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The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe



In contrast to other ancient philosophers, Epicurus and his followers famously maintained the infinity of matter, and consequently of worlds. This was inferred from the infinity of space, because they believed that a limited amount of matter would inevitably be scattered through infinite space, and hence be unable to meet and form stable compounds. By contrast, the Stoics claimed that there was only a finite amount of matter in infinite space, which stayed together because of a general centripetal tendency. The Roman Epicurean poet Lucretius tried to defend the Epicurean conception of infinity against this Stoic alternative view, but not very convincingly. One might suspect, therefore, that the Epicureans’ adherence to the infinity of matter was not so much dictated by physical arguments as it was motivated by other, mostly theological and ethical, concerns. More specifically, the infinity of atoms and worlds was used as a premise in several arguments against divine intervention in the universe. The infinity of worlds was claimed to rule out divine intervention directly, while the infinity of atoms lent plausibility to the chance formation of worlds. Moreover, the infinity of atoms and worlds was used to ensure the truth of multiple explanations, which was presented by Epicurus as the only way to ward off divine intervention in the realm of celestial phenomena. However, it will be argued that in all of these arguments the infinity of matter is either unnecessary or insufficient for reaching the desired conclusion.
41© Springer Nature Switzerland AG 2018
F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to
the Early Modern Period, Studies in History and Philosophy of Science 48,
Chapter 3
The End ofEpicurean Innity: Critical
Reections ontheEpicurean Innite
Abstract In contrast to other ancient philosophers, Epicurus and his followers
famously maintained the innity of matter, and consequently of worlds. This was
inferred from the innity of space, because they believed that a limited amount of
matter would inevitably be scattered through innite space, and hence be unable to
meet and form stable compounds. By contrast, the Stoics claimed that there was
only a nite amount of matter in innite space, which stayed together because of a
general centripetal tendency. The Roman Epicurean poet Lucretius tried to defend
the Epicurean conception of innity against this Stoic alternative view, but not very
convincingly. One might suspect, therefore, that the Epicureans’ adherence to the
innity of matter was not so much dictated by physical arguments as it was moti-
vated by other, mostly theological and ethical, concerns. More specically, the
innity of atoms and worlds was used as a premise in several arguments against
divine intervention in the universe. The innity of worlds was claimed to rule out
divine intervention directly, while the innity of atoms lent plausibility to the chance
formation of worlds. Moreover, the innity of atoms and worlds was used to ensure
the truth of multiple explanations, which was presented by Epicurus as the only way
to ward off divine intervention in the realm of celestial phenomena. However, it will
be argued that in all of these arguments the innity of matter is either unnecessary
or insufcient for reaching the desired conclusion.
F. A. Bakker (*)
Center for the History of Philosophy and Science, Radboud University,
Nijmegen, The Netherlands
The original version of this chapter was revised. This chapter was considered as an Open Access
chapter. A correction to this chapter can be found at
3.1 Introduction
A prominent feature of ancient atomism that still captures the imagination is its
endorsement of the innity of the universe and, associated with it, the innite num-
ber of worlds.1 Whereas most ancient philosophers argued for a single cosmos,
either identied with a nite universe, as in Plato’s and Aristotle’s cosmologies, or
placed in an innite void, as in Stoic cosmology, the atomists made our cosmos a
negligible and utterly unremarkable part of the innite matter-lled universe.2
The innity of the universe, in terms of space as well as bodies, was arrived at
through rigorous argumentation, much of which may go back to the earlier atomists,
but which has come down to us mainly through the works of Epicurus and Lucretius,
who adopted and reinforced some of the earlier arguments.3 The centrality of this
theory to Epicurean cosmology is clear from the prominent place given to it in
Epicurus’ Letter to Herodotus (close to the beginning) and in Lucretius’ De rerum
natura (in the nal and concluding parts of books one and two).
However, the dual innity of matter and void, and the consequent innite number
of worlds, are not simply curious but otherwise sterile logical consequences of the
basic tenets of Epicurean physics, but they also serve as the starting points for fur-
ther inferences: the innity of the universe is argued to rule out divine governance,
to make the spontaneous formation of a cosmos not merely possible but inevitable,
and to guarantee the simultaneous truth of multiple, mutually incompatible explana-
tions. Moreover, all of these consequences relate directly or indirectly to the ques-
tion of the gods’ involvement in the world.
In this chapter I will investigate the innity of the universe from both points of
view. First, I will critically examine the Epicurean arguments for the innity of
space and bodies, as well as the way in which they deal with a rival view, and, sec-
ond, I will look into some of the corollaries to the innity of space and bodies, and
the role these corollaries play in underpinning the Epicurean view of the gods, in
order to see whether this role may serve as an additional motivation for the
Epicureans’ insistence on the innity of bodies and worlds.
1 See e.g. Mash 1993, 204–210; Dick 1996, 12–13, Dowd 2015, 56, Traphagan 2015, 18; and
Darling 2016, s.vv. ‘atomism,’ ‘Leucippus,’ ‘Democritus,’ ‘Metrodorus,’ ‘Epicurus’ and
2 See e.g. Lucretius 6.649–652. Henceforth all references to Lucretius will follow the text and
translation of Rouse and Smith 1992, unless otherwise specied.
3 For the Presocratic antecedents of these arguments see Furley 1989, 110–114; Avotins 1983;
Asmis 1984, 261–267.
F. A. Bakker
3.2 Cosmological Arguments fortheInnity oftheUniverse
Two Epicurean accounts for the innity of the universe have come down to us. One
is found in Epicurus’ Letter to Herodotus 41–42, and another, longer one in
Lucretius’ De rerum natura 1.951–1113. In both accounts the arguments presup-
pose the Epicurean division of being into bodies and void. In order to clarify these
two somewhat ambiguous concepts and to provide a background for the discussion
of Epicurean innity, I will start with a brief discussion of these two concepts.
3.2.1 Clarication ofConcepts: Bodies andVoid
According to Epicurus the universe (τ πν) consists of bodies and void (κενόν).4
The existence of bodies is directly attested by the evidence of the senses,5 but the
existence of void, being inaccessible to sense perception, has to be inferred from
other phenomena (Letter to Herodotus 40):
And if there were not that which we term void and room and intangible nature, bodies
would have nowhere to exist and nothing through which to move, as they are seen to move.6
In this statement void (κενόν) is connected with two other spatial concepts, room
(χώρα) and intangible nature (ναφς φύσις). In the Letter to Herodotus Epicurus
does not provide a denition for any of these three terms, but a later source, Sextus
Empiricus, Against the Professors 10.2, provides the following testimony:
According to Epicurus, of ‘intangible nature,’ as he calls it, one kind is named ‘void,’
another ‘place,’ and another ‘room,’ the names varying according to the different ways of
looking at it, since the same nature when empty of all body is called ‘void,’ when occupied
by a body is named ‘place,’ and when bodies roam through it becomes ‘room.7
So, although Epicurus apparently did sometimes distinguish these spatial terms, in
Letter to Herodotus 40 these distinctions are observed neither nominally – for
Epicurus presents the three terms as mere synonyms –,8 nor conceptually– for the
4 Epicurus, Letter to Herodotus 39. Henceforth all references to Epicurus’ letters will follow the
text edition of Arrighetti 1973. See also Lucretius 1.419–20.
5 Epicurus, Letter to Herodotus 39. See also Lucretius 1.422–25.
6 Epicurus, Letter to Herodotus 40: ε <δ> μ ν κενν κα χώραν κα ναφ φύσιν νομάζομεν,
οκ ν εχε τ σώματα που ν οδ διο κινετο, καθάπερ φαίνεται κινούμενα. Translation
in Bailey 1926, 23 (slightly modied). See also Lucretius 1.329–69.
7 Sextus Empiricus, Against the Professors 10.2: κατ τν πίκουρον τς ναφος καλουμένης
φύσεως τ μέν τι νομάζεται κενόν, τ δ τόπος, τ δ χώρα, μεταλαμβανομένων κατ
διαφόρους πιβολς τν νομάτων, πείπερ ατ φύσις ρημος μν καθεστηκυα παντς
σώματος κενν προσαγορεύεται, καταλαμβανομένη δ π σώματος τόπος καλεται, χωρούντων
δ διατς σωμάτων χώρα γίνεται. Text in Long and Sedley 1987b, 22; translation in Long and
Sedley 1987a, 28 (slightly modied).
8 Similarly Lucretius 1.334 “quapropter locus est intactus inane vacansque;” 1.954-955 “quod
inane repertumst/seu locus ac spatium;” and 1.1074 “omnis enim locus ac spatium, quod in<ane
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
existence of void is inferred from the fact that bodies (1)need to be somewhere,
which is place, and (2) need something to move through, which is room. This means
that in Letter to Herodotus 40, and possibly also other passages, the term ‘void’ is
used to denote not just empty space, but also occupied space (i.e. ‘place’) and the
space through which bodies move (i.e. ‘room’). In other words, ‘void’ is used as a
stand-in for the generic term ‘intangible nature,’ which may also be translated as
Another ambiguity that must be addressed concerns the concept of body. Bodies,
according to Epicurus (Letter to Herodotus 40–41), come in two kinds: compounds
and atoms. Now, when Epicurus claims that the existence of bodies is attested by the
evidence of the senses (see above), he must be thinking primarily of compounds,
since atoms cannot be perceived (Letter to Herodotus 56). However, since in com-
pound bodies there is always an admixture of void (Lucretius 1.358-369), concep-
tual purity requires that, in those contexts where bodies are opposed to void, we
think primarily of atoms.
3.2.2 Positive Arguments fortheInnity oftheUniverse,
Bodies andVoid
In section 41 of his Letter to Herodotus, Epicurus provides the following argument
for the innity of the universe:
Moreover, the universe is boundless. For that which is bounded has an extreme point, and
the extreme point is seen against something else, <but the universe is not seen against some-
thing else,>10 so that, as it has no extreme point, it has no limit, and as it has no limit, it must
be boundless and not bounded.11
The same view is also defended by Lucretius (1.951-1007), who offers no fewer
than four arguments.12 In the rst place (1.958-967), Lucretius argues, whatever is
nite must have a boundary, but a boundary requires something external to bound it;
however, since there is nothing external to the universe, the universe cannot have a
9 See Long and Sedley 1987a, 29–30; Algra 1995, 52–58. However, Inwood 1981, and more
recently Konstan 2014, claim that Epicurus uses the term ‘void’ (τ κενόν) exclusively to refer to
empty space.’ (Concerning these two interpretations see also n18 below.) In this article I will fol-
low the rst-mentioned interpretation, which I nd to be the more convincing of the two. My own
conclusions concerning the Epicurean theory of innity do not, however, essentially depend on this
choice, and could also agree with the alternative interpretation.
10 Addition suggested by Usener 1887, xviii, on the basis of Cicero’s version of Epicurus’ argument
in De divinatione 2.103; it is rejected by Bailey 1926, 22 and 184, but accepted by Arrighetti 1973,
11 Epicurus, Letter to Herodotus 41: λλ μν κα τ πν πειρόν στι· τ γρ πεπερασμένον
κρον χει· τ δ κρον παρτερόν τι θεωρεται· <λλ μν τ πν ο παρ τερόν τι
θεωρεται·> στε οκ χον κρον πέρας οκ χει· πέρας δ οκ χον πειρον ν εη κα ο
πεπερασμένον. Translation in Bailey 1926, 23 (modied).
12 See Bailey 1947, vol. 2, 763–764; Asmis 1984, 262–264; Bakker 2016, 182–184.
F. A. Bakker
boundary, and hence must be innite. Secondly (1.968-983), if the universe had a
boundary and someone threw a spear towards it, the spear would either stop or con-
tinue: if it stops, there must be matter outside to obstruct it, but if it continues there
must be empty space to receive it: in either case there must be something outside,
and the boundary of the universe turns out to be no boundary at all; this result
repeats itself wherever one assumes the presence of a boundary. As a consequence
the universe cannot have a boundary, and is proved to be innite. Thirdly (1.984-
997), if space were nite and bounded on all sides, all bodies would be heaped up at
the ‘bottom,’ i.e. the lower boundary, by strength of their weight, and nothing fur-
ther would happen, but this is not the case; therefore the universe must be innite.
Finally (1.998-1001), we see that everything that is bounded is always bounded by
something else, but in the case of the universe there is nothing else to bound it;
therefore the universe must be innite.
The rst of Lucretius’ arguments basically repeats Epicurus’ argument from the
Letter to Herodotus 41, and may go back to the earlier atomists: one version is pre-
sented and rejected by Aristotle in Physics 3.4, 203b20-22. The second argument is
a famous thought experiment that goes back to the Pythagorean Archytas and was
also used by the Stoics.13 Both these arguments, as well as the fourth, exploit the
notion of limit, which seems to include the notion of a ‘beyond.14 Lucretius’ third
argument is of a different nature. Presupposing the Epicurean conception of down-
ward motion as a motion along parallel lines from innity to innity,15 and hypo-
thetically enclosing the universe in boundaries, Lucretius argues that the lower
boundary, the ‘bottom,’ would obstruct this natural downward motion and cause
matter to be compacted into one inert mass.16 However, at this point of the argument
the Epicurean theory of parallel downward motion has not yet been proved: in fact,
its proof depends upon the rejection of centripetal gravity in 1.1052-1093 (see the
next section), which in turn presupposes the innity of space – the very thing
Lucretius is arguing for here. In short: Lucretius’ third argument presents a petitio
principii. The fourth argument seems to be nothing but a restatement of the rst. A
version of this argument is also used by the Stoic Cleomedes (1.1, 112–122).
13 Archytas fr. A24in Diels and Kranz 1951–1952; Stoics SVF II 535–536 (Here and elsewhere I
use the standard abbreviation SVF for references to Arnim 1903–1905). For an analysis of the vari-
ous ancient versions of this thought experiment, see Ierodiakonou 2011. For early modern versions
of the thought experiment see Granada’s and Palmerino’s Chapters 8 and 12 in this volume.
14 Furley 1989, 111; Avotins 1983, 427; Asmis 1984, 262–263.
15 See Epicurus, Letter to Herodotus 60, with the comments on the same in Konstan 1972, and
Lucretius 2.216-250, with the comments on the same in Bakker 2016, 214–216.
16 It might be argued that, were the existence of a centripetal downward motion assumed, the centre
would provide a similar ‘bottom,’ and the same argument would apply (on which see p.51 below).
However, in the present context Lucretius is clearly thinking of external boundaries, and his iden-
tication of one of these external boundaries as the ‘bottom’ indicates that he is assuming the
existence of a parallel downward motion.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
With the innity of the universe proven, and given the fact that the universe con-
sists of bodies and void, the question naturally arises how the innity of the universe
relates to each of its two components. In sections 41–42 of the Letter to Herodotus,
Epicurus argues for the innity of both bodies and void:
Furthermore, the universe is boundless both in the number of the bodies and in the extent of
the void. For if on the one hand the void were boundless, and the bodies limited in number,
the bodies could not stay anywhere, but would be carried about and scattered through the
innite void, not having other bodies to support them and keep them in place by means of
collisions. But if, on the other hand, the void were limited, the innite bodies would not
have a place to be in.17
Here too, ‘void’ seems to be used in the sense of ‘space,’ encompassing both that
through which bodies move (i.e. ‘room’) and that where bodies are (i.e. ‘place’).18
However, this should not mislead us into thinking that bodies and space might be
coextensive, with bodies (i.e. atoms) lling up every portion of space. Lucretius
offers three arguments for the existence of actually empty space. Firstly, motion
requires the existence of pockets of empty space, in order to provide a beginning of
motion (1.335-345); secondly, the penetration of sound and cold into bodies, but
also the dispersion of food through the living body require the existence of empty
passageways (1.346-357), and thirdly, differences in specic weight must be due to
differing amounts of empty space in (compound) bodies (1.358-369).19 When,
therefore, the Epicureans state that both the extent of space and the number of bod-
ies are innite, what they have in mind is an innite alternation of (atomic) bodies
and (empty) space.20 In an expanded version of Epicurus’ argument for the innite
number of bodies Lucretius (1.1008-1051) species that our world is being main-
tained by external bodies, which constantly either replace atoms or beat them back
into line.21
17 Epicurus, Letter to Herodotus 41–42: Κα μν κα τ πλήθει τν σωμάτων πειρόν στι τ πν
κα τ μεγέθει το κενο· ε τε γρ ν τ κενν πειρον, τ δ σώματα ρισμένα, οθαμο ν
μενε τ σώματα, λλφέρετο κατ τ πειρον κενν διεσπαρμένα, οκ χοντα τ περείδοντα
κα στέλλοντα κατ τς νακοπάς· ε τε τ κενν ν ρισμένον, οκ ν εχε τ πειρα σώματα
που νέστη. Translation in Bailey 1926, 23 (slightly modied).
18 According to Algra 1995, 56–57, ‘being in’ and ‘moving through’ imply that ‘void’ is here
thought of as occupied, and therefore not empty. Konstan 2014, 90–91, retorts that ‘being in’
means ‘being surrounded by’ and ‘being separated by,’ and since bodies are always surrounded and
separated by empty space (because otherwise they would not be able to move), the innity of bod-
ies implies an innite amount of surrounding empty space.
19 Algra 1995, 57.
20 Cf. Lucretius 1.1008-1011 “Ipsa modum porro sibi rerum summa parare/ne possit, natura tenet,
quae corpus inani/et quod inane autem est niri corpore cogit,/ut sic alternis innita omnia red-
dat.” Text from Rouse and Smith 1992, 82 and 84.
21 A similar argument is also found in fragment 67 (in Smith 1993, 259–260) of the Epicurean
inscription of Diogenes of Oenoanda.
F. A. Bakker
3.2.3 Refutation ofaRival Theory
At rst sight the Epicurean argument for an innite number of bodies seems quite
plausible. However, the assumption it is based on– that in innite space a limited
number of bodies would not be able to nd a stable foothold, and would therefore
be dispersed throughout the void – is not self-evident. While Epicurus simply
assumes that this is true, Lucretius is aware of, and actively engages with, a rival
theory that challenges precisely this implication. In 1.1052-1093, Lucretius warns
Memmius, his addressee, to “avoid and keep afar” the view
that, as some say, all things press towards the centre of the whole and that for this reason the
nature of the world stands rm without any external blows, and […] cannot be set loose in
any direction, because all presses towards the centre.22
If, as these unnamed rivals claim, all bodies have a natural tendency to move towards
a central point, even a limited amount of bodies would be able to remain together
and be safe from dispersal into the innite void, without the need for external blows
to keep the bodies in check, or to repair the losses. One could even argue– although
Lucretius does not make this point– that the assumption of a general centripetal
tendency of bodies would actually preclude their innite number, because otherwise
the world would experience continuous growth due to the incessant accrual of new
atoms converging on the centre from the innite stock of surrounding matter, which
is not the case.23
Lucretius does not identify the proponents of this theory, and over the years vari-
ous candidates have been proposed. The common, and in my opinion the most plau-
sible, view is that Lucretius was thinking of the Stoics.24 Although several ancient
philosophers and schools of philosophy endorsed some kind of centripetal gravity,
only the Stoics deployed this theory in order to safeguard the integrity of a single
and nite cosmos in innite space, and only they extended this centripetal tendency
to all bodies, heavy and light alike. Other proposed candidates, like Aristotle or the
early Platonists, simply rejected extra-cosmic space, and therefore did not have to
account for the coherence of the cosmos as such, or to counterbalance the centrifu-
gal tendency of air and re with a centripetal one.25 However, although Lucretius
probably had the Stoics in mind, this does not necessarily mean that he understood
22 Lucretius 1.1052–1055: “Illud in his rebus longe fuge credere, Memmi, /in medium summae
quod dicunt omnia niti,/atque ideo mundi naturam stare sine ullis /ictibus externis, neque quo-
quam posse resolvi, /[…] quod in medium sint omnia nixa.” Text and translation from Rouse and
Smith 1992, 87–89.
23 Compare Aristotle, De caelo 1.8, 276a18-b21, where Aristotle argues that, if one assumes the
universe to consist of the same elements having the same nature and potentialities everywhere, the
universe must also have a single centre towards (or away from, or around) which all the elements
would move; hence there can only be one world, because every part of matter in another world
would take up position with respect to this single centre.
24 For a more extended argument see Bakker 2016, 191–202.
25 Aristotle was proposed by Furley 1989, 187–195, and the early Platonists by Sedley 1998, 78–82.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
or represented their theory correctly in every respect. The clearest ancient testimony
as to the Stoic theory in question is preserved by Stobaeus:
In the case of all things in the cosmos that have a hexis of their own the parts tend towards
the centre of the whole thing. Similarly in the case of the cosmos itself; and it is in virtue of
this fact that it is rightly said that all parts of the cosmos have a tendency to move towards
the centre of the cosmos, most of all the things possessing weight. The same thing is respon-
sible both for the immobility of the cosmos in the innite void and for the earth’s immobil-
ity in the cosmos, as it is situated around the centre of it [viz. of the cosmos] in a state of
equal balance. Still it is not unrestrictedly so that body has weight, but air and re are
weightless. However, also these elements tend towards the centre of the whole globe of the
cosmos, although they nd their relative position in the direction of the periphery of the
cosmos. For by their own nature they are upward moving because they don’t have any share
in weight.26
According to the Stoics, just as individual things within the cosmos are held together
by a cohesive force or hexis, so the cosmos as a whole has a hexis, which causes all
its parts to converge on its centre. This tendency is felt most strongly by the heaviest
parts, which take up a more central position, but less by the weightless bodies,
which therefore move towards, and settle at, the periphery.
After describing the rival theory and mockingly highlighting some of its para-
doxical corollaries– that on the underside of the earth gravity is directed upwards,
and animals and humans stand upside down (1058–1067)– Lucretius proceeds with
his refutation. His main arguments are, rst (1070–1071), that the universe, being
innite, does not have a centre for the parts of the cosmos to move towards; second
(1071–1080), that the centre, even if it existed, would be a spatial and hence incor-
poreal entity, and as such incapable of exerting any effect on bodies; and, third
(1083–1093), that the rival theory is internally inconsistent in also claiming that air
and re tend away from the centre.
Given that the rival theory stands in the way of a central Epicurean tenet, one
would expect a particularly strong effort to refute it. In fact, however, Lucretius’
arguments seem to be rather weak. In order to demonstrate this I will now discuss
Lucretius’ arguments one by one. I will start with the rst and third arguments,
whose inadequacy is the most obvious, and leave the second argument, which pres-
ents some difculties, for last.
Lucretius rst argues that there is no centre, because the (innite) universe can
have no centre. This seems to be a good point. However, if we take a closer look at
the Stoic theory as reported by Stobaeus (see above) and other sources, we see that
26 Stobaeus, Eclogae Physicae 1.166, 2–22 (= Arius Didymus fr.23 / SVF I 99): Τν δν τ
κόσμ πάντων τν κατδίαν ξιν συνεστώτων τ μέρη τν φορν χειν ες τ το λου μέσον,
μοίως δ κα ατο το κόσμου· διόπερ ρθς λέγεσθαι πάντα τ μέρη το κόσμου π τ
μέσον το κόσμου τν φορν χειν, μάλιστα δ τ βάρος χοντα. τατν δατιον εναι κα τς
το κόσμου μονς ν πείρ κεν κα τς γς παραπλησίως ν τ κόσμ, περ τ τούτου
κέντρον καθιδρυμένης σοκρατς. ο πάντως δ σμα βάρος χειν, λλβαρ εναι έρα κα
πρ· τείνεσθαι δ κα τατά πως π τ τς λης σφαίρας το κόσμου μέσον, τν δ σύστασιν
πρς τν περιφέρειαν ατο ποιεσθαι. φύσει γρ νώφοιτα ταυτεναι δι τ μηδενς μετέχειν
βάρους. Text from Arnim 1903–1905, vol. 1, 27; translation in Algra 1988, 160.
F. A. Bakker
the centre in question is not the centre of the universe at all, but the centre of the
(nite) cosmos.27 Lucretius’ rst argument, then, simply turns out to be unfounded.
Lucretius’ third argument consists in pointing out an internal inconsistency in his
rivals’ position. In line 1052 Lucretius still reported that, according to the unnamed
rivals, ‘all things press towards the centre of the whole’ (‘in medium summae […]
omnia niti’) (my emphasis). Now, in lines 1083–1084, we are told that according to
these same opponents ‘not all bodies press towards the centre’ (‘non omnia corpora
[…] in medium niti’) (my emphasis), but only those which make up earth and water,
whereas air and re are naturally centrifugal.28 We do not exactly know how the
argument was developed because the relevant portion of Lucretius’ text is lost in a
lacuna, but Bailey’s suggestion that Lucretius would have rst charged his rivals
with inconsistency, and then pointed out that their thesis of centrifugal air and re
undermines the very coherence of the cosmos which their original thesis was meant
to safeguard, is quite plausible.29 However, if we compare Lucretius’ criticism with
the actual statements of the Stoics, we can see both where it came from, and why it
may not be justied. On the one hand, Stobaeus conrms that the Stoics did, in fact,
make these two, apparently inconsistent, claims, asserting both that all the elements,
including air and re, show a tendency to move towards the centre, and that air and
re have a natural tendency to move upwards, i.e. away from the centre. On the
other hand, however, Stobaeus’ testimony also shows that, in reality, these two
claims are neither inconsistent with each other nor deserving of Lucretius’ criti-
cism, since Stobaeus clearly states that the centrifugal tendency of air and re is
only secondary and subordinate to their centripetal tendency, and will not take them
beyond the connes of the cosmos. On the basis of this and other testimonies some
commentators ascribe to the Stoics a version of the ancient extrusion or buoyancy
theory, according to which lighter bodies, such as those which make up air and re,
have a natural tendency to move downwards (i.e. towards the centre), but are
extruded and forced upwards (i.e. away from the centre) against their nature by
heavier ones, and hence they will not move beyond the sphere of these heavier ele-
ments, but instead position themselves at the periphery.30 Whether or not this inter-
pretation is correct, it at least shows that it would be possible to resolve the apparent
inconsistency in a way that the Epicureans could hardly object to, since they them-
selves endorsed a version of the buoyancy theory, albeit one that did not dene
27 See e.g. Plutarch, De Stoicorum repugnantiis 44, 1055a 1–2 (SVF II 550, 31–32), quoting
Chrysippus: πιθανν πσι τος σώμασιν εναι τν πρώτην κατ φύσιν κίνησιν πρς τ το
κόσμου μέσον; and Cleomedes 1.1, 91–92: νένευκε γρ {sc. κόσμος} π τ αυτο μέσον κα
τοτο χει κάτω, που νένευκεν.
28 Furley 1989, 189, claims without offering an argument that no such inconsistency is implied:
‘omnia’ in l. 1052 would refer only to bodies that are heavy, and coming from all sides, while
‘omnia corpora’ in l. 1083 would refer to all bodies, both heavy and light. Furley’s claim is sup-
ported by Sedley 1998, 79. See, however, Schmidt 1990, 213, and Bakker 2016, 197.
29 Bailey 1947, vol. 2, 787–788.
30 Sambursky 1959, 111; Wolff 1988, 507 et passim; Furley 1989, 192–193; idem 1999, 444–445.
For arguments against the attribution of this theory to the Stoics see Bakker 2016, 197–198.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
upwards and downwards in centrifocal,31 but in parallel terms. Thus Lucretius’ third
argument is dissipated, too.
This brings us to Lucretius’ second argument. In lines 1.1074-1080 we read:
For all place and space, which we call void, must yield a passage through middle or not-
middle equally to weights, wherever their movements tend. Nor is there any place in which
bodies, when they have come thither, can lose the force of weight and stand still in the void;
nor again must that which is void ever give support for anything, but, as its nature craves, it
must proceed to give place.32
Here Lucretius points out that, even if it existed, the centre, being a place and hence
incorporeal, would not be able to affect bodies in the way the anonymous rivals
want it to. This seems to be a legitimate point.33 The Stoics indeed held that a centre
was a place or a limit, and that places and limits as such were incorporeal.34 They
also held that incorporeal entities were incapable of producing effects in bodies.35
On these matters Stoics and Epicureans could, in fact, see eye to eye.36 Consequently,
the centre would not be able to attract bodies to itself or to check their motion. Here,
too, however, a closer look at our sources reveals that Lucretius may not quite have
captured the Stoic theory. Indeed, although the precise interpretation of the relevant
testimonies is disputed, it seems clear that the Stoics did not assign some miracu-
lous power of attraction to the centre, but rather considered the centripetal motion to
be the resultant effect of a cohesive force that somehow draws all the parts of the
cosmos to each other.37 In other words, the centripetal tendency of bodies is not
attributable to the incorporeal centre, but to the corporeal whole to which the
31 For the buoyancy theory see Epicurus fr. 276 (in Usener 1887, 196–197) and Lucretius 2.184–
215, with the comments on the same in Bakker 2016, 211–213. ‘Centrifocal’ is a term coined by
Furley 1989, 15, 234–235, to describe systems in which ‘up’ and ‘down’ are dened in relation to
a centre; for the contrast between centrifocal and parallel dynamics see Bakker 2016, 177–179.
32 Lucretius 1.1074–1080: “omnis enim locus ac spatium, quod inane vocamus,/per medium, per
non medium, concedere debet / aeque ponderibus, motus quacumque feruntur./nec quisquam
locus est, quo corpora cum venere,/ ponderis amissa vi possint stare in inani;/nec quod inane
autem est ulli subsistere debet,/quin, sua quod natura petit, concedere pergat.” Text and translation
from Rouse and Smith 1992, 88–91.
33 A similar point against the Stoic theory is made by Plutarch in De facie in orbe lunae 7, 924b 4–8
and 11, 926a 10– b 7.
34 On the centre as a place see Plutarch, De facie 6, 923e 5 and 926a 2; on the centre being a limit
see ibid. 10, 925e 10–11 and 11, 926b 9 (cf. Aristotle, De caelo 2.13, 293a 33). On the incorporeal
nature of place see SVF II 331; on that of limits see SVF II 487 and 488.
35 SVF I 89; II 336, 340, 341, 343, 363, 387: only corporeal things can produce an effect.
36 On place/space/void being incapable of affecting bodies in Epicurean cosmology see e.g.
Lucretius 1.437-439, 443 and 2.235-237. Cf. also Sextus Empiricus, Against the Professors
10.221-222 and the scholion to Epicurus, Letter to Herodotus 43.
37 Sambursky 1959, 111–113; Wolff 1988, 505–507; Furley 1989, 8, 192; 1999, 443–448. Another
indication that the centripetal tendency was merely a resultant is provided by the later Stoic
Cleomedes (1.1, 164–172), who claims that only in spherical bodies the inward tendency of their
parts is always directed towards the centre; in oblong bodies, on the other hand, the focus of each
part’s motion does not necessarily coincide with the centre of the whole.
F. A. Bakker
individual bodies belong, whence it is communicated to the individual bodies
As a matter of fact, Lucretius even seems to hint at this possibility, perhaps unwit-
tingly, when writing, at 1.1077-1078: “Nor is there any place in which bodies, when
they have come thither, can lose the force of weight and stand still in the void.” In
these lines he seems to envisage, and reject, the thesis that upon reaching the centre
bodies would actively lay down their weight and come to a standstill. Although this
account comes closer to the Stoics’ actual theory, Lucretius’ words still betray an
Epicurean bias: according to the Stoic theory bodies would stop at the centre not
because they lose their weight, but rather because upon reaching the centre their
downward or centripetal tendency, which is weight, is fullled or actualized. For the
Epicureans, on the other hand, downward motion is motion along parallel lines from
innity to innity, a motion which can neither be ‘laid down,’ nor be checked by the
resistance of some immaterial ‘centre.’38 At this point, however, Lucretius has not yet
established the Epicurean theory of weight and downward motion, nor would he have
been able to, before the Stoic alternative was fully refuted.
Moreover, it is not clear on what grounds the Stoic theory is rejected. Evidently the
Epicureans could not accept the Stoic theory of centripetal gravity tout court, as this
requires a complete contiguity of bodies– Stoics and Epicureans alike rejected the
possibility of action at a distance –39 that is at odds with the Epicurean duality of atoms
and void. Yet there does not seem to be a cogent reason why bodies could not have an
inbuilt tendency to move towards a specic point. After all, the Epicureans themselves
endorsed the view that weight is a tendency to move in a certain direction, albeit a
motion along parallel lines, and not along lines converging to a single point.40
In reaction against this view Lucretius could have repeated his earlier argument
of 1.984-997.41 There he had argued that if the universe had a bottom, all matter
would be heaped up there to form one compact and inert mass, putting an end to all
activity and change.42 Now, on the assumption of a centripetal downward motion,
the ‘centre’ would provide just such a ‘bottom,’ so that the same conclusion would
apply. However, I do not believe such a conclusion would be warranted, as it does
not seem to take into account a crucial aspect of the Epicurean theory of atomic
motion. According to the Epicureans (including Lucretius) the atoms are in constant
motion, and when their motion is checked they will simply rebound and continue to
move in the opposite direction43: accordingly, even with the assumption of an
absolute ‘bottom,’ no complete cessation of activity and change would result.
Anyway, Lucretius does not invoke this argument against the rival theory.
38 For the Epicureans’ endorsement of a parallel downward motion see n15 above.
39 For the Stoics see Sambursky 1962, 102–103; Long 1986, 160; Wolff 1988, 507, 522. For the
Epicureans see Furley 1989, 12, 78; O’Keefe 2005, 80–81.
40 See Konstan 2014, 96.
41 See also Bakker 2016, 208–209.
42 See p.45 above.
43 Epicurus, Letter to Herodotus 43–44; idem fr. 280 (in Usener 1887, 199); Lucretius 2.80–88.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
What is more, later on in the De rerum natura, he seems to actually endorse the
centrifocal theory that he just rejected. In 5.449-508 Lucretius describes the coming-
into- being of our cosmos in terms that strongly suggest that a centripetal gravity is
at work.44 In lines 449–454, for instance, we read:
For in plain fact rstly all the bodies of earth, because they were heavy and entangled, came
together in the centre and all took the lowest place; and the more entangled they came
together, the more they squeezed out those particles which could make sea, stars, sun, and
moon and the walls of the great world[.]45
The entire process starts with earthy particles moving towards, and settling in, the
centre, or “the lowest place,” “because they were heavy and entangled.As they
settle and become even more entangled they squeeze out all the lighter stuffs that
will eventually make up the sea, the heavenly bodies and the outer boundary of the
cosmos. Later on we learn how in this way ether, which is the lightest element, takes
up the highest and outermost region of the cosmos, “fencing in all the rest with
greedy embrace,”46 and how the other elements and the individual heavenly bodies
take up intermediate positions in proportion to their relative weights.
Nowhere in this passage we are told why heavy bodies should move to the centre;
Lucretius simply assumes that they do, as if it were natural for them to do so.
However, if heavy bodies naturally move towards the centre, but also by denition
tend downwards, then ‘to the centre’ and ‘downwards’ must be the same thing, as
indeed Lucretius seems to imply, and as was denitely the case in Stoic cosmolo-
gy. 47 In other words, Lucretius’ cosmogony assumes a theory of centripetal gravity
that is virtually indistinguishable from the rival theory he rejected earlier.
As it turns out, then, none of Lucretius’ three arguments against centripetal grav-
ity seems cogent. Two arguments are simply misguided, while another can be easily
circumvented and is, in fact, contradicted by Lucretius himself.
3.2.4 The Status ofLucretius 1.1052-1093 and5.449-508
In the preceding section we encountered two mutually inconsistent Lucretian pas-
sages. In the rst of these (1.1052-1093) Lucretius refutes a rival theory that may be
attributed to the Stoics. Now, since it is generally assumed that Epicurus himself did
not yet engage the Stoics, who had then only recently come into the picture,
44 For a more extensive discussion of this passage see Bakker 2016, 223–235.
45 Lucretius 5.449–454: “Quippe etenim primum terrai corpora quaeque, / propterea quod erant
gravia et perplexa, coibant/in medio atque imas capiebant omnia sedes;/quae quanto magis inter
se perplexa coibant,/ tam magis expressere ea quae mare sidera solem/lunamque efcerent et
magni moenia mundi.” Text and translation (slightly modied) from Rouse and Smith 1992,
46 Lucretius 5.457-470 and 498-501.
47 See e.g. Cicero, De natura deorum 2.84, reporting the Stoic view: “in medium locum mundi, qui
est inmus.”
F. A. Bakker
Lucretius’ anti-Stoic polemic must postdate Epicurus.48 In that case Lucretius’ refu-
tation can be seen as a defence of the orthodox Epicurean position against a chal-
lenge that Epicurus himself will not have been aware of. That the passage should be
a later addition to Epicurus’ argumentation even seems to be borne out by the order
of Lucretius’ account: without any prior reference to the Stoic alternative Lucretius
rst emphatically concludes that “there is need of an innite quantity of matter on
all sides,”49 and only then sets out to refute the rival theory which threatens to under-
mine this conclusion.
The second passage (5.449-508), by contrast, is hard to reconcile with the ortho-
dox Epicurean view. Whereas Epicurus himself endorses a parallel conception of
downward motion, to which Lucretius generally also subscribes, this passage
assumes a centripetal downward tendency. Moreover, the account nds no parallel
in any other known Epicurean writing. The only parallel passage is found in Aëtius’
Placita 1.4, where a very similar theory is reported without attribution.50 Yet the
explicit reference to atoms and to the non-providential nature of the world’s coming-
into- being make it clear that the account must be atomistic. Moreover, certain
details– weight difference rather than a vortex as the formative principle, and the
tenuous rather than heavy nature of the heavenly bodies– clearly place the account
on the Epicurean rather than the Democritean side.51 In fact, the theory is Epicurean
in every respect other than the assumption of a centripetal instead of parallel gravity.
And yet, precisely this assumption makes the theory anomalous within the frame-
work of orthodox Epicurean cosmology, and virtually irreconcilable with the inn-
ity of atoms and worlds.
3.2.5 Provisional Conclusion
While in the Letter to Herodotus Epicurus could still condently claim to have
proved, once and for all, the joint innity of space and bodies, the subsequent appear-
ance of an alternative theory which allowed for a nite amount of matter to remain
together in innite space posed a challenge which later Epicureans had to meet. In
Lucretius’ De rerum natura we nd an attempt to refute this rival theory and re-
establish the orthodox Epicurean position, which in the rest of his work is simply
taken for granted. As we have seen, however, Lucretius’ refutation is not entirely
convincing. The question arises, therefore, why Lucretius, like most other Epicureans,
chose to stick to the orthodox view. An answer may be found in the important con-
sequences of this view, especially with respect to Epicurean theology.
48 For the early Epicureans’ lack of engagement with Stoic philosophy see Sedley 1998, 73, and
especially Kechagia 2010.
49 Lucretius 1.1051: “innita opus est vis undique materiai.” Text and translation from Rouse and
Smith 1992, 86–87.
50 For a comparison of Lucretius’ and Aëtius’ cosmogonical accounts, see Bakker 2016, 224–227.
51 Spoerri 1959, 8–29; Bakker 2016, 226–227.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
3.3 Theological Consequences oftheInnity oftheUniverse
The innity of the universe and its two component parts appears to have some
remarkable consequences. Firstly, it spawns an innity of other worlds beside the
one we inhabit; secondly, it makes the spontaneous coming-into-being of a world
not merely possible but necessary; and, nally, it allows for the simultaneous truth
of multiple, even mutually incompatible, explanations. What is more, all these cor-
ollaries have been argued by Epicurus himself or by his modern interpreters to be
crucial, in one way or another, to the Epicurean mission to free the world from
divine intervention. If it can be shown that they are, indeed, crucial, this might
explain why the Epicureans were so committed to the innity of the universe, and
had to defend this view against rival theories.
In the following part I will discuss each of these corollaries of the innity of
space and bodies, with special attention to their theological aspects. First, however,
it will be expedient to give some account of the Epicurean concept of divinity, to
serve as a background for the following discussion of innity.
3.3.1 The Epicurean Concept ofDivinity
The most important thing to know about the gods, according to Epicurus, is that they
are not involved in the creation and administration of the world or any of its parts in
any way. This does not mean that they do not exist, for we do have a preconception
of them– a preconceived notion resulting from repeated impressions, such as occur
to us in dreams.52 This preconception not only tells us that the gods exist, but also that
they are immortal and blissful.53 And since, being perfectly blissful, the gods have
neither need nor care for anything besides themselves, any involvement on their part
in the creation and governance of the world or any part thereof must be rejected.54
In addition to this conceptual proof of the gods’ inactivity with respect to the
world, the Epicureans also had a store of empirical arguments to bolster their view.
Since the opposite view was often supported by some form of the argument from
design, in which the observation of functional and orderly structures in the world
led to the assumption of a grand design and hence a designer god, the Epicureans
could simply point to the many instances of disorderly and useless, or even harmful,
things and phenomena in order to disprove the idea of such a grand design.55 To the
52 Cicero, De natura deorum 1.43–44; Epicurus, Letter to Menoeceus 123–124. For gods appearing
in dreams see Lucretius 5.1169-1171
53 Cicero, De natura deorum 1.45; Epicurus, Letter to Menoeceus 123–124. Cf. Lucretius
54 Epicurus, Letter to Herodotus 76 and 81; idem, Letter to Pythocles, 97; Cicero, De natura deo-
rum 1.51-53; Lucretius 5.156-173
55 Lucretius 5.195-234. Cf. Diogenes of Oenoanda “Theological Physics-sequence” (= NF 167 +
NF 126/127 + fr. 20 + NF 182), cols. XIV-XVI, in Hammerstaedt and Smith 2014, 263–270.
F. A. Bakker
Epicureans it was evident, therefore, that the gods neither created nor took care of
the world or any of its parts or inhabitants.
It is with this view of the gods in mind that we will now look into some corollar-
ies of the innity of bodies and space.
3.3.2 Innite Worlds andtheDemiurge
One consequence of the innity of atoms is the existence of not just a plurality, but
even an innity of worlds. In Letter to Herodotus 45, Epicurus writes:
Furthermore, there are innite worlds both like and unlike this world of ours. For the atoms
being innite in number, as was proved already, are borne on far out into space. For those
atoms, which are of such nature that a world could be created out of them or made by them,
have not been used up either on one world or on a limited number of worlds, nor again on
all the worlds which are alike, or on those which are different from these. So that there
nowhere exists an obstacle to the innite number of the worlds.56
In this passage Epicurus seems to take on Plato, who in Timaeus 32c-d states that
the composition of our world used up all the elements, leaving nothing outside, and
in Timaeus 55c-d, conceding that there might be more than one world– say, ve–
still emphatically rejects the notion that there might be innitely many.57
Epicurus’ statement is repeated by Lucretius, De rerum natura 2.1048-1066,
who then adds the following argument:
Besides, when abundant matter is ready, when space is to hand, and no thing and no cause
hinders, things must assuredly be done and completed. And if there is at this moment both
so great store of seeds as all the time of living existence could not sufce to tell, and if the
same power and the same nature abides, able to throw the seeds of things together in any
place in the same way as they have been thrown together into this place, then you are bound
to confess that there are other worlds in other regions and different races of men and genera-
tions of wild beasts.58
If the atoms were able to form a cosmos in this part of the universe they must have
been able to do so elsewhere, and given the innity of the universe, a possibility
56 Epicurus, Letter to Herodotus 45: λλ μν κα κόσμοι πειροί εσιν, ο θμοιοι τούτ κα
νόμοιοι. α τε γρ τομοι πειροι οσαι, ς ρτι πεδείχθη, φέρονται κα πορρώτατω· ο γρ
κατανήλωνται α τοιαται τομοι, ξ ν ν γένοιτο κόσμος φν ν ποιηθείη, οτες να
οτες πεπερασμένους, οθσοι τοιοτοι οθσοι διάφοροι τούτοις. στε οδν τ
μποδοστατσόν στι πρς τν πειρίαν τν κόσμων. Translation in Bailey 1926, 25.
57 See also Plato, Timaeus 31a–b.
58 Lucretius 2.1067-1076: “Praeterea cum materies est multa parata,/cum locus est praesto, nec res
nec causa moratur/ulla, geri debent nimirum et coneri res./nunc et seminibus si tanta est copia
quantam/enumerare aetas animantum non queat omnis,/visque eadem et natura manet, quae
semina rerum/conicere inloca quaeque queat simili ratione/atque huc sunt coniecta, necesse est
conteare/esse alios aliis terrarum in partibus orbis/et varias hominum gentis et saecla ferarum.
Text and translation in Rouse and Smith 1992, 178–179.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
cannot fail to be realised, and not once, but innitely many times. Hence there must
be an innity of worlds.
Lucretius’ conclusion rests upon the application of two principles: the principle
of uniformity, which assumes that the same circumstances obtain always and
everywhere,59 and a version of the so-called principle of plenitude, which states that
whatever can be done, will be done at some time or place.60
Having concluded that there are innitely many worlds, Lucretius proceeds to
use this conclusion as a premise in his argument against the notion of a divinely
governed universe:
If you hold fast to these convictions, nature is seen to be free at once and rid of proud mas-
ters, herself doing all by herself of her own accord, without the help of the gods. For I
appeal to the holy hearts of the gods, which in tranquil peace pass untroubled days and a life
serene: who is strong enough to rule the sum of the immeasurable, who to hold in hand and
control the mighty bridle of the unfathomable? who to turn about all the heavens at one time
and warm the fruitful worlds with ethereal res, or to be present in all places and at all
Lucretius’ conclusion takes the form of a series of rhetorical questions which invite
the answer ‘nobody’: nobody is strong enough to rule and control an innite number
of worlds, and nobody is able to be present always and everywhere throughout the
innite expanse of time and space.
However, as James Warren notes, this is not a particularly strong argument.62
Several responses come to mind that would avoid Lucretius’ desired conclusion that
innite worlds rule out divine intervention.
It might be suggested, for instance, that each world is governed individually by
its own god. In Lucretius’ defence, David Sedley points out that even those of
Lucretius’ opponents who were willing to assume a plurality of gods still assumed
a single overall command by a supreme deity, and would thus, after all, be subject
to Lucretius’ implied criticism.63
59 See e.g. Darling 2016, 416, and Mash 1993, 209, who explicitly identies ‘uniformitarianism’ as
one of the assumptions underlying the Lucretian argument.
60 The ‘Principle of Plenitude’ was rst described by Lovejoy 1936, 52 et passim. For the attribu-
tion of this principle to the ancient atomists see e.g. Dick 1996, 12–13; Fowler 2002, 368–369;
Sedley 2007, 138; 2013, ch. 4 (ad 5.416-770); Darling 2016, 329; and Bakker 2016, 21–24, 28–31,
74, 210. Versions of Lucretius’ argument– e.g. Drake’s Equation– are still invoked today by those
arguing for the likely existence of extra-terrestrial life and intelligence: see e.g. Mash 1993, and
Darling 2016, 329. For Bruno’s application of the principle see Section 8.2 of Granada’s Chapter
8 in this volume.
61 Lucretius 2.1090–1099: “Quae bene cognita si teneas, natura videtur/libera continuo, dominis
privata superbis,/ipsa sua per se sponte omnia dis agere expers./nam pro sancta deum tranquilla
pectora pace,/quae placidum degunt aevom vitamque serenam,/quis regere immensi summam,
quis habere profundi/indu manu validas potis est moderanter habenas,/quis pariter caelos omnis
convertere et omnis/ignibus aetheriis terras sufre feracis,/omnibus inve locis esse omni tempore
praesto.” Text and translation in Rouse and Smith 1992, 178–181.
62 Warren 2004, 363–364. See also Sedley’s critical response in Sedley 2007, 148–149.
63 Sedley 2007, 149 n33, cites Xenophon, Memorabilia 4.3.13, where “he who organizes and holds
together the whole world” (my translation) is singled out over the other gods. One might also think
F. A. Bakker
One might also respond that god is, in fact, strong enough to rule the innite. In
Lucretius’ defence, David Sedley points out that this would imply an innitely
extended god, a view which the Epicureans attributed to certain Presocratic philoso-
phers, and which they strongly opposed, on the grounds that this would make it
impossible for god to experience sensation, due to the lack of bodily extremities to
sense with.64 Perhaps, however, we do not even need to suppose that such a criticism
was implied. Lucretius’ most obvious opponents in the present context are not the
Presocratics, but thinkers like Plato and the Stoics, who equated innity with inde-
terminacy and imperfection, which have no place in divine creation65; and who
therefore emphasized the limited and nite nature of the created world.66 It was not
until the third century A.D. that, among Neoplatonists and Christians, innity began
to be seen as perfection and a tting attribute for a god.67
In short, Lucretius’ argument is aimed at thinkers who not only believe in a
divine involvement with the universe, but also think that this involvement needs to
be a unied and limited affair.
Although, at rst sight, this assumption seems to rescue Lucretius’ anti-
interventionist argument from such responses as were suggested above, it actually
undermines his argument even further. Lucretius’ argument is based on the innity
of worlds, a theory which in turn relies, among other things, on the application of
the principle of uniformity – the assumption that the same circumstances apply
everywhere. The validity of this assumption may be obvious if one adopts the
Epicurean view of a universe lled with atoms that all obey the same physical laws,
and hence may be assumed to produce the same effects everywhere. If, on the other
hand, one adopts the theory that the world is created by a supreme deity, and that
this act of creation is necessarily both unique and limited, it is clear that this result
cannot be applied universally: even in an innite universe lled with innite matter
the creation of one cosmos in no way implies the creation of another, let alone of an
of Plato’s Timaeus 40a–d, where the lesser, created gods are said to partake in the creation of the
world at the Demiurge’s behest. In fact, several centuries after Epicurus, in the second century AD,
the Platonist Plutarch, conceding that there might, in fact, be more than one world (though not
innitely many), suggests that while each world might be governed by its own supreme deity, all
the worlds together would still be subject to the single rule and reason of one divine overlord
(Plutarch, De defectu oraculorum 29, 425f2– 426b1).
64 Sedley 2007, 149, citing the Epicurean arguments reported by Cicero in De natura deorum
65 On Plato see Clarke 1994, 70–72, who specically quotes Plato’s Philebus 16–18, 23c–30,
61–67; Statesman 283b–285a; Laws 716c; Sophist 265e. For Plato’s application of the notion of
limit to the creation of the world see Plato Timaeus 31a-b, 32c-33a, 55c-d. For the Stoics, see
Plutarch, De communibus notitiis 30, 1074b7-c3 (SVF II 525, p.167.28– 168.1), which links inn-
ity to indeterminacy, incompletion and disorderliness; Sextus Empiricus, Against the Professors
9.148–149, which rehearses a Stoic argument for the limited nature of the divine; and Cleomedes
1.1, 7–17 (SVF II 534), which emphasises the limited nature of the created world.
66 Even Plutarch, while admitting a plurality of worlds (see n63 above), still stresses the nitude of
nature (Plutarch, De defectu oraculorum 24, 423c7-11 and 25, 424a8-12) and god (ibid. 30,
67 Clarke 1994, 75–79.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
innite number of others.68 Therefore, Lucretius’ argument against divine interven-
tion will convince only those who are already convinced that worlds do not come
about due to divine intervention.
3.3.3 Chance andthePower ofInnity
What the Epicureans had to do, therefore, was to show that the world could have
come into being even without divine intervention, as a result of mere chance. Now,
that such an orderly and complex structure as our world should arise by chance
seems exceedingly unlikely. The odds are dramatically increased, however, if inn-
ity is brought into play: according to the principle of plenitude, given innite oppor-
tunity, everything that is possible must be realised. Accordingly, even without divine
intervention, the innity of the universe makes the coming-into-being of a world
like ours not only possible but even inevitable.69
However, as James Warren notes, for this conclusion to obtain the Epicureans did
not have to postulate the innity of matter and space; the innity of time alone,
which the Epicureans commonly accepted, would sufce to guarantee that any pos-
sible conguration would be realized, and not once, but innitely many times.70
What is more, in the two passages where Lucretius actually applies the principle
of plenitude to the formation of the cosmos (1.1021–1028 and 5.419–431), he only
refers to the innity of time, not of matter and space. I quote the second passage,
which is the clearest in this respect:
For certainly it was no design of the rst-beginnings that led them to place themselves each
in its own order with keen intelligence, nor assuredly did they make any bargain what
motions each should produce; but because many rst-beginnings of things in many ways,
struck with blows and carried along by their own weight from innite time up to the present,
have been accustomed to move and to meet in all manner of ways, and to try all combina-
tions, whatsoever they could produce by coming together, for this reason it comes to pass
that being spread abroad through a vast time, by attempting every sort of combination and
motion, at length those come together which, being suddenly brought together, often
become the beginnings of great things, of earth and sea and sky and the generation of living
68 So also Asmis 1984, 66 n19: “a demiurge would provide a reason why the number of possibilities
should be restricted to a single possibility.
69 For a lucid and very attractive exposition of this theory, see Sedley 2007, 137–139 and
70 Warren 2004, 364, citing David Hume’s Dialogues Concerning Natural Religion, part 8. For the
Epicureans’ implicit endorsement of the innity of time see Sedley 1999, 373.
71 Lucretius 5.419-431: “nam certe neque consilio primordia rerum/ordine se suo quaeque sagaci
mente locarunt/nec quos quaeque darent motus pepigere profecto,/sed quia multa modis multis
primordia rerum/ex innito iam tempore percita plagis/ponderibusque suis consuerunt concita
ferri / omnimodisque coire atque omnia pertemptare, / quaecumque inter se possent congressa
creare, / propterea t uti magnum volgata per aevom, / omne genus coetus et motus experi-
undo,/tandem conveniant ea quae convecta repente/magnarum rerum unt exordia saepe,/terrai
maris et caeli generisque animantum.” Text and translation in Rouse and Smith 1992, 410–413 (my
F. A. Bakker
The same observation applies to Epicurus as well, who, according to one ancient
testimony, stated that “nothing unfamiliar comes about in the universe, due to the
innity of time that has already passed.”72
In short, although it is often stated that the innity of the universe was a neces-
sary part of the Epicureans’ anti-teleological argument, the argument actually works
just as well on the assumption of innite time, and was, in fact, applied in this way
by Lucretius and Epicurus themselves.
3.3.4 Innity andtheTruth ofMultiple Explanations
The Epicurean theory of innite worlds also carries important epistemological con-
sequences. In astronomical and meteorological matters the Epicureans famously
prescribed the use of multiple explanations to account for each phenomenon, instead
of just one.73 This might just be considered a kind of epistemic modesty: since in
such matters the evidence does not allow us to discriminate between various expla-
nations, all explanations that agree with the observations and do not violate the
general principles of Epicurean physics must be retained. However, there is ample
evidence that the Epicureans went beyond a mere sceptical afrmation of doubt.
They did not doubt which of the accepted explanations was true: they were adamant
that all accepted explanations– even mutually incompatible ones– were true.74
But how could the Epicureans assert the simultaneous truth of multiple explana-
tions? Lucretius offers the following argument (DRN 5.526-533):
For which of these causes holds in our world it is difcult to say for certain; but what may
be done and is done through the whole universe in the various worlds made in various ways,
that is what I teach, proceeding to set forth several causes which may account for the move-
ments of the stars throughout the whole universe; one of which, however, must be that
which gives force to the movement of the signs in our world also; but which may be the true
one, is not his to lay down who proceeds step by step.75
There may be doubt as to which cause is operative in our world, but this does not
mean that other explanations are not true: in the innity of the universe every pos-
sible explanation must be actualized somewhere, and in this sense every possible
72 Epicurus fr. 266 (in Usener 1887, 191) = ps.-Plutarch, Stromateis 8: οδν ξένον ν τ παντ
ποτελεται παρ τν δη γεγενημένον χρόνον πειρον (translation mine).
73 For an overview see e.g. Taub 2009, 110–112, 115, 120–123.
74 On the truth of multiple explanations see Striker 1974; Sedley 1982, 263–272; Asmis 1984,
178–180, 193–196, 211, 321–336; Long and Sedley 1987a, 90–97; Asmis 1999, 285–294; Allen
2001, 194–205 and 239–241; Bénatouïl 2003, 42–44; Verde 2013, 134–135; Bakker 2016, 13–31.
75 Lucretius 5.526–533: “Nam quid in hoc mundo sit eorum ponere certum/difcile est; sed quid
possit atque per omne/in variis mundis varia ratione creatis,/id doceo, plurisque sequor dispo-
nere causas,/motibus astrorum quae possint esse per omne;/e quibus una tamen siet hic quoque
causa necessest/quae vegeat motum signis; sed quae sit earum/praecipere haudquaquamst pede-
temptim progredientis.” Text and translation from Rouse and Smith 1992, 418–419.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
explanation is also true. This is yet another application of the principle of
This method of multiple explanations was the Epicureans’ response to the dog-
matic certainty with which other philosophers propounded single explanations. A
sceptic detachment would not do, because this would leave open the possibility that
the other philosophers were right after all. The Epicureans therefore countered the
dogmatic assertion of single explanations with an equally dogmatic assertion of a
multiple account.76
But why would the Epicureans want to oppose single explanations in the rst
place? As Epicurus himself repeatedly states, the principal reason for engaging in
physical inquiry is to exclude the divine from the workings of nature, see e.g.
Epicurus’ Letter to Herodotus 76–77:
Furthermore, the motions of the heavenly bodies and their turnings and eclipses and risings
and settings, and kindred phenomena to these, must not be thought to be due to any being
who controls and ordains or has ordained them and at the same time enjoys perfect bliss
together with immortality (for trouble and care and anger and kindness are not consistent
with a life of blessedness, but these things come to pass where there is weakness and fear
and dependence on neighbours).77
Elsewhere, too, Epicurus enjoins his reader not to resort to myth.78 However, if
physical inquiry is all about excluding myth and divine intervention, why is one
naturalistic explanation not enough?79 The answer to this question may be found in
a number of passages in Epicurus’ Letter to Pythocles. In §87, for instance, Epicurus
But whenever one accepts one explanation while rejecting another that harmonizes just as
well with the phenomenon, it is clear that one falls from scientic inquiry altogether and is
plunged into myth.80
According to Epicurus, providing a single explanation when other explanations are
equally plausible is in itself a kind of myth. But why should a single explanation
amount to myth? Another relevant passage that may provide some further clues is
76 See Warren 2004, 361: “With the addition of the conception of innite kosmoi the Epicureans can
claim not only that one of the possible explanations is the true one but that in fact all of them are
true. In this way they can hope to bridge the gap between offering multiple merely possible expla-
nations and the provision of sure, tranquillity-producing, conviction.
77 Epicurus, Letter to Herodotus 76–77: Κα μν ν τος μετεώροις φορν κα τροπν κα κλειψιν
κα νατολν κα δύσιν κα τ σύστοιχα τούτοις μήτε λειτουργοντός τινος νομίζειν δε
γίνεσθαι κα διατάττοντος διατάξαντος κα μα τν πσαν μακαριότητα χοντος μετ
φθαρσίας· ο γρ συμφωνοσι πραγματεαι κα φροντίδες κα ργα κα χάριτες μακαριότητι,
λλν σθενεί κα φόβ κα προσδεήσει τν πλησίον τατα γίνεται. Translation in Bailey
1926, 49.
78 Epicurus, Letter to Pythocles 104.3: μόνον μθος πέστω. Cf. ibid. 115.8.
79 Similarly Verde 2013, 130.
80 Epicurus, Letter to Pythocles 87: ταν δέ τις τ μν πολίπ τ δ κβάλ μοίως σύμφωνον
ν τ φαινομέν, δλον τι κα κ παντς κπίπτει φυσιολογήματος, π δ τν μθον καταρρε.
Translation mine.
F. A. Bakker
But to assign a single cause for these phenomena, when the phenomena call for a plural
account, is madness, and is unttingly practised by those who are devoted to idle astronomy
and vainly assign causes for certain phenomena, since (ταν) they do not free divine nature
in any way from the burden of responsibilities.81
Providing single explanations for celestial phenomena is typically practised by dev-
otees of astronomy– not just professional astronomers, but also those who accepted
and incorporated the astronomers’ ndings into their own cosmologies, like Plato,
Aristotle and the Stoics.82 However, Epicurus’ criticism is not limited to these devo-
tees of astronomy, but also applies to others who provide single explanations when
the phenomena call for several, whether one is dealing with astronomical or atmo-
spheric occurrences. Nor should the explanations provided by these devotees of
astronomy and other proponents of single causes be spurned as such: this is made
clear by the inclusion of many such views in Epicurus’ and Lucretius’ lists of mul-
tiple explanations.83 Apparently these views are only objectionable in so far as they
are claimed to be uniquely true. But why would this be objectionable? The answer
to this question is given in the concluding, subordinate clause of the cited passage.
Unfortunately, the Greek here presents an ambiguity. According to Liddell and
Scott’s Greek-English Lexicon, ταν, the conjunction which starts the clause, nor-
mally means “whenever, with a conditional force.84 Yet if the conjunction is taken
in this sense, one might conclude that assigning single causes is okay after all, as
long as the gods are not involved. This would be a very weak conclusion after
Epicurus’ insistence on the need for multiple explanations both in the present pas-
sage and throughout the Letter to Pythocles, and would also be at odds with the
previously quoted passage (from §87), where rashly opting for a single explanation
(apparently regardless of its content) was equated to myth. However, Liddell and
Scott also report a second meaning. Occasionally, ταν is also used in a causal sense
(attested from Aristotle onwards), which may be rendered as ‘since.85 If we take the
conjunction in this sense, the nal clause turns out to provide the very answer we
were looking for: assigning single causes, when the phenomena call for several, is
wrong, because this would imply divine involvement in the world. This conclusion
seems to be conrmed by §97:
And divine nature must not be applied to these things in any way, but must be preserved
unburdened by responsibilities and in complete blessedness. For if this practice is not
observed the entire inquiry into the causes of celestial phenomena will be idle, as it has
already been for certain people who have not clung to the possible method, but have fallen
back into idle talk by believing that things only happen in one way, and rejecting all other
81 Epicurus, Letter to Pythocles 113: τ δ μίαν ατίαν τούτων ποδιδόναι, πλεοναχς τν
φαινομένων κκαλουμένων, μανικν κα ο καθηκόντως πραττόμενον π τν τν ματαίαν
στρολογίαν ζηλωκότων κα ες τ κενν ατίας τινν ποδιδόντων, ταν τν θείαν φύσιν
μηθαμ λειτουργιν πολύωσι. Translation (and emphasis) mine.
82 See Bakker 2016, 57.
83 For the incorporation of the astronomers’ views in Epicurus’ and Lucretius’ lists of alternative
explanations, see Bakker 2016, 42–58.
84 Liddell and Scott 1940, 1264, lemma ταν.
85 Admittedly, the use of ταν in this sense is otherwise unattested in Epicurus’ works.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
explanations that follow from the possible method, being driven thus to what is inconceiv-
able, and unable to make a survey of the phenomena that must be accepted as signs.86
Although the statement is quite convoluted, it seems to imply that those “people
who […] have fallen back into […] believing that things only happen in one way”
have thereby failed to observe the practice of preserving divine nature “unburdened
by responsibilities and in complete blessedness.”
In short, according to Epicurus, assigning single explanations to celestial phe-
nomena in itself (i.e. regardless of the content of each explanation) already amounts
to involving the gods in the workings of nature. Why this should be so is not stated
clearly anywhere by Epicurus. However, his explicit reference to the devotees of
astronomy in §113 suggests that his quarrel is not so much with those who provide
single causes on one or two occasions, but with those who do so systematically, like
professional astronomers and their followers. Elsewhere I have argued, on the basis
of the above and other passages, that Epicurus was opposed to the astronomers and
their followers because of their groundless reliance on a preconceived theoretical
model in which phenomena were accounted for with single explanations according
to a unied explanatory principle.87 It was the belief in these general explanatory
theories, often illustrated by means of tangible mechanical models,88 that Epicurus
especially opposed, considering them to be nothing more than “empty assumptions
and arbitrary principles,”89 without a rm basis in the phenomena.
Moreover, by embracing these models the devotees of astronomy grant the world
an amount of coherence and regularity that seems to point to an overall design.90 In
fact, both Plato and the Stoics explicitly link the orderly nature of the world, and
especially the heavenly sphere, to its being designed by a god. In Timaeus 34b-40d,
Plato describes how the Demiurge successively created the heavens, the celestial
orbits, and nally the heavenly bodies themselves as living gods, according to a
single coherent and intelligent plan, the details of which can only be understood by
the use of visible models; and in Laws 820e-822c he prescribes the study of astron-
omy in order to eradicate the erroneous and blasphemous view that the planets,
being gods, should wander about aimlessly. The Stoics even made the order and
86 Epicurus, Letter to Pythocles 97: κα θεία φύσις πρς τατα μηδαμ προσαγέσθω, λλ
λειτούργητος διατηρείσθω κα ν τ πάσ μακαριότητι. ς ε τοτο μ πραχθήσεται πασα
τν μετεώρων ατιολογία ματαία σται, καθάπερ τισν δη γένετο ο δυνατο τρόπου
φαψαμένοις, ες δ τ μάταιον κπεσοσι τ καθνα τρόπον μόνον οεσθαι γίνεσθαι, τος δ
λλους πάντας τος κατ τ νδεχόμενον κβάλλειν, ες τε τ διανόητον φερομένους κα τ
φαινόμενα δε σημεα ποδέχεσθαι μ δυναμένους συνθεωρεν. Translation mine.
87 Bakker 2016, 32–33, 263, 266–267; see also 57–58.
88 On the use of mechanical models in astronomy see Cornford 1935, 74–76; and Evans 1998,
78–84. On Epicurus’ opposition to this practice see Sedley 1976, 32, 37–39.
89 Epicurus, Letter to Pythocles 86: Ο γρ κατ ξιώματα κεν κα νομοθεσίας φυσιολογητέον,
λλς τ φαινόμενα κκαλεται. Translation in Bailey 1926, 59.
90 Similarly Verde 2013, 131, 135.
F. A. Bakker
regularity of the celestial motions a prime exhibit in their argument from design,
likening the heavenly sphere to a man-made orrery.91
In this way the systematic application of single explanations could be taken to
imply a belief in divine creation, to which the systematic and dogmatic assertion of
multiple explanations would provide an effective antidote. However, in order to
perform this function, each of these multiple explanations has to be not merely pos-
sible, but actually true. And this is where, as we have seen, the innity of worlds
comes in: the principle of plenitude stipulates that in the innity of the universe
every possible explanation must be true somewhere.
However, to this line of reasoning several objections can be made. Firstly, one
might call into question whether single explanations really do imply divine gover-
nance. Epicurus may have believed so, but Lucretius, in those passages where he
either expounds or applies the method of multiple explanations, never claims that
multiple explanations as such are necessary to eliminate divine intervention. In fact,
on several occasions where one might have expected a multiple account, Lucretius
is content to give a single explanation, apparently without fearing thereby to make
the gods responsible. A later Epicurean, Diogenes of Oenoanda, even gives up on
the simultaneous truth of multiple explanations altogether, claiming instead that,
“while all explanations are possible, this one is more plausible than that,” without
worrying about theological consequences.92
Secondly, even if one accepts that the dogmatic assertion of multiple explana-
tions is necessary to rule out divine involvement, one might still doubt whether a
plurality of worlds is required to guarantee the truth of each individual explanation.
In a recent article Francesco Verde has suggested that Lucretius may not have ren-
dered Epicurus’ thought adequately in this respect.93 While emphasizing– even
more clearly than Epicurus himself– the truth of every given explanation in the
universe at large, Lucretius at the same time seems to slip right back into the scepti-
cism that Epicurus wanted to avoid, by stressing that in this world only one
explanation applies, although we do not know which one. Since in similar contexts
Epicurus himself never refers to other worlds, the various individual explanations
should be thought of as true even within this world: compatible explanations could
be true at the same time, while incompatible ones may still be true sequentially. If
Verde is right, then however important the method of multiple explanations may
have been to demythologize the world, the innity of the universe may not have
played any part in it.
91 Cicero, De natura deorum II 88.
92 Diogenes of Oenoanda fr.13 iii 10–12 (in Smith 1993, 171). For the epistemological import of
this passage see Verde 2013, 136–137; Bakker 2016, 37–42, 242; Leone 2017, 97–100; and espe-
cially Corsi 2017, 277–282.
93 Verde 2013, 139–141. See also Corsi 2017, 262–263.
3 The End ofEpicurean Innity: Critical Reections ontheEpicurean Innite Universe
3.3.5 Summary
Although the innity of atoms, and consequently of worlds, appears as a premise in
several actual or presumed Epicurean arguments against divine intervention, it turns
out to be neither sufcient nor necessary to arrive at the desired conclusion. True,
the innity of worlds rules out divine intervention (at least as conceived by Plato
and the Stoics), but this can only be established after divine intervention has been
ruled out already. True, the joint innity of atoms and void guarantees that any con-
guration of atoms, including our cosmos, will be realized even without divine
intervention, but so does the innity of time, and, in fact, the Epicureans only
invoked the latter. True, the innity of worlds would ensure that every objectively
possible explanation is also true, as Lucretius claims; but it is debatable, rstly, to
what extent Epicurus himself used or needed the innity of worlds to account for the
truth of multiple explanations; secondly, to what extent later Epicureans still
endorsed the truth of multiple explanations, as opposed to their mere possibility or
probability; and thirdly, to what extent later Epicureans were still committed to the
thesis that divine intervention can only be eliminated by multiple, as opposed to
single, naturalistic explanations. In sum, there is no reason to assume that the
Epicureans had strong theological motives for positing and upholding the joint
innity of atoms and void.
3.4 Conclusion
In this chapter I have tried to establish why the Epicureans, in contrast to every other
ancient school of philosophy, posited an innite amount of matter. I have approached
this question from two different angles. In the rst half of the chapter the physical
arguments for the innity of matter were discussed. In both Epicurus’ Letter to
Herodotus and Lucretius’ De rerum natura the innite number of atoms is inferred
from the innity of space, on the assumption that a nite number of atoms would be
scattered abroad and not be able to meet and produce anything. For Epicurus this
was the end of the matter, but later Epicureans had to deal with a rival theory that
threatened to undermine the Epicurean argument: by assuming a theory of centrip-
etal gravity the Stoics were able to account for the innity of space without the need
for a corresponding innity of matter. Lucretius offers a refutation of the Stoic view,
but his counter-arguments appear to be either unfounded or unconvincing, and are
further undermined by Lucretius’ implicit endorsement, later on in his work, of
centripetal gravity.
In the second half of the chapter I have looked at the question from another point
of view. If the physical arguments are not strong enough to prove the innity of
atoms, the Epicureans may have had other– theological and ethical – motives to
uphold this thesis. In the writings of Epicurus and Lucretius several arguments are
found or are thought to be implied in which the innity of matter rules out divine
F. A. Bakker
intervention in the world. However, as we have just seen, none of these arguments
holds up to scrutiny.
The somewhat disappointing conclusion is that the Epicurean endorsement of
the innity of matter, and hence of worlds, was warranted neither by physical nor by
ethical considerations. Epicurus himself, blissfully ignorant of the challenge that
would be posed by the Stoics, may still have believed that his proof of the innity
of atoms was conclusive, and hence could be used, perhaps not as sufcient, but at
least as supporting evidence against divine intervention. Later Epicureans, however,
felt obliged to defend a thesis that was neither consequent upon the principles of
Epicurean physics, nor antecedent to the main doctrines of Epicurean ethics, but one
that nevertheless had become a dening tenet of their sect.94
Algra, Keimpe. 1988. The Early Stoics on the Immobility and Coherence of the Cosmos. Phronesis
33: 155–180.
———. 1995. Concepts of Space in Greek Thought. Leiden/New York/Cologne: Brill.
Allen, James. 2001. Inference from Signs. Ancient Debates about the Nature of Evidence. Oxford:
Oxford University Press.
Arnim, Hans von. 1903–1905. Stoicorum veterum fragmenta [= SVF], 3 vols. Leipzig: Teubner.
Arrighetti, Graziano. 1973. Epicuro: Opere. Turin: Einaudi.
Asmis, Elizabeth. 1984. Epicurus’ Scientic Method. Ithaca/London: Cornell University Press.
———. 1999. Epicurean Epistemology. In The Cambridge History of Hellenistic Philosophy, ed.
Keimpe Algra, Jonathan Barnes, Jaap Mansfeld, and Malcolm Schoeld, 260–294. Cambridge:
Cambridge University Press.
Avotins, Ivars. 1983. On Some Epicurean and Lucretian Arguments for the Innity of the Universe.
The Classical Quarterly 33: 421–427.
Bailey, Cyril. 1926. Epicurus, the Extant Remains. Oxford: Clarendon Press.
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The term fp - indicating the fraction of suitable stars with planetary systems - is anachronistic to much of the time period under discussion. This chapter will survey a number of theories about planetary systems in Western thought prior to 1961 and will consider what values the term would have been assigned based on the natural philosophy or science of periods before 1961. In antiquity, two strands of thought, the Aristotelian and the atomistic, would have provided very different values for fp. The former proposed a very clear value: zero. There are no planetary systems other than our own. The value that the latter would have proposed, however, presents a more complex situation, as atomists believed there are infinite other inhabited worlds, though none could be seen from our own. The Aristotelian view held sway in the West until the Copernican Revolution sparked a dramatic shift in cosmological ideas. Ultimately, the notion that our solar system was merely one of many planetary systems won out. Such a view was promoted, alongside the idea of plentiful extraterrestrial life, by two popularizers from the late seventeenth century: Christiaan Huygens and Bernard le Bovier de Fontenelle. The view that planetary systems were plentiful persisted through the nineteenth century, and so fp must be understood to have a value of close to 1. Numerous authors posited life even in other places, such as comets and the Sun; planetary systems, then, were not the only abode for extraterrestrial life during this period of optimism about the plurality of worlds, suggesting that fp was an inadequate criterion for the location of life. In the second half of the nineteenth century, William Whewell posited that little was scientifically known about other planetary systems and made various arguments against their commonality.
In Epicurean Meteorology Frederik Bakker discusses the meteorology (including astronomy) as laid out by Epicurus (341-270 BCE) and Lucretius (1st century BCE). Although in scope and organization their ideas are clearly rooted in the Peripatetic tradition, their meteorology sets itself apart from this tradition by its systematic use of multiple explanations and its sole reliance on sensory evidence as opposed to mathematics and other axiomatic principles. Through a thorough investigation of the available evidence Bakker offers an updated and qualified account of Epicurean meteorology, arguing against Theophrastus’ authorship of the Syriac meteorology, highlighting the originality of Lucretius’ treatment of mirabilia, and refuting the oft-repeated claim that the Epicureans held the earth to be flat.
A goal of Epicurean philosophy was the achievement of calm and freedom from anxiety. Epicurus believed that if people can be freed from fear-including fears relating to the actions of gods-they can then achieve ataraxia (‘being undisturbed’). Epicurean cosmology and meteorology were motivated by the desire to alleviate fear of gods. While Epicurus recognized the existence of gods, he denied the possibility that they have any cosmic influence. He developed a strict materialist philosophy, designed to offer natural explanations of phenomena that were often seen as due to activities of gods. Questions about the origin and order of the world, its possible beginning and end, are potentially disturbing: Violent natural phenomena, particularly thunder, lightning, hail and earthquakes, can be terrifying and destructive. If such phenomena are not due to gods, there is no reason to fear the gods' involvement in our world. Epicurean meteorology explained the meteora (the phenomena of the sky, and earthquakes); cosmology focused on the nature of our local cosmos (kosmos), while acknowledging the existence of an infinite number of kosmoi (worlds). The Greek word kosmos carried a range of meanings; its use in natural philosophy was coloured by the worldview of the user.