Doxographical Reverberations of Hellenistic Discussions on Space
1 Four Placita chapters and a parallel
Four chapters in ps.Plutarch’s Placita contain doxai pertinent to Hellenistic discussions on space. I cite the chapter numbers and their headings: 1, 18, On void (Περὶ κενοῦ), 1, 19, On place 
1, 20, On space 
,418 and 2, 9*,419 On what is outside the cosmos, whether a void exists 
μου, εἰ ἔστι κενόν).420 They have not been transcribed by Eusebius, but were translated into Arabic by Qusta ibn Luqa (accessible in Hans Daiber’s German translation). In Stobaeus’ Anthologium, 1, 18, the lemmata of all four chapters have been coalesced with some changes and an omission (and in the usual Stobaean way combined with other material)421 in a chapter with the collective heading On void and place and space 
No trace of the heading of Plac. 2, 9* is found in the Anthology or in Photius’ index. Theodoret, Graecarum
affectionum curatio 4, 18, only provides excerpts (from Aëtius) corresponding to Plac. 1, 18, and only this chapter, again, is excerpted from ps.Plutarch by ps.Galen, Historia philosopha ch. 30.
Book 1 of Aëtius is concerned with the principles and elements of physics and the accompanying main concepts, while Book 2 turns to what follows therefrom.422 But subjects and themes may sometimes overlap from Book 1 to Book 2 and conversely, at least to some extent. The lengthy and detailed ch. 1, 4, How did the cosmos come to be, could also have been located in the cosmological Book 2; its theme is related to those of chs. 2, 4*, Whether the cosmos is indestructible (the lemmata include references to its generation) and 2, 6*, From what kind of first element did the god make the cosmos. Aët. 1, 5, Whether the All is one, shares some of its material and issues with 2, 1*, On the cosmos. The same holds for two of the chapters at issue now, Aët. 1, 18, On the void, and 2, 9*, On what is outside the cosmos, whether a void exists. In Book 1, which is for the most part conceptualist, chapters 1, 5 and 1, 18 comprise cosmological ingredients, and so are not purely conceptual. In the proem to the whole work the questions “whether the cosmos is infinite, and whether there is something outside the cosmos” are instances of a theoretical issue in physics423 (according to the Peripatetics) as distinguished from one in ethics. Such theoretical questions clearly may have both a general and preliminary character, i. e. a conceptual character and a more specific one, i. e. one at home in a cosmological context. Without doubt a proprium originis, attesting to the tenacity of the tradition, is also at issue.424 Aristotle discusses the void both in the Physics and in On the Heavens: in the Physics especially at 4, 6 – 9, chs. 6 – 8 being about void per se and the assumption of a void outside the cosmos, ch. 9 about internal void; in On the Heavens in chs. 1, 9. 2, 4. 3, 7 and 4, 2.425 Place is discussed in Physics 4, 1– 5. The chapter headings 
(1, 18) and 
(1, 19) are paralleled in Aristotle as embedded references to the subjects treated, but 
(1, 20) is not paralleled in this way – not only in Aristotle, but nowhere else in this sense.426
Recently the remains of a Commentary on the Categories preserved in the Archimedes Palimpsest have been published. Illustrating the fourfold classification “of things there are” at Cat. 2, 1, a20 – b9, the author cites two examples of a division into four, both of which are concerned with the attribution of two attributes to one subject. To facilitate understanding, these examples deal with the cosmos.427 The first example deals with the four ways in which the attributes “generated” plus “destructible” can be predicated of “cosmos”,428 and does not concern us here. The second example deals with the four ways in which the attributes “inside (the cosmos)” and “outside the cosmos” can be predicated of “void”.429 After the restoration of the text, this passage contains four doxai, two of which are paralleled in ps.Plu. Plac. 1, 18, and one in 2, 9*. Accordingly, it agrees with Stobaeus’ comprehensive treatment of the material. I discuss and compare this passage first:
[…] as void is believed to be place bereft of body, and as we take what is ‘inside’ and ‘outside of the cosmos’ as two, we shall say, when the void, being one, is qualified according to two (predicates), that four propositions come about according to a division:
(1) either there is void both outside and inside the cosmos, as Democritus and Epicurus held,
(2) or neither inside not outside, as Aristotle and Plato [held],
(3) or outside but not inside, 
as the followers of Zeno [held],
(4) or inside but not outside 
, as Strato supposed […].430
It is important that the commentator calls this a presentation “according to a di vision”, διαίρεσις. David Runia has emphasized that in the majority of cases the doxai in a Placita chapter are indeed presented according to a diaeresis. This entails that a problem is cut up into a multiplicity of views, which are arranged according to affinity and contrast.431 That the lemmata are here called propositions, προτάσεις, and not δóξαι or δóγματα or κεφάλαια, is due to the fact that this commentator on a logical treatise is concerned with the attribution of predicates. Both his examples correspond to material that was readily available in a doxographical treatise.
The four lemmata of his second example are not concerned with the bare existence, or not, of the void per se, as is the case at Plac. 1, 18, 1– 3, but with the void in relation to the cosmos, as is the case at Plac. 1, 18, 4 – 6 and in all four lemmata of ch. 2, 9*.432 Yet the heading of the latter chapter (quoted above) intimates that the issue of the existence or not of the void is included, and this is confirmed by the content of its lemmata. The first lemma of the passage in the Commentary is exactly paralleled at Plac. 2, 9, 4*; the second is not exactly paralleled either in ch. 1, 18 or in ch. 2, 9*, but only partially at 1, 18, 3; the third is virtually exactly paralleled at 1, 18, 5, and the fourth at 1, 18, 4 – accordingly, as pointed out already, the parallels are divided over the two Placita chapters.
In the world of the Placita and the wider doxographical tradition the Hellenistic schools and philosophers coexist (far from always peacefully) with the Presocratics, with Plato and Aristotle and their followers, with astronomers, doctors, and even with historians. In the four Aëtian chapters that concern us here the troupe consists of philosophers only:
Presocratics: the physicist followers of Thales up to Plato (1, 18, 1), the followers of Pythagoras (2, 9, 1*), Empedocles (1, 18, 2), Leucippus, Democritus, Demetrius and Metrodorus (1, 18, 3);
Plato (1, 18, 1. 1, 19, 1. 2, 9, 4*);
Aristotle (1, 18, 6. 1, 19, 2. 2, 9, 4*);
and Hellenistic philosophers: Epicurus (1, 18, 3. 1, 19, 2), Strato (1, 18, 4. 1, 19, 3), Zeno and his followers (1, 18, 5. 1, 19, 1, plus the Stoics 2, 9, 2*) and Posidonius (2, 9, 3*).
We recognize (sections of) the Successions of the Philosophers: the Ionian diadochē, viz. Thales to Plato, at 1, 18, 1, and the Italian diadochē, viz. the followers of Pythagoras, at 2, 9. 1*. We should note that the two successions are implicitly referred to in the first lemma of their respective chapters, where they are often placed. We also note an Atomist diadochē ending with Epicurus, at 1, 18, 3, which is a section of the Italian or Eleatic Succession.
2 On void
The agenda with the question-types to be treated when dealing with the void was set by Aristotle at the beginning of his discussion of this issue, “the philosopher of nature has to inquire about the void, whether it is or not, and how it is, and what it is”.433 He also stipulated that a discussion of opposed views is needed: “We must begin the investigation by looking at what those who say that it [scil. the void] exists say, and what those who deny this, and thirdly at the common views”.434 The representative of those against in this chapter of the Physics is Anaxagoras (not mentioned explicitly at Aët. 1, 18, 1, but not excluded either), while those in favour are represented by “Democritus and Leucippus [cf. Aët. 1, 18, 3] and numerous other natural philosophers”, and subsequently also by the Pythagoreans [cf. 2, 9, 1*].
The heading of ch. 1, 18, 
, is an example of the bland περί-plus-genitive type that predominates in the Placita. That of 2, 9*, 
κόσμου, εἰ ἔστι κενόν, tells us a bit more by means of the additional specification formulated in its second part, “whether a void exists”, especially if we accept the translation by Mansfeld / Runia 2009b. A different translation is also possible, viz. “whether it (scil. what is outside the cosmos) is a void”. But the final lemma of 2, 9*, “Plato and Aristotle (declare that) there is no void either outside the cosmos or inside it” shows that the translation of Mansfeld / Runia 2009b is to be preferred.
The followers of Pythagoras, the Stoics, and Posidonius, listed in 2, 9, 1 – 3*, variously posit the existence of a void outside the cosmos, so answer the question
posed in the chapter heading in the affirmative. Plato and Aristotle, found at 2, 9, 4*, answer the question in the negative. This entails that in 2, 9* the question-type εἰ ἔστιν ἢ 
is at issue, and that both those in favour and those against have been recruited, on either side of a diaphōnia.435 Though the bland heading of 1, 18 is silent on this point, the contents of the chapter’s lemmata show that the question-type of existence is certainly at issue here too: the physicist followers of Thales up to Plato and Empedocles in 1, 18, 1– 2 reject the void, while the philosophers listed in 1, 18, 3 – 6 posit the existence of the void in various ways. And while in 2, 9* the purported void inside the cosmos is only mentioned in a final lemma that denies its existence, the possibility of a void inside the cosmos is admitted in 1, 18, 4, under the name-label of Strato, but denied by Zeno and his followers.
The question-type of the 
ἔστι (attribute) is represented by two categories. The first half of the heading of 2, 9*, “On what is outside the cosmos”, clearly pertains to the (originally Aristotelian) category of the ποῦ, of place, and the first three lemmata of the chapter accordingly locate the void outside the cosmos; the varieties are something that is of unknown size, or something infinite, or something just large enough to expand into. The nature of these varieties shows that also the category of the ποσóν, of quantity, is involved. These two categories are also at issue in 1, 18. Quantity in 1, 18, 3, where the atoms are infinitely many and the void infinite in size (number and size being standard subdivisions of this category), in 1, 18, 5, where the void outside the cosmos is infinite (scil. in size), and in 1, 18, 6, where (cf. 2, 9, 3*) it is just large enough to breathe into. Place is relevant to 1, 18, 4: no void outside but possibly inside the cosmos; in 1, 18, 5, no void inside but infinite void outside the cosmos;436 and 1.18.6, a void outside the cosmos large enough to sustain breathing.
The category of οὐσία, substance, and the question-type τί ἐστι, “what is it”, are not at issue in either ch. 1, 18 or 2, 9*. For we are not told what the void is, that is, are not provided with a definition, but only hear where it is, or may be, located, and/or how large it is – provided it does exist. For a definition437 we have
to go to ch. 1, 20, 1, under the name-label of Zeno and his followers: τὸ μὲν κενὸν 
, “the void is a vacancy of body”.
Surprisingly enough there is no reference in 1, 18 and 2, 9* (or, for that matter, in 1, 23, On motion) to the well-known view of Melissus or the Atomists that motion is only possible if a void exists, or because of the existence of the void,438 which plays such an important part in Aristotle’s discussion of the issue. Its inclusion would have permitted the deployment of the question-type of the cause or explanation, διὰ τί, familiar of course from the Problemata literature and represented four times with this formula in the headings of other Placita chapters, and once in the text.439
The Hellenistic philosophers mentioned in this chapter are Epicurus (firmly anchored to an earlier tradition as the last representative of a Succession of Atomists beginning with Leucippus), Strato, and Zeno and his followers. We should recall that ps.Plutarch omits the Strato lemma. The doxa in the lemma dealing with Epicurus, 1, 18, 3, 
, τὸ 
, is virtually identical with part of the doxa attributed to Epicurus at 1, 3, 18, 
… 
σώματα ἄπειρα. That is to say, notwithstanding the presence of other Atomists at 1, 18, 3, the doxa is Epicurean (as formulated in the Placita) rather than Leucip-pean or Democritean (as in Aristotle), or Metrodorean.440 The doxa of the lemma has been updated. Accordingly, the Hellenistic philosophy of nature is represented by the two rival schools, that of Epicurus and that of Zeno, characterized as distancing themselves, each in its own way, from the Ionian tradition from Thales to Plato (and including Empedocles); with a small similar role for Strato. One would have expected Aristotle to join Plato, as happens at 2, 9, 4*, but in the present chapter – if my preference for the lemma as transmitted in P is right – he is turned into a (quasi)-Pythagorean, and made to join the company of the Hellenistic supporters of the void. In the parallel chapter in the related doxography of Achilles, Isag. ch. 8, we find the same positions on either side of the diaphōnia:441 the views of Epicurus and the Stoics (the latter in a Posidonianesque
version) are opposed to that of Anonymi who deny the existence of the void; their arguments suggest that Aristotle may be behind them.
3 On place
The agenda with the question-types to be dealt with in ch. 1, 19 was set by Aristotle, just as for ch. 1.18, and in identical terms.442 Our chapter 
has only three lemmata against the six lemmata of ch. 1,18. It contains three different definitions of place, with the name-labels Plato, Aristotle, and Strato, and so is concerned with the category of substance and the question-type of “what is it”. The bland heading of the standard περί-plus-genitive-type could easily have accommodated the extensions 
, which occasionally appear in headings of Placita chapters.443
The question-type of the attribute (
) is also at issue, viz. in the various qualifications of the idea of place in each of the three lemmata. And because it is “about place”, the chapter is, obviously, also concerned with the category of place–per se, so to speak, but also, paradoxically, with the place of “place”. For two opposed doxai are cited at 1, 19, 2–3, the first of which (under the name-label of Aristotle) places place at the periphery of the object, as “the outermost of what surrounds connecting with what is surrounded”, 444 while the other (name-label Strato) locates it inside, as “the interval between what surrounds and what is surrounded”.445 The question-type of existence, which plays such an important part in Aristotle’s account of place, is not at issue in the chapter.
In his discussion of 
in the Physics Aristotle lists exactly four possible denotations: (1) form (
or ), (2) matter (ὕλη), (3) the interval between the extremities, and (4) the extremities themselves, and then argues in favour of the fourth. These different possibilities are also listed by, e. g., Sextus Empiricus and Simplicius,446 and so may be seen as having become standard. Of these four, three are present in our chapter of the Placita (2) matter, (4) the extremities, and (3) the interval between the extremities. So the first listed, 
as form, is lacking, presumably because it had never been adopted. Aristotle himself cites a
view of Plato as instantiating (2), ὕλη, while his own view turns out to be (4) –see below, p. 190.
The first lemma of 1, 19 is “Plato (said place is) what partakes (τὸ μεταληπτικóν)447 of the Forms as a sort of wet-nurse and recipient; he has metaphorically denoted matter (
)”. This is a virtually verbatim reproduction of a conflation of two passages in Aristotle (with the addition of Platonic designations of χώρα) that provide a critical account of Plato’s view of space. Interpreting the third principle of the Timaeus not entirely correctly,448 he affirms that
Plato says in the Timaeus that matter (
) and space (
) are the same; for what partakes (τὸ … μεταληπτικóν) and space (
) are one and the same thing. His account of what partakes differs in the Timaeus and the so-called Unwritten Doctrines, but he still declared that place and space are the same (
ἀπεφήνατο). […] One has to inquire of Plato […] why the Forms and numbers are not in place, if place is what partakes [scil. of them] (
).449
Our lemma combines the phrase about participation in the Forms with the identification of what participates as place. Aristotle adds that Plato is the only one among his predecessors who provided a definition of τóπος, as the others are merely assuming its existence.450
We duly note that the lemma at 1, 19, 1 belongs with the set of Placita abstracts derived not directly from the original source, but from Aristotle’s critical reportage. By this interpretative move Plato’s view of 
is made to dovetail into the pattern of the four options, filling the slot of (2), “matter”. This background also helps to explain the presence of the lemma under the heading 
rather than under 
. We also note that Aristotle’s claim (not reproduced in the lemma) that according to Plato place and space are one and the same preludes upon the theme of Aët. 1, 20, where the differences, or lack of difference, of the reference(s) of void, place, and space are at issue. The
suppressed or at any rate hidden past of the lemma apparently contributes to the thematic agenda of our triad of Placita chapters.
Aristotle’s definition at 1, 19, 2, “(it is) the outermost of what surrounds connecting with what is surrounded”, is a shorter version of one of the formulae in Physics Book 4, 
.451 It corresponds to the last of the four options listed above, i. e., (4) the extremities themselves.
The definition attributed to Strato at 1, 19, 3, “(it is) the interval between what surrounds and what is surrounded”, corresponds to the third of these options, (3) the interval between the extremities.
Accordingly, the theme and structure of this chapter, as well as the gist of the alternative definitions it provides derive without exception (but with some loss of issues to be discussed) from Aristotle’s dialectical overview in Book 4 of the Physics. The only Hellenistic philosopher present in 1, 19, Strato, must have been included because he actually defended theoretical position (3), the interval between the extremities. We may assume that the Stoic452 and Epicurean definitions are not cited because they can be subsumed under (3),453 but the name-labels could of course have been added to the lemma. In other words, it is Strato, and Strato alone, who is made to represent Hellenistic philosophy here, so it is true to form, but nevertheless unsatisfactory, that ps.Plutarch omitted this lemma.454
4 On space
For the agenda of this chapter there are no antecedents in Aristotle, apart from his point that Plato identifies 
. The bilemmatic ch. 1, 20, Περὶ χώρας, provides Hellenistic views only, with the name-labels Zeno and his followers and Epicurus. No Presocratics, Plato, or Aristotle this time. The chapter, a sort of semantic appendix to chs. 1, 19 – 20, is an example of the smallest type of Placita chapter in which a conflict of opinion can still be presented. The heading ,
again of the bland περί-plus-genitive type, significantly fails to represent the contents. Qua heading of a treatment or discussion of space or place this formula only occurs again as late as Psellus.455
The lemmata are not concerned with a multiplicity of views about χώρα alone, but with the difference between the Stoics and Epicurus regarding their use of the three interconnected terms κενόν, τόπος, and χώρα.456 It is clear that the specifically Hellenistic theme of the chapter called for separate treatment. Its heading was formulated pour le besoin de la cause, that is, to stress the link with the two previous chapters, the term χώρα being still available (so a fine distinction with the meaning of κενόν and 
is maintained in the heading). We have of course seen that the κενόν is dealt with in ch. 1, 18 (and then in 2, 9*), and 
in ch. 19. Zeno and his followers plus Epicurus are among the authorities cited in ch. 1, 18, but are absent in ch. 1, 19. Brief definitions of each of these three concepts are cited for the Stoics,457 but not for Epicurus. As a matter of fact we are not told at all what Epicurus meant by these terms, and at ch. 1, 18, 3 we were merely informed about the infinity of the void according to Epicurus, not about what it is according to him.
The contrast between Stoics and Epicurus as to the semantic distinctions or lack of distinction between the three terms at issue is paralleled in Sextus,458 but with an important difference. Aëtius posits that the Stoics attributed a different meaning to each term, while Epicurus used them interchangeably. But Sextus, who mentions Epicurus first and the Stoics in the second place, attributes to Epicurus distinctions similar to those made by the Stoics. The 
or ‘intangible nature’ (note that the word 
does not occur in the Placita) according to Sextus can be called void when vacant of body, place when occupied by body, and space when bodies are moving through it, for it is the “same nature”: “generically the name is ‘intangible nature’”.459 These subtle dis-
tinctions are not really supported by the evidence of Epicurus’ authentic remains. An unfortunately too terse passage in the Letter to Herodotus speaks of “what we call ‘void’, ‘space’ and ‘intangible nature’”– so here the term τóπος is absent, and there is no intimation either of distinctions between the three terms that are listed.460 Clearly, in the Letter “intangible nature” is not an overarching concept, but is placed on a par with space and void. The conceptual equality of void, place and space at 1, 20, 2461 agrees with that of the Letter. Checks are possible only where the original works are extant, as is the case for Plato, Aristotle, and Epicurus in connection with chs. 1, 18 – 20 and 2, 9*. I am therefore disinclined to underrate the evidence of the Letter to Herodotus and the parallel evidence of Lucretius.462 Nevertheless one should acknowledge that the difference between the Stoics and Epicurus may have been blown up in Aëtius more doxographico the better to formulate a diaphōnia.463
If we did not have Stobaeus we would perhaps be puzzled by ps.Plutarch’s monolemmatic version of the chapter. He only has the first lemma, in which he has inserted the name-label Epicurus. Adding one or more name-labels to a doxa and omitting the other doxai they derive from is a standard technique of epito-mization in ps.Plutarch. To be sure, this identification of the Epicurean view with that of the Stoics recalls Sextus Empiricus’ account. But without doubt an intelligent intention of this kind should not be attributed to ps.Plutarch, who merely “ein 200 Jahre älteres Buch klein macht”.464
5 Epilogue
The reverberations in the Placita of Hellenistic views on space, that is to say on void, space, and place, fail to provide a satisfactory picture, let alone a complete one. I have tried to show that the agenda and methodology of the discussion are for the most part originally Aristotelian. In the doxographical chapters discussed in the present paper the views of the Hellenistic philosophers, that is, of the Stoics, Epicurus, and Strato (to the exclusion of other Peripatetics, and of Academics or Platonists), fall within a spectrum that includes representatives of the Presocratics, as well as Plato and Aristotle. They are clearly represented (as of course also elsewhere in the Placita) as belonging with the mainstream tradition of Greek philosophy, which at the very least may serve as a reminder not to treat them in isolation, but to recognize that the problems they are dealing with or had to deal with already had a history.
In our attempt to understand the information provided in these chapters we have noted the extreme economy of the contents of the lemmata. I am not only thinking of their proverbial and almost telegrammatic brevity, which deprives us of certain finer and perhaps philosophically more interesting aspects of the views at issue, but also of the fact that what is in the lemma of one chapter is often indispensable enough or at least most helpful for understanding what is in a lemma of another chapter. Repetition is as a rule not favoured, though there are exceptions. On the other hand crucial information is sometimes not found in the chapter where one would expect to find it, but in a related chapter nearby. We have noted, for example, that the Stoic definition of void occurs in 1, 20 instead of 1, 18. The reason often is that in the other location an effective (or more effective) diaphōnia can be obtained, as is clearly the case in 1, 20.
Further information is provided not explicitly but implicitly, that is, by means of the artful arrangement of lemmata according to contrast and affinity, which reveals how and where and to what extent philosophers (or scientists) disagreed or (partially) agreed with each other. But one should realize that both affinities and contrasts may have been exaggerated in order to heighten the effect of the presentation, or even to provide an extra stimulus for discussion.
Some subjects were more popular, or believed to be more interesting, than others. The contents of individual Aëtian Placita chapters may differ substantially in respect of the variety, multiplicity, and length of the doxai that are included. The three chapters on void, place, and space, when combined and considered sub specie of their interrelated themes, are of middling length and variety (those on the principles and the gods in Book I and on aspects of human biology in Book V are very much longer and more detailed). We have moreover noted that from ch. 1, 18 to ch. 1, 20, passing through ch. 1, 19, their individual size diminishes from six to three to two lemmata in Aëtius, and from five to two to one in his epitomator ps.Plutarch, while ch. 2, 9* has again four lemmata. In Aëtius this is not so much a matter of diminishing interest as of a scarcity of available alternatives, while ps.Plutarch was obliged to be even more brief. Even so, quand on n’a pas ce qu’on aime il faut aimer ce qu’on a.