parmenidescontends that the One is wholly unalterable.

(6) The One is phenomenally homogeneous. Last among the non-basicfeatures of the One is its lack of apparent differentiation. Since the Oneis complete in respect to time, space and quality, it lacks any internalvariability and, as such, it can only appear as a uniform mass.16 The Oneis phenomenally homogeneous.

Anaxagoras (1): Principles

Anaxagoras proposes four principles within his physics: the principle ofno becoming (PNB), the principle of universal mixture (PUM), the principleof predominance (PP), and the principle of infinite divisibility (PID).17 PNB is

15 What is especially interesting about Parmenides' treatment of the possibility ofgenerating a numerical plurality out of the One is his assumption that internallocomotion would require a cutting, or splitting, within the One and, thus, wouldrequire the generation of empty space. If Parmenides' argument is to work, it mustbe the case that dispersal and gathering can be achieved only through cutting. Yet,there is no necessary connection between these processes and cutting. For, cyclicalmotion causes dispersal and gathering, and it is conceptually possible for suchmotion to occur in a void-less plenum. (Strata's experiment of taking a sealed jarfull of water with a pebble inside and turning it upside down was meant to showas much. See J. Barnes, 1979, v.2,99.) Parmenides does not consider the possibilityof cyclical motion when he theorized about the plenum. But, Anaxagoras does. And(as we shall see) by supposing that cyclical morion can occur in a material plenum,Anaxagoras is able to bring plurality to light within Parmenides' One.

16 See Gallop, 1984,16.

17 For PNB, see DK 59 B 10 & 17; for PUM, see B 1,4,6, & 12; for PP, see B 12; and forPID, see B1,3, & 6.1 shall not discuss the supposed principle of homoiomerity, since,




Table 1ParmenldesThe One

Eternal VInfinitely extended plenum VPredicationally saturated VImmobile VUnalterable VPhenomenally homogeneous V

a Parmenidean legacy. But, as Anaxagoras understands this principle, itallows for the appearance of change within the cosmos: while there isneither true generation nor true destruction, there can be change as afunction of the redistribution of pre-existing things. Anaxagoras states,

The Greeks do not employ (the words) "coming to be" and "perishing"correctly, for nothing comes into being or is even destroyed; rather,from (pre-)existing things there is combining and breaking up. Theywould, therefore, be correct to call coming-to-be "combining"(συμμίσγεσθαι) and perishing "breaking up" (διακρίνεσθαι). (DK 59 B17, trans. Sider)

Other post-Parmenidean pluralists share this general view. But thespecial nature of Anaxagoras' physics becomes apparent once we con-sider his treatment of the basic material stuffs of the cosmos. Here PUM

on the evidence of the fragments alone, there is no basis for attributing this principleto Anaxagoras. For an excellent discussion of the logical relations amongAnaxagoras' principles, see D. Graham, 1994. The standard critical edition of thefragments with English translation is D. Sider, The Fragments of Anaxagoras: editedwith Introduction and Commentary (Meisenheim am Glan: Verlag Anton Hain 1981).A translation and commentary, by Patricia Curd, is due to be published in the nearfuture.



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and PP are crucial. According to Anaxagoras, each kind of thing that isis contained within each kind of thing that is. This is PUM. This principlerequires that a body of water (for instance) contains not only a portionof water but also portions of each and every other kind of thing that is.Such a body contains earth, flesh, heat, cold and all the other sorts ofthings that exist. What makes it water, as opposed to something else, isthat it has water as a predominant ingredient. The (phenomenal) sub-stance water is what it is, because there is more (elemental) water withinit than any other substance.18 This is PP. If the body of water were tochange, say, if some of the water were to disperse, leaving behind whatappears to be salt, this change would be brought about through aredistribution of things that had existed within the water (conjoined witha redistribution of some of the things that had existed outside of thewater). The deposit left behind would be salt, because salt would havebecome its predominant ingredient. (Yet the deposit would still have aportion of each kind of thing within it, including a portion of water.) Suchredistribution might be thought to introduce the possibility of pureelements and, as a consequence, place PUM in jeopardy. For, one mightsuppose that if we were to continue extracting the other elements fromthe sal t, we would eventually be left with a sample of pure salt. However,PID saves Anaxagoras' system from this inconsistency. P1D requires thatthere is no smallest bit of what is and, so, redistribution need not, andcannot, reveal a pure element.19 For whatever we might (mistakenly)

18 The distinction between phenomenal substances and elemental substances is intro-duced by C. Strang. See his 'The Physical Theory of Anaxagoras', Archiv f rGeschichte der Philosophie 45 (1963) 101-18. The distinction is merely a relative one.That is, while at one level of analysis Υ shall be an elemental substance within thephenomenal substance X, once some of this Υ is extracted from X, that which isextracted becomes a phenomenal substance which can, in turn, be analyzed in termsof the elemental substances which it contains. On Strang's account there is noultimate (or pure) elemental substance.

19 Graham argues that, if we assume the starting point of the Primordial Chaos,Anaxagoras' principles would be forever maintained in the cosmos only if one wereto posit a Law of Distribution such that ' ... if <any> Body A were divided intoBodies Β and C, the quantity of element Ε in A would be distributed between Β andC.' (Graham, 1994, 100). Graham supposes that, for Anaxagoras, this law is acontingent fact about the universe. My thesis implies that the Law of Distributionis motivated by the Parmenidean demand for predicational saturation.




suppose to be the smallest bit of a thing would still have room in it forbits of every other kind of thing.

And yet, to speak of T?its' of matter in Anaxagorean physics is,technically, a mistake. Anaxagoras did not propose a particulate theoryof matter and, if his theory is to hang together, one must suppose thatAnaxagorean 'things' are something like inter-penetrating fluids (orinfinitesimal powders).20 PUM, together with PID, suggests that matteris continuous and has the nature of a fluid. On Anaxagoras' view, thevarious phenomenal items that are constituted by matter are nothingmore than localized pockets in which one sort of fluid material predomi-nates over the other sorts. Thus, all change, on his model, reduces tolocalized shifts of predominance among the various types of matter.Further, these types of matter inter-penetrate one another to the extentthat there cannot be a location, no mater how small, from which any onetype is absent.21 Finally, Anaxagoras supposes that the cosmos is infinitein size.22 For, he not only flat-out states,'... [the] surrounding matter [ofthe heavens] is infinite in amount' (DK 59 B 2), but he also offers apositive rationale for taking reality to be both infinitely extended andinfinitely divisible. He states,

... of the small there is no smallest, but always a smaller ... Moreover,there is always (something) larger than the large; and it is equal to thesmall in plenitude, but in relation to itself it is both large and small. (DK59 B 3, trans. Sider)

Here Anaxagoras contends that for any given spatial magnitude there isnot only another that is smaller by a given proportion, but there is inaddition yet another that is larger by the same proportion. This explainswhy he thinks that any one thing can be said to be both large and smallin respect to itself. While some object may be half the size of a givenobject, there is yet another object that is double the size. Thus, any given

20 See Graham, 1994,102-4 and R. Sorabji, Matter, Space and Motion (London: Duck-worth 1988), 64.

21 Reeve puts this clearly, when he states, Tor every entity x, place p, and time t: x isat ρ at t: See his 1981,104.

22 Most scholars agree. For representative arguments see Sider, 1981,54; McKirahan,1994,227; Taran, 1965,152 and Schofield, 1980,83.



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object shall be in one respect a double and in another respect a half: itshall be large and small in respect to itself. So, Anaxagoras understandsthe cosmos to be an infinite sea of inter-penetrating fluid material, a seain which the predominance of some material in a given location deter-mines the nature of the phenomenal thing that is constituted at thatlocation.

It is generally acknowledged that the material principles of Anaxa-goras' physics are not sufficient to explain the occurrence of changewithin the cosmos. These principles might govern an entirely staticworld. And Anaxagoras seems to treat the cosmos as if it were up to aunique moment in time a static plenum. In order to explain the apparentemergence of change within the cosmos, Anaxagoras introduced a mo-tive cause. This cause is nous (or mind). Nous, he suggests, is responsiblefor the emergence of a whirl (or vortex) within the otherwise staticcosmos and this whirl sets off a redistribution of matter, which is thebasis for all subsequent change within the cosmos. By introducing nousas motive cause, Anaxagoras ostensibly divides the history of the cosmosinto two periods: an initial static period and a subsequent dynamicperiod.23 Let us consider each period in turn.

Anaxagoras (2): Primordial Chaos

Simplicius tells us that Anaxagoras began his book with the followingdescription of the Primordial Chaos:

All things were together, infinite in regard to plenitude; for the smalltoo was infinite. Since all things were together, nothing was clearbecause of smallness; for aer and aither pervaded all things, both beinginfinite. (DK 59 B 1, trans. Sider)

Anaxagoras' Primordial Chaos is an infinitely extended mass whichlacks any manifest characteristics. The Chaos has no evident nature,because aer and aither, themselves possessing opposed qualities (aer is

23 It shall be argued (below) that the bifurcation of the history of the cosmos is, forAnaxagoras, merely a heuristic device. There is, for Anaxagoras, not a singlemoment in the history of the heavens in which there is absolutely no motion.




dense, cold, dark and heavy, while aither is rare, hot, bright and light24),jointly predominate within the mixture. As a result, each of these twoelements prevents the other from becoming manifest. The Chaos, thus,remains as a murky and qualitatively indeterminate mass (a primordialsoup, if you will).

Recent discussion of Anaxagoras' theory has focused on the ways inwhich his account seems to challenge the Parmenidean world-view.25

Anaxagoras speaks of a plurality of 'things' (πάντα; DK 59 B 1.1), whereasParmenides speaks of a 'unity' (ev; DK 28 B 8.6). Further, Anaxagorassuggests that some things have existed in the past which do not exist inthe present and some things that exist in the present shall not exist in thefuture (DK 59 B 12.17-19), whereas Parmenides proclaims that what-isexists alone throughout all time (DK 28 B 8.5 and 8.14). In each case,Anaxagoras' language is in strict opposition to the language that we findin Parmenides' poem. However, such differences in language should notbe taken to suggest that Anaxagoras' Primordial Chaos fails to meet thedefinitional requirements for Parmenides' One. For, the Chaos does, infact, meet these requirements. First, the Chaos is complete in respect totime and space, and quality. It is eternal, lacking a beginning and lackingany internal temporal distinctions. It is infinitely extended, having nospatial boundary. And it is predicationally saturated: each positivepredicate can be meaningfully attributed to any location within theChaos. Thus, Anaxagoras' Primordial Chaos possesses each of the basicfeature of the One. Second, the Chaos is unmoved, unaltered, and, as astatic plenum, lacking any internal differentiation, it stands as a phe-nomenally homogeneous mass. Thus, the Chaos possesses each of thenon-basic features of the One. So, as Anaxagoras describes the PrimordialChaos, it meets each of the definitional requirements for Parmenides'One and, up to this point, Anaxagoras' physics does not stand in oppo-sition to Parmenidean Monism. Clearly, Anaxagoras posits the Primor-dial Chaos as a surrogate for Parmenides' One.

24 See Sider, 1981,47.

25 See Owen, 1974 (/1966), 276 and Schofield, 1980,Brought to you by | St Josephs University

Authenticated | 129.68.65.223Download Date | 9/3/13 2:35 PM

102 John E. Sisko

Table 2

EternalInfinitely extended plenumPredicationally saturatedImmobileUnalterablePhenomenally homogeneous

ParmenidesThe One

VVVVVV

AnaxagorasThe Chaos

VVVUnmovedUnalteredV

Anaxagoras (3): The Whirl

The Primordial Chaos is a uniform and undifferentiated sea of matter.Yet, once the whirl surfaces, we enter into a new age. This is an age ofseeming plurality: it is an age in which the world as we now it comes tobe formed. The cosmos of the whirl is a cosmos of motion and phenome-nal change. It is (in part) our familiar world of appearance. It is the veryworld that Parmenides rejects as illusory. For this reason, scholars stand-ardly suppose that the cosmos of the whirl fails to meet the definitionalrequirements for Parmenides' One. This, however, is not correct. A closeexamination of the fragments shows that Anaxagoras' dynamic cosmosis akin to the One. The cosmos of the whirl possesses each of the basicproperties of the One and it approximates each of its non-basic properties.Further, in regard to the limited differences (between the whirl and theOne), Anaxagoras provides a clear rationale for diverging from Par-menides' position.

Let us turn to the account of nous and the whirl. Anaxagoras states,

... Nous came to control the whole revolution, so that revolution wouldbegin (την αρχήν). And at first it began to revolve out from a small area(και πρώτον από του σμικρού ήρζατο περιχωρεΐν), it then revolves morewidely, and will revolve over a still greater area. And Nous gave heedto all the things coming together, separating out and breaking up; andwhatever sorts of things were to be — what were and are no longer,what are, and what will be — Nous put all in order, as well as thisBrought to you by | St Josephs University



revolution (την περιχώρησιν τούτην) through which now revolve thestars, sun, moon, aer, and aither which separated .... (DK 59 Β 12.13-21,trans. Sider)

Anaxagoras claims that nous, beginning from a small area, controls anever-expanding vortex. All change within this dynamic cosmos isbrought about through a cyclical redistribution of matter. But, thisredistribution can never be completed, owing to PUM together with theinfinite extension and infinite divisibility of the cosmos.

The cosmos of the whirl, like the Primordial Chaos, possesses the basicfeatures of Parmenides' One. First, this dynamic cosmos has no spatialboundary: it is infinite in size. Second, since the cosmos of the whirl isgoverned by PUM, it remains a predicationally saturated plenum. Andthird, since this cosmos is a development of the Chaos, it too is eternal.26

Anaxagoras' dynamic cosmos does not possess the non-basic proper-ties of Parmenides' One; for, within it, we find local motion together withphenomenal alteration and heterogeneity. However, this cosmos doesapproximate the non-basic properties of the One. First, it possesses globalphenomenal homogeneity. Since there is an unlimited quantity of matterwithin the cosmos and the relative portions of each type of matter remainconstant, aer and aither continue to jointly predominate throughout thehistory of the whirl such that the cosmos as a whole shall continuallyseem to be a static and qualitatively uniform mass. Yet, deep within thismass, localized shifts in predominance cause the emergence of phe-nomenal differences. And this certainly marks a departure from Par-menides' One. But, Anaxagoras does not beg the question againstParmenides in regard to phenomenal homogeneity. For Parmenidesdoes not offer an argument for homogeneity. He merely assumes thatthoroughgoing homogeneity would be an immediate consequence ofpredicational saturation. Anaxagoras shows us that Parmenides' as-sumption is faulty. He does so by developing an account that allows forphenomenal heterogeneity without sacrificing predicational saturation.While phenomenal heterogeneity is caused by localized shifts amongtypes of matter, no type of matter is ever excluded from any region of

26 One might argue that even if the whirl has no temporal terminus, it has a temporalbeginning and, thus, fails to be eternal. This would be correct, if Anaxagoras'bifurcation of the history of the heavens were not merely a heuristic device. It shallbe argued (below) that the whirl has no temporal beginning.



104 John E. Sisko

the cosmos (no matter how small that region might be) and, so, predica-tional saturation is maintained throughout.27 Thus, by introducing alimited form of non-homogeneity, Anaxagoras marks out a conceptualpossibility that Parmenides does not effectively preclude and he does sowithout doing violence to Parmenides' own basic definitional require-ments for the One.

Second, the cosmos of the whirl possesses global unalterability as animmediate consequence of its global homogeneity. And, in respect to itsbasic material make-up, no part of the cosmos is altered, since every partremains predicationally saturated. However, this cosmos fails to possessthoroughgoing unalterability and herein lies an obvious difference be-tween the whirl and the One. But, this difference is not, in itself, prob-lematic. For, on Anaxagoras' account, all (phenomenal) alteration iscaused by locomotion, while in Parmenides' argument against altera-tion, it is assumed that locomotion and alteration are functionally inde-pendent modes of change. So, we cannot impugn the propriety ofAnaxagoras' approach to alteration without first determining whetherhis position on locomotion is adequately justified. This suggests that ifAnaxagoras provides a plausible rationale for locomotion, then it cannotbe said that he begs the question against Parmenides in respect to eitherlocomotion or alteration.

Anaxagoras' dynamic cosmos is an infinitely extended plenum and,as such, it possesses global immobility. Simply put, it has nowhere to go.However, this cosmos lacks thoroughgoing immobility. The whirl isclearly a source of morion within an otherwise static plenum and hereinlies the crucial difference between the whirl and the One. Yet, oddlyenough, it is a difference that does no violence to Parmenides' explicitprohibition against motion. For Parmenides' argument against motionrests on the principle that what-is is a material plenum together with theauxiliary assumption that motion requires the existence, or emergence,of vacancies in space. A void-less plenum is, as he understands it,entirely 'chained up' and is, as such, immobile (DK 28 B 8.31). However,Parmenides does not consider the possibility of cyclical motion within

27 See Reeve, 1981,102-3. Linguistically speaking, it is not the case that all predicatesapply to every part of the cosmos. For, at the phenomenal level an object is what itmost is at the elemental level: the level of υποκείμενα. However, at the elementallevel all portions of the cosmos consist of every type of ύποκείμενον.




the plenum and this is precisely the sort of motion that Anaxagorashimself takes into account.

Anaxagoras suggests that cyclical motion is possible within a Par-menidean framework and this, in itself, is sufficient to circumvent Par-menides' own argument against motion.28 For all that Anaxagoras needshow is that cyclical motion does not violate any of the basic definitionalrequirements for the One. Clearly, cyclical motion does not jeopardizethe infinite extension of the One and it does not jeopardize the One'setemality. Rather, as Parmenides' own argument makes clear, the driv-ing concern is over whether motion would rob the One of its status as apredicationally saturated material plenum, by requiring the emergenceof empty spaces. Anaxagoras is keenly aware of this concern. For, in afragment that echoes Parmenides' treatment of dispersal and gathering(in DK 28 B 4), he suggests that the process of cyclical motion will notviolate the principle of predicational saturation.29 Anaxagoras states,

The stuff of this universe has not been separated (ου κεχώπισται) onefrom the other; not even with an axe has the hot been hacked from(άποκεκέπται) the cold, nor the cold from the hot. (DK 59 Β 8, trans.Sider)

Anaxagoras maintains that predicational saturation shall not be jeopard-ized within the cosmos of the whirl. The hot shall not be cleaved fromthe cold and no part of what-is shall be split off from what-is. Thus,together with Parmenides, Anaxagoras holds that no void-space can begenerated within the material plenum. Nevertheless, Anaxagoras goeson to provide empirically based arguments, which are meant to showthat cyclical motion is possible in a void-less plenum. Aristotle tells usthat Anaxagoras performed experiments with clepsydras in order to

28 Barnes develops a Neo-Melissian argument against the possibility of rearrangementthrough cyclical motion. He suggests that, since rearrangement is a form of altera-tion, Melissus' argument against alteration can be used to show the impossibility ofany motion that produces rearrangement See Barnes, 1979b, v.2,130-1. Anaxagoras'target is, however, Parmenides and not Melissus. Parmenides' own rejection ofalteration rests on the assumption that alteration is a mode of change which isindependent of locomotion. Thus, Parmenides' argument against alteration cannotbe used to defeat Anaxagoras' thesis.

29 Both Schofield and Coxon assert that DK 59 Β 8 echoes DK 28 Β 4. See Schofield,1980,63 and Coxon, 1986,188-9.



106 JohnE.Sisko

show that void does not exist.30 The experiments were not especiallycomplex. In the first experiment, Anaxagoras covered the top of aclepsydra, immersed it in fluid and then removed it, showing thatnothing had entered the air-filled chamber. In the second experiment, heimmersed the uncovered clepsydra, covered its top, and then removedthe clepsydra, showing that the fluid had (in this case) entered thechamber. These experiments not only provide some evidence against theexistence of void, they also provide evidence in support of cyclicalmotion. For the fluid entered the clepsydra only once the air that hadbeen trapped inside was permitted to cycle out. These experimentsprovide sufficient justification for the contention that cyclical motion,governed by PUM and PID, does not violate the basic definitional re-quirements for the One. And this suggests that Anaxagoras, whileadhering to Parmenides' basic definitional requirements, provides uswith a plausible rationale for diverging from Parmenides' position inregard to the One's non-basic properties. For, Anaxagoras' position oncyclical motion allows him to explain alteration as a function of locomo-tion and this is a possibility that Parmenides does not envision.

Table 3


ParmenidesThe One

VVVVVV

AnaxagorasThe Chaos One World

V VV VV VUnmoved Global 1.Unaltered Global U.V Global H.

30 See Aristotle, Physics IV 6,213a22-28; cf. de Caelo IV 2,309al9-26 and de RespirationeI 470b35-lal9. Empedocles performed similar experiments with clepsydras. SeeAristotle, de Respiratione 7,473b9-21.




We have found that, for Anaxagoras, the emergence of our worldwithin the Chaos does little to diminish its basic kinship with Par-menides' One. So, at this point we might be tempted to conclude that thefundamental unity of Anaxagoras' dynamic cosmos and the One hasbeen successfully maintained. However, as things stand, this conclusion isnot wholly justified. A problem remains. Anaxagoras claims that nous con-trols a revolution which '... at first... began to revolve out from a smallarea ...' (DK 59 B 12.13-14) and, so, he seems to propose the occurrence ofa first event. Surely this is how most scholars interpret Anaxagoras'claim.31 Yet, if this is correct, then we must admit that, however success-ful his journey has been up to this point, Anaxagoras' enterprise is ulti-mately ruined, owing to a collision with Parmenides' prohibition againsta first event. This seems to be a serious problem, but, thankfully, the frag-ments show us a way to navigate through it: the textual evidence sug-gests that Anaxagoras dodges the problem of a first event.

Anaxagoras (4): A First Event?

It is thought that the only way for Anaxagoras to avoid the problem ofa first event, would be for him to specify a feature of nous or of the Chaosthat accounts for the initiation of the whirl.32 Along these lines, it hasbeen suggested that nous, being cognizant of the features of the Chaos,might have chosen the correct time and place for initiating the whirl.However, this suggestion falls flat, since each time and each place withinthe Chaos differs in no substantive way from any other time or place.33

31 See Owen, 1974 (/1966), 279-82; Schofield, 1980,9-10; Reeve, 1981,103; Sider, 1981,102-4; McKirahan, 1994, 223-4; and Felix Cleve, The Philosophy of Anaxagoras (NewYork: Columbia University Press 1949), 131.

32 See McKirahan, 1994, 224. McKirahan insists that Anaxagoras fails to circumventthe problem.

33 Graham suggests the view that I criticize. He states: 'Choosing, then, the correcttime, place, and rate of morion for an incipient vortex, Mind can set in order allthings past, present, and future' (Graham, 1994, 111). This approach leavesAnaxagoras with, not only the temporal problem of a first event, but with an addedspatial problem. For, given that the Chaos is infinite in extension, there is nosufficient reason for having the vortex emerge at any one location as opposed toanother.



108 John E. Sisko

It might also be suggested that nous could have initiated the whirl out ofsheer caprice. But, there is no textual evidence to support this view.

Another approach to the issue is suggested by Simplicius. He states,'[Anaxagoras] ... assumed a beginning of cosmogony [just] for thepurpose of a didactic arrangement of presentation.'34 Of course, if therewere no temporal beginning of the whirl, then Anaxagoras would nolonger be faced with the problem of a first event and α fortiori he need notspecify some feature of nous or of the Chaos in order to explain theinitiation of the whirl. Simplicius, in discussing Anaxagoras' cosmog-ony, is motivated to provide an interpretation that harmonizes withparts of his own account of Plato's cosmogony in the Timaeus. Thismotivation is highly dubious. But, whatever the cause, Simplicius' sug-gestion is worth exploring. It is, in fact, dead-on right. An examinationof the fragments strongly suggests that Anaxagoras treats the history ofthe cosmos as if it were divided into two periods only so that he mighteffectively mark out the important similarities between his own cosmol-ogy and Parmenides' account of the One. Anaxagoras' division betweenthe static Chaos and the dynamic whirl is a matter of heuristic conven-ience and Anaxagoras himself understands the cosmos of the whirl to be(strictly) eternal.

Let us begin by considering some details from Empedocles' cosmol-ogy. Empedocles is a contemporary of Anaxagoras. He too is a post-Par-menidean pluralist. In response to Parmenides, Empedocles maintainsthat all seeming generation and destruction is the product of an unend-ing cyclical process involving eternal and unchangeable elements. Em-pedocles' cycle has four stages (see DK 31Β17,22,26 and 35). First, underthe complete dominion of Love, the cosmos is an homogeneous mixtureof the four elements. Second, under the ascendancy of Strife, the cosmosis a dynamic mass in which unlike elements separate from one another.This process of separation continues until we reach the third stage, whenStrife has complete dominion and the cosmos is a perfectly heterogene-ous whole, consisting of four nested levels, one for each element. Finally,Love begins its own ascendancy, drawing unlike elements together, untilit once again comes to have complete dominion over the cosmos. WithinEmpedocles' cycle, the world as we know it comes to be formed in one,if not in each, of the dynamic stages of ascendancy. Importantly, in

34 Simplicius, in Physica 1121,21Brought to you by | St Josephs University



Empedocles' system there is no initial cosmogonical happening and, so,Empedocles' does not run afoul of the problem of z first event. His cyclehas neither a temporal beginning nor a temporal end. But, this truth doesnot keep Empedocles himself from occasionally speaking as if his cycledid have a beginning. For example, he states:

But come, I shall first tell you the beginning (αρχήν)... from which allthat we now look upon came to be clear, earth and sea with many wavesand moist air and the Titan aither, squeezing all things round about ina circle. (DK 31 Β 38, trans. McKirahan)

For ease of exposition, Empedocles lapses into treating the start of aperiod of ascendancy as if it were a first event and he does this eventhough he knows that there is no true cosmogonical beginning withinhis own system. Anaxagoras' own occasional mentions of a beginningcan, and must, be understood in the same way.

Consider Anaxagoras' statement that the nous-caused whirl'... at first... began to revolve out from a small area (και πρώτον από σμικρού ήπξατοπεριχωρεΐν) ... ' (DK 59 Β 12.13-14). This claim can be understood tosuggest, not an unqualified first moment of change within the Chaos,but a phenomenal beginning to some one stage in the development of adynamic cosmos. Other claims made by Anaxagoras show that this viewis to be favoured. Anaxagoras states that 'nous put all in order, as wellas this revolution (την περιχώπησιν ταύτην) through which now revolvethe stars, sun, moon, aer, and aither which separated' (DK 59 Β 12.18-21).Here Anaxagoras' use of the demonstrative pronoun, ταύτην, suggeststhat there is more than one stage in the expansion of the dynamic cosmosand that our world (with its stars, sun and moon) constitutes just oneamong these stages (or revolutions). More forceful support for this viewcan be developed from DK 59 Β 12. There Anaxagoras claims that thewhirl' ... began to revolve out from a small area (άπο του σμικρού) ... 'and we have already learned a good deal about Anaxagoras' conceptionof the small. According to Anaxagoras, neither the small nor the large isobjectively what it is named. Rather, each thing is both small and largein respect to itself (see DK 59 Β 3). This requires that whatever area mightbe considered, at one level of analysis, to be small is, at another level ofanalysis, vastly large. So, it follows that the small area from which thewhirl purportedly first emerges is also, at the same time, an enormousarea within which there must also be a small region from which the whirlfirst emerges. Further, this second small region is additionally, at thesame time, a large area within which there also must be a small regionBrought to you by | St Josephs University


110 fohn E. Sisko

from which the whirl first emerges. This pattern of emerging whirls (orwhirlings) continues ad infinitum into the temporal past. So, it turns outthat Anaxagoras' whirl has no beginning: there is, for Anaxagoras, nofirst event. The whirl has always existed, in smaller and smaller regionsof extended reality, and it shall never cease to exist, for it expandscontinually into larger and larger regions of the Chaos. The dynamiccosmos of the whirl is strictly eternal.

Anaxagoras (5): Another World

Now that we have come to see how Anaxagoras circumvents the prob-lem of a first event, our final question is whether, given his emphasis onthe recurrence of structure-within-structure, Anaxagoras postulates theexistence of multiple worlds.35 Famously, there is one fragment in whichAnaxagoras speaks of another world. He states,

These things being so, it is necessary to suppose that in all things thatare being mixed together there are many things of all kinds ... and thathumans too were compounded and all other animals that possess life;and that there are inhabited cities and cultivated fields for the humansjust as with us, and that there are for them a sun and a moon and therest just as with us, and that the earth grows many things of all kindsfor them, of which they gather the most useful into their dwellings anduse it. I have said these things about the separating off, because it wouldhave occurred not only with us, but elsewhere too. (DK 59 B 4a, trans.McKirahan)*

Anaxagoras suggests that there is another world just like our own andthis second world has come to be formed through the same processesthat have formed our own world. Scholars have offered a variety ofinterpretations of this passage: (1) It has been suggested that Anaxa-goras' other world had existed only in the distant past prior to the genesis

35 I have borrowed the phrase 'structure-within-structure' from Mansfeld, 1980,3.

36 In addition to this fragment, Simplicius quotes a passage from Theophrastus inwhich it is said that Anaxagoras discussed the generation of 'the worlds'. (Sim-plicius, in Physicu 27.15-17)




of our own world.37 (2) It has been suggested that the other world is nota unique world at all, but merely some other inhabited location on thesurface of our Earth.38 (3) It has been suggested that the other worldexists, like an atomist world, being roughly the same size as our world,but occupying a different region in space.39 (4) And it has been suggestedthat the other world is a microscopic world, a dimunitive world, whichsomehow exists within our own world.40 Much ink has been spilled overthis issue. But when we consider the texts, it becomes evident that theonly location available for this other world in Anaxagoras' system iswithin our own world. First, the other world exists at the same time asdoes ours; for Anaxagoras uses the present indicative to describe theactions of humans in that world.41 So, interpretation (1) is untenable.Second, the other world is not some other location upon our Earth, forAnaxagoras claims that it has both a sun and a moon: he does not saythat it has the sun (that is, our sun) or the moon (that is, our moon).42 So,interpretation (2) is untenable. And third, the other world is not anatomist world, for Anaxagoras never speaks of a plurality of vortices,which might cause like-sized worlds to appear here and there through-out the heavens.43 Anaxagoras speaks only of one vortex and he speaks,quite explicitly, of just one cosmos (τφ ένί κοσμώ; DK 59 B 8): one orderedwhole. So, interpretation (3) is untenable. By comparison, nothing thatAnaxagoras says stands in opposition to the thesis that a microscopic

37 This view is suggested by Simplicius only to be immediately rejected. See Sim-plicius, in Physica 157.18-20; cf. Malcolm Schofield, 'Anaxagoras' Other WorldRevisited', in Keimpe Algra, Pieter van der Horst, & David Runia, eds. Polyhistor:Studies in the History and Historiography of Ancient Philosophy (Leiden: E.J. Brill 1996),3-20, esp. 5.

38 This view is championed in P.M. Cornford, 'Innumerable Worlds in PresocraticPhilosophy', Classical Quarterly 28 (1934), 1-16.

39 J. Bumet defends this view in his Early Creek Philosophy, 4th ed. (London 1930),269-70.

40 Versions of this view are defended in P. Leon, 'The Homoiomeries of Anaxagoras',Classical Quarterly 21 (1927), 133-41; Mansfeld, 1980; and Schofield, 1996.

41 See Simplicius, m Physica 157.18-20; cf. Schofield, 1996,5.

42 See Simplicius, in Physica 157.20-24; cf. Schofield, 1996,5.

43 See Mansfeld, 1980,3.Brought to you by | St Josephs University


112 JohnE.Sisko

world exists within our own world. Further, once we are confronted withthe possibility of a single microscopic world, Anaxagoras' own generalemphasis on the repetition of structure-within-structure in infinitelyexpansive and infinitely divisible space suggests the existence of aplurality of such worlds. A plurality thesis of this sort (and in thiscontext) has been articulated in a pair of ways: First (4a), it has beensuggested that, for Anaxagoras, a multitude of microscopic worlds isspread throughout or own world, existing like quasi-Leibnizian worldsin every bit of available matter.44 Second (4b), it has been suggested that,for Anaxagoras, a plurality of microscopic worlds exists at smaller andsmaller levels nested concentrically within our own world.45 The latterinterpretation (4b) is the more plausible of the two. First, 'world', as atype, is not among the basic stuffs (or basic sortals) in the PrimordialChaos. So, worlds are not subject to PUM and we should not expect themto exist, just like Anaxagoras' basic material stuffs (such as water andsalt), in all things. Yet, the quasi-Leibnizian view places worlds in allthings. Second (and more importantly), since the genera tive cause of anymicroscopic world must be the one vortex that has generated our ownworld, we should expect that any world other than our own will becentered about the locus of the vortex, just as our world is centered aboutthis locus. Yet, the quasi-Leibnizian view places worlds eccentricallywithin the vortex. Third (and most importantly), if the whirl, prior toforming our world, had been expanding from the infinite past with itsown unique pattern of motion, then we should expect that this motionhad effects at (what is for us) the microscopic level that are akin to theeffects which it now has at our own macroscopic level. Given the eternalexpansion of the whirl, we should expect a series of nested worlds.Finally, there is a clear and tractable logic to this view: once we have asecond world within our own, the notion that that world is just like ourown suggests that it too may have another world nested within it. Andsince our own world is just like that other world (the second one), our

44 This view is defended in Leon, 1927, and in Schofield, 1996.

45 This view is defended in Mansfeld, 1980. Schofield offers his account as a defenseof Mansfeld's position, but he sanctions the Leibnizian view, whereas Mansfeldenvisions a plurality worlds contained successively within one another; for hecompares these worlds to 'tins of Droste chocolates, on one side of which a girlappeared who held such a tin of Droste chocolates picturing the same girl holdingthe same tin, etc.' (Mansfeld, ibid., 4 n 11.).




world may itself be nested within another larger world. So, the textualevidence clearly suggests that, according to Anaxagoras, there exists avast series of worlds nested within worlds lying concentrically withinthe Chaos.46

Interestingly, an Anaxagorean theory of worlds within worlds standson par with the theory of a lone world that is commonly attributed toAnaxagoras, when it comes to any link with Parmenides' definitionalrequirements for the One. The universe of multiple worlds is eternal. Itis, in fact, strictly eternal, whereas, on the common view, a loneAnaxagorean world requires a temporal beginning, a triggering firstevent. Further, the universe of worlds within worlds remains both infi-nitely extended and predicationally saturated. It possesses global immo-bility and global unalterability, not to mention global homogeneity.

Table 4


ParmenidesThe One

VVVVVV

The Chaos

VΛ/

VUnmovedUnalteredV

AnaxagorasOne World Many Worlds

V VV VV VGlobal 1. Global 1.Global U. Global U.Global H. Global H.

46 Each of these worlds must be so large compared to the one below it that the onebelow is (relatively) microscopic and, thus, imperceptible. But, even if the worldthat is nested immediately below our own is so small that it is not within our powerto perceive it, one might ask why it is not possible to perceive the world that isimmediately above our own. In response, Anaxagoras could suggest that as we gazeupon the heavens, we gaze upon a body in which aer and aither predominate and,thus, from our vantage point, the world above us must be Imperceptible: it is, in amanner, swallowed up by the aer and aither which jointly predominate within thewhole of physical reality.



114 fohnE.Sisko

In conclusion, this investigation has revealed a limited solution to thelong-standing puzzle. In so far as the puzzle concerns the relationbetween Anaxagoras' physical theory and Parmenides' arguments, weneed not suppose that Anaxagoras somehow fails to adequately considerParmenides' basic principles. Anaxagoras does not attack these princi-ples, because he takes them to be compatible with a specific sort ofpluralism. Anaxagoras not only provides a brilliant explanation of theemergence of our world within the Chaos, he also posits a bold cosmol-ogy of worlds within worlds within the Chaos. And since his Chaos isParmenides' One, Anaxagoras offers an essentially Parmenidean cos-mology: a cosmology of worlds within worlds within the One.47

Department of Philosophy and ReligionThe College of New Jersey

PO Box 7718Ewing, NJ 08628-0718

U.S.A.e-mail: [email protected]

47 Earlier versions of this paper have been read at Notre Dame, New York, Ewing, SanBernardino and Budapest, Hungary. I would like to thank Sarah Broadie, PatriciaCurd, Brie Gertler, Daniel Graham and Tony Roy for especially helpful commentson earlier drafts. In addition, I would like to thank the editor and my threeanonymous referees for useful advice and guidance. All errors are my own.



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