## 1. Atomism in Classical Indian Philosophy



The beginnings of atomism in classical Indian philosophy are difficult
to ascertain, but it likely has origins several centuries before the
common era. Two distinct systems that regard Vedic texts as
authoritative, Nyaya and Vaisesika, favoured atomist
accounts of the material world. Quite different atomist theories are
found in Buddhist and Jaina systems. Other Indian philosophical
systems were critical of atomism, arguing instead for an idealist
account of experience. The Buddhist philosopher Vasubandhu (5th c.
CE), whose earlier *Treasury of Metaphysics* is often
considered an atomist account, critiqued atomism in his *Twenty
Verses*.



The terms translated 'atom' in Indian philosophy
(*anu*, *param**anu*) refer
primarily to the smallness of parts (Gangopadhyaya 1980): this notion
of smallness, found in the Upanishads, was developed into atomist
theories in the commentary tradition. A classic argument for atomism
reasons by analogy from the fact that perceptible objects seem to be
composed of parts (Chatterjee 2017). Yet, the argument ran, bodies
cannot be infinitely divisible because this would lead to the
paradoxical result that a mountain and a mustard seed would be equal
in size. This rebuttal--closely echoed in Islamic
debates--is based on the kind of paradox about summation of
infinite series also found in the ancient Greek tradition (Bhaduri
1947, 55). The comparison of mountain and mustard seed was also
deployed to argue that the concepts of small and large would be
indistinguishable unless smallness had a defined magnitude
(Gangopadhyaya 1980, 29).



Not all Indian atomist theories regard minima as substantial entities.
Carpenter (2021) describes the trope theory of Vasubandhu as
'absolute atomism': this characterization challenges the
notion that atomism canonically centres on the positing of enduring
particles. Instead, the focus is on minimal units in time as well as
space, which are simultaneously minimal components of ontological
units and not substance-attribute composites.



A tradition that the Greek atomist Democritus was acquainted with the
ideas of the 'gymnosophists' or 'naked wise
men' of India is difficult to authenticate. Claims that Indian
atomism was shaped by Greek influences (Keith 1921, 17) are uncommon
in recent scholarship. The possibility that Islamic atomism was
impacted by debates in classical Indian philosophy has been more
extensively considered, particularly given parallel arguments and the
shared view that atoms never exist in isolation (Pines 1997; Wolfson
1976). Another feature common to both traditions is a willingness to
ascribe sensible qualities to atoms, in contrast to Greek atomist
theories. Indian Buddhist scholars introduced atomist theories to
China from the second century CE onward, but they seem not to have
been adopted into ancient Chinese natural philosophy (Needham 1969,
22).


### 1.1 Nyaya-Vaisesika atomism



The Nyaya and Vaisesika systems developed separately,
the former focusing on epistemological issues and the latter on
ontology. Nonetheless, there were enough overlap and later
reconciliations between them that scholars often consider their
picture of the natural world together. Both schools developed as
traditions of commentary on the Upanishads, dating back to 800 BCE
(Phillips 1995). In contrast to the Buddhist tradition, atoms in these
systems of thought were regarded as external material substances that
persist through change, although--in line with the teachings of
the Vedic scriptures--the atoms were thought to be created.
Important figures in the textual tradition include Kanada,
regarded as founder of the Vaisesika school;
Prasastapada, author of the first surviving commentary;
Gautama (ca. 150 CE); Vatsyayana (ca. 400 CE). The work of
Udayana (11th c. CE) and Gangesa (c. 1325 CE) gave rise to
a new school, Navya- Nyaya, that largely merged the two
traditions (Matilal 1977; Phillips 1995; Ganeri 2019).



Nyaya-Vaisesika atomism developed in constant dialogue
with other Indian philosophical schools: in a context where Buddhism
offered a compelling narrative of personal salvation through
detachment from the unrealities of the experienced world, some Hindu
philosophers responded by bolstering their case for the realism of the
experienced world, and real atomic substances were invoked to explain
both mental and physical events (Ganeri 2011, 167-8). The idea
that experienced properties inhere in real external substances was
used to account for intersubjective agreement about the external
world.



The Nyaya-Vaisesika theory posited different kinds of
atoms for each of the elements earth, water, air and fire, in contrast
to the Jaina theory that there is a single homogenous matter out of
which everything is composed (Gangopadhyaya 1980). Atoms were regarded
as substances and bearers of different attributes. Different clusters
of properties were ascribed to atoms of different kinds (Dasgupta
1987; Chatterjee 2017). In contrast to the Greek atomists, who denied
that sensible properties really inhere in atoms at all, atoms of
different elements are thought to have perceptible properties, such as
cold for water atoms. Some theorists allow for the possibility of
altering the fundamental properties of atoms by heating (Thakar 2003).
For atomists in the Nyaya-Vaisesika systems, who held
that the atoms are made of fundamentally different matter, there is a
problem of explaining how properties of one kind of atom can affect an
atom of a different kind, i.e. how the viscosity of water atoms is
able to combine with earth atoms and to change their consistency
(Gangopadhyaya 1980, 34).



Atoms combine into dyads and triads before they aggregate into bodies
of a kind that can be perceived. The theory however faced a question
how atoms can combine, if they are indeed partless: unless we can
distinguish different parts to an atom, it is difficult to see how
they can be said to be *next* to one another--side by
side--any more than mathematical points can be said to join
together rather than collapsing into a single point. The response is
to deny the analogy to points, since atoms are tangible entities and
two of them cannot occupy the same place (Bhaduri 1947, 63), thus
atoms do not lose their identity when they aggregate. Another approach
to the problem is due to Vasubandhu in the Buddhist tradition (see
Carpenter 2021).



Nyaya-Vaisesika atomism also faced the challenge that
their theory was only based on logical inference and could not be
confirmed by experience (Bhaduri 1947, 58). In the atomism of Gautama,
recognizing the reality of composites is important to secure the basis
for knowledge, since atoms themselves are too small to be seen.
Vatsyayana supports this conclusion empirically, pointing
out that a forest may be visible from a distance where the individual
trees are not (Sarkar 2021). In an ongoing controversy with Buddhist
philosophers over the reality of composite entities, Nyaya
atomists denied that we are aware of composites only indirectly or by
means of awareness of individual parts (Matilal 1986, 268).



Nyaya and Vaisesika atomists held that the world was
created when order was imposed on pre-existing matter: the motion of
atoms was ascribed to a divine source. Their analysis of motion and
its causes employs concepts that have been compared to modern notions
of force (Kumar 2019). Although the systems had naturalistic leanings,
unusual motions such as the action of a magnet might be
ascribed--as it was in the European middle ages--to the
moral condition of human agents (Matilal 1977, 58). The organization
of atoms was cited as a proof for the existence of God by the 11th
century CE atomist Udayana (Gangopadhyaya 1980, 36). The mind and self
or soul--like time and space--was regarded as a distinct
category from material elements, a distinction traced back to the
classical scriptures.


### 1.2 Buddhist atomist theories



Developed in the centuries after the Buddha (6th c. BCE), Buddhist
philosophies, especially the Abhidhamma school, systematized the
underlying philosophy of a body of texts that focused on human lived
experience. The entities in Buddhist theory that are considered
atomistic are not substances but momentary events, *dharmas* or
*dhammas*: 'the constituents of sentient experience, the
irreducible "building blocks" that make up one's
world' (Ronkin 2005, 41). These atomic particulars can be mental
or physical, and have been compared to trope theories or process
metaphysics in contemporary scholarship. Unlike theories of atomic
substances, Buddhist atoms are not composed of multiple properties. In
contrast to Nyaya-Vaisesika atomists, Buddhists deny
that there is an underlying substance uniting different properties
like the colour and the weight of a jar (Bhaduri 1947). Atomic
property-instances do not occur in isolation, any more than nouns and
verbs made sense alone.



Despite the phenomenological character that atoms sometimes bear in
Buddhist thought, questions about compositionality occur which
parallel issues in other ancient atomist theories (Goodman 2004,
Carpenter 2021). Vaisesika thought--which accepted
categories like substance and soul--impacted the articulation of
Abhidhamma ontology, an articulation that sometimes led to charges of
'ontologization,' i.e. of moving away from the
experiential focus of Buddhist thought towards a more systematic
metaphysics (Ronkin 2005). Material atoms are first found in Buddhist
thought in the work of Dharmasri (2nd c. CE), and feature in the work
of Vasubandhu and Sanghabhadra (both 5th c. CE) (Ronkin 2005, 56).



Buddhist versions of atomism differ from
Nyaya-Vaisesika versions on the status of the wholes
composed of atoms, with the former treating composites as mere
aggregates, the latter regarding them as distinct entities in their
own right (Sarkar 2021). The Buddhist emphasis on the transitory
nature of material reality was part of the motivation for their
interest in atomist explanations (Gangopadhyaya 1980, 52; Ronkin 2005,
59). In the enumeration of different kinds of mental states, notions
that correspond to materiality are included, although earth, water,
wind and fire are typically considered to be merely mental constructs
in Buddhist thought.



Atoms were nonetheless used in materialist explanations, which account
for physical phenomena such as the combination of different elements
to form macroscopic materials. Because we appear to see visible
particles of dust, or rays of light shining on glass or mirrors, it
seemed reasonable to suppose that interactions too small to perceive
produce observed changes in the macroscopic world (Dasgupta 1987).
Heat and light were thought to be produced by minute corpuscles
entering other bodies. Buddhist atomism regarded atomic properties
such as solidity, heat and motion as producing perceptible changes at
the macroscopic level (Gangopadhyaya 1980, 13-14). Even with
non-material atoms, the question of their occupation of space was
considered: Matilal suggests that tangibility may have been regarded
as a latent property of the atoms, which emerges like visibility when
they cluster (Matilal 1986, 361). Different Buddhist schools disagreed
on the answer to these questions.



Problems about the possibility of motion, developed especially by the
Buddhist Nagarjuna (2nd c. CE), prompted responses in other
schools of thought (Matilal 1977, 79; Dasgupta 1987). Although the
persistence of macroscopic bodies might be illusory, there were
discussions about the momentum or persisting tendencies of moving
bodies, the different directions exhibited by these tendencies in a
rotating wheel, and the cohesion of particles within moving
bodies.


### 1.3 Jaina atomism



Jaina atomist theory treats matter, space and time as composed of
indivisible smallest parts (Pines 1987). Although natural philosophy
may not have occupied a large role in Jaina thought, the reason for
positing atoms is as the ultimate cause of perceived physical
qualities (Nyayavijayaji 1998). They posited a homogenous matter out
of which every material body is composed, in contrast to the atomism
of the Nyaya-Vaisesika and Buddhist systems, which
posited atoms of different kinds for each of the elements earth,
water, fire and air (Gangopadhyaya 1980). Atoms thus bring different
properties to aggregates, as, for example, the addition of water atoms
causes earth atoms to stick together (Dasgupta 1987). The tendency of
atoms to cohere into aggregates was thought to come from their own
nature and not from external pressures (Nyayavijayaji 1998).



Jaina atomists also regarded soul as a distinct kind of entity,
although they held that material atoms can percolate into soul and
affect it. Space was also treated as a distinct kind of substance
(Mehta 1954). Jaina tradition claims to have been the oldest atomist
system and to have inspired Vaisesika atomism, although
recent scholarship suggests that the reverse is true (Matilal 1977,
60; Thakar 2003, 7-8, 450).


## 2. Ancient Greek Atomism



Ancient Greek atomists developed a systematic and comprehensive
natural philosophy accounting for the origins of everything from the
interaction of indivisible bodies, as these atoms--which have
only a few intrinsic properties like size and shape--strike
against one another, rebound and interlock in an infinite void. In
both its Democritean and its Epicurean versions, Greek atomism
eschewed teleological explanation and denied divine intervention or
design, regarding every composite of atoms as produced purely by
material interactions of bodies, and accounting for the perceived
properties of macroscopic bodies as produced by these same atomic
interactions. Ancient Greek atomists formulated views on ethics,
theology, political philosophy and epistemology consistent with this
physical system. This powerful and consistent materialism was regarded
by Aristotle as a chief competitor to teleological natural philosophy;
following his criticisms, the theory was reformulated by Epicurus and
had a second life as the philosophy of a school devoted to the pursuit
of tranquillity and a communal life of simple pleasures.


### 2.1 Leucippus and Democritus



Leucippus (5th c. BCE) is usually credited with inventing atomism in
the Greek tradition. According to a passing remark by the geographer
Strabo, Posidonius (1st c. BCE Stoic philosopher) reported
that ancient Greek atomism can be traced back to a figure known as
Moschus or Mochus of Sidon, who lived at the time of the Trojan wars.
This report was given credence in the seventeenth century: the
Cambridge Platonist Henry More traced the origins of ancient atomism
back, via Pythagoras and Moschus, to Moses. This theologically
motivated view appealed to those who saw revelation as the source of
all truth and wanted to trace ancient Greek ideas to Biblical sources.
An ancient Greek source commenting on the travels of Democritus
credits his mathematical interests to time spent among Egyptian
geometers and suggests that he may have learned from the philosophers
of India.



In 1877, Tannery argued that Zeno of Elea's arguments
about divisibility would make most sense if formulated in response to
an atomist theory supposedly held by some early Pythagoreans.
Tannery's thesis has been thoroughly challenged since
then: most scholars instead consider atomism to be one of a number of
positions formulated in response to the arguments of Parmenides and
Zeno (first half of the fifth century).



Little is known about Leucippus, while the ideas of his student
Democritus--who is said to have taken over and systematized his
teacher's theory--are known from a large number of reports
and fragments quoted by others. These early atomists theorized that
the two fundamental and oppositely characterized constituents of the
natural world are indivisible bodies--atoms--and void. The
latter is described simply as nothing, or as the negation of being.
Atoms were said to be intrinsically unchangeable; they can move about
in the void and combine into different clusters, which give rise to
the macroscopic bodies of the perceived world. Because all macroscopic
objects are in fact combinations of atoms, everything in the world of
our experience is transitory and subject to dissolution while the
atoms themselves persist through all time.



According to Aristotle's presentation (*On Generation and
Corruption* I 8), the motivation for the first postulation of
indivisible bodies is to answer a metaphysical puzzle about the
possibility of change and multiplicity. Parmenides had argued that any
differentiation or change in Being implies that 'what is
not' either is or comes to be. Although there are problems in
interpreting Parmenides' precise meaning, he was understood to
have raised a problem about how change can be possible without
something coming from nothing. Several Presocratics formulated, in
response, philosophical systems in which change is not considered to
require something coming into being from complete nonexistence, but
rather the arrangement of pre-existing elements into new combinations.
The atomists held that, the atoms are unchangeable and contain no
internal differentiation of a sort that would allow for division.



By positing indivisible bodies, the atomists were also thought to be
answering Zeno's paradoxes about the impossibility of motion.
Zeno had argued that, if magnitudes can be divided to infinity, it
would be impossible for motion to occur. The problem seems to be that
a body moving would have to traverse an infinite number of spaces in a
finite time. By supposing that the atoms form the lowest limit to
division, the atomists escape from this dilemma: a total space
traversed has only a finite number of parts. As it is unclear whether
the earliest atomists understood the atoms to be physically or
theoretically indivisible, they may not have made the distinction.
Makin's argument that atomic indivisibility is based on the
homogeneity of substance and not smallness explains why Democritus
allowed for the possibility of even very large atoms (Makin 1993,
55).



Atoms can differ in size, shape, order and position; they move about
in the void, and--depending on their shape--some can
temporarily bond with one another by means of tiny hooks and barbs on
their surfaces. Thus the shape of individual atoms affects the
macroscopic texture of clusters of atoms, which may be fluid and
yielding or firm and resistant, depending on the amount of void space
between and the coalescence of the atomic shapes. The texture of
surfaces and the relative density and fragility of different materials
are also accounted for by the same means. Atoms cannot fuse, but
rather repel one another when they collide. Observations about the
tendencies of bodies bumping one another were frequently exploited to
explain the apparently patterned motions of macroscopic bodies in the
visible world.



The atomists accounted for perception by means of films of atoms
sloughed off from their surfaces by external objects, and entering and
impacting the sense organs. They tried to account for all sensible
effects by means of contact, and regarded all sense perceptions as
caused by the properties of the atoms making up the films acting on
the atoms of animals' sense organs. Perceptions of color are
caused by the 'turning' or position of the atoms; tastes
are caused by the shape of the atoms contacting the tongue, e.g.,
bitter tastes by the tearing caused by sharp atoms; feelings of heat
are ascribed to friction. Heat itself is said to be caused by the
admixture of tiny fire atoms. Democritus considered thought to be a
material process involving the local rearrangement of bodies, just as
much as is perception.



A famous quotation from Democritus distinguishes between perceived
properties like colors and tastes, which exist only 'by
convention,' in contrast to the reality, which is atoms and
void. However, he apparently recognized an epistemological problem for
an empiricist philosophy that nonetheless regards the objects of sense
as unreal. In another famous quotation, the senses accuse the mind of
overthrowing them, although mind is dependent on the senses. The
accusation is that, by developing an atomist theory that undermines
the basis for confidence in sense perception, thought has in effect
undercut its own foundation on knowledge gained through the senses.
Democritus sometimes seems to doubt or deny the possibility of
knowledge.



The early Greek atomists try to account for the formation of the
natural world by means of their simple ontology of atoms and void
alone. Leucippus held that there are an infinite number of atoms
moving for all time in an infinite void, and that these can form into
cosmic systems or *kosmoi* by means of a whirling motion which
randomly establishes itself in a large enough cluster of atoms. It is
controversial whether atoms are thought to have weight as an intrinsic
property, causing them all to fall in some given direction, or whether
weight is simply a tendency for atoms (which otherwise move in any and
every direction, except when struck) to move towards the centre of a
system, created by the whirling of the cosmic vortices. When a vortex
is formed, it creates a membrane of atoms at its outer edge, and the
outer band of atoms catches fire, forming a sun and stars. These
*kosmoi* are impermanent, and are not accounted for by purpose
or design. The earth is described as a flat cylindrical drum at the
center of our cosmos.



Species are not regarded as permanent abstract forms, but as chance
combinations of atoms. Living things are regarded as having a
*psyche* or principle of life; this is identified with
fiery atoms. Organisms are thought to reproduce by means of seed:
Democritus seems to have held that both parents produce seeds composed
of fragments from each organ of their body. Whichever of the parts
drawn from the relevant organ of the parents predominates in the new
mixture determines which characteristics are inherited by the
offspring. Democritus is reported to have given an account of the
origin of human beings from the earth. He is also said to be the
founder of a kind of cultural anthropology (Cole 1967), since his
account of the origin of the cosmos includes an account of the origin
of human institutions, including language and social and political
organization.



A large group of reports about Democritus' views concern ethical
maxims: some scholars have tried to regard these as systematic or
dependent on atomist physics, while others doubt the closeness of the
connection. Because several maxims stress the value of
'cheerfulness,' Democritus is sometimes portrayed as
'the laughing philosopher.' The frequent association
between hedonism and atomism may stem from the denial of any source of
good other than immediate experience; the tendency to reduce
experience to the rubbing together of atoms may have contributed to
the impression that atomists are preoccupied with physical
pleasure.


### 2.2 Plato, Platonists and Pythagoreans



Although the Greek term *atomos* is most commony associated
with the solid and impenetrable bodies posited by Leucippus and
Democritus, Plato's *Timaeus* presents a different kind
of physical theory based on indivisibles and was also regarded as a
kind of atomism. Plato's discussion of the composition of solids
from plane surfaces is sometimes thought to be based on fourth-century
Pythagorean theories. A fourth-century Pythagorean, Ecphantus,
interpreted the Pythagorean monads as indivisible bodies: he is
reported to have been sympathetic to atomism of a kind similar to
Democritus'.



Plato's *Timaeus* elaborates an account of the world
wherein the four different basic kinds of body--earth, air, fire,
and water--are regular solids composed from plane figures:
isosceles and scalene right-angled triangles. Because the same
triangles can form into different regular solids, the theory thus
explains how some of the elements can transform into one another, as
was widely believed. In this theory, it is the elemental triangles
composing the solids that are regarded as indivisible, not the solids
themselves. When Aristotle discusses the hypothesis that the natural
world is composed of indivisibles, the two views he considers are
those of Plato and Democritus. Aristotle criticizes both Plato and
fourth-century Pythagoreans for constructing natural bodies possessing
weight from indivisible mathematical abstractions, whether plane
surfaces or numbers. It has been suggested that Plato accepted time
atoms, i.e., indivisible minima in time, but this is
controversial.



A treatise in the Aristotelian corpus probably not by Aristotle
himself (*On Indivisible Lines*) addresses and refutes a number
of arguments offered for the existence of indivisible lines, without
naming their author. Plato's student Xenocrates (396-314
BCE), third head of the Academy, is reported to believe in indivisible
lines, and he may well be the target of the Aristotelian treatise. One
of the arguments attacked addresses a Zenonian problem about
traversing or touching in succession an infinite series of parts. The
idea that there are indivisible lines offers an alternative to the
view that any extended magnitude must be divisible to infinity. A
distinct argument claims that, if the physical elements composing a
body are regarded as the ultimate parts, they cannot be further
divisible. Although this does not argue for indivisible lines *per
se*, it is used to suggest that the objects of sense as well as
those of thought must include things without parts.



A further argument depends on thinking that opposite properties must
have opposite characteristics: if 'many' or
'large' things have infinite parts, it is argued, then
'few' or 'small' things must have only a
finite number of parts. It is then concluded that there must be a
magnitude without parts, apparently so that it is not further
divisible and thus composed of an infinite number of parts. The last
argument depends on the idea that mathematicians talk of commensurable
lines, and posit a single unit of measurement: this would not be
possible if the unit were divisible, because the parts of the unit, if
measured, would be measured by the unit measure and it would then turn
out to contain multiple units within itself.



In late antiquity, the Neoplatonist Proclus defended Plato's
account against Aristotle's objections; these arguments are
preserved in Simplicius' commentary on Aristotle's *On
the Heavens*. Simplicius credits the Pythagoreans as well as Plato
with a theory composing bodies from plane surfaces. Simplicius also
compares Pythagorean views to Democritean atomism, inasmuch as both
theories posit a cause for hot and cold rather than taking these to be
fundamental principles, as the Aristotelians do.


### 2.3 Minima Naturalia in Aristotelian Thought



An argument in Aristotle (*Physics* 1.4, 187b14-21) is
sometimes taken by later writers as evidence that Aristotle allowed
for the existence of minima in natural things. Aristotle writes that
there is a smallest size of material substrate on which it is possible
for the form of a given natural tissue to occur. Blood and bone, say,
are all materially composed of given proportions of earth, air, fire,
and water: there needs to be a certain minimal amount of these
material components present before the form of blood or bone can
occur. This doctrine--while surely compatible with
Aristotle's view that the material components are nonetheless
continuous and divisible at any point--is sometimes read by
Neoplatonist commentators and later sources interested in
*rapprochement* with atomism as evidence that Aristotle
endorsed the existence of minimal physical parts.



In late antiquity, this debate seems to have moved away from the
radical solution of positing minimal physical parts or atoms--a
view that seems to have had few advocates--into a puzzle about
the possibilities of 'bottom up' explanation versus the
need to regard emergent properties as 'supervening' and
not mere products of the necessary material base. The term
traditionally translated 'supervene'
here--*epigignomai*--refers to the idea that forms
are thought to come from a distinct source and inhere in suitable
material, rather than to be produced by the material substrate: it
does not exactly correspond to the technical notion of supervenience
formulated in late-20th century philosophy of mind. The reasons for
positing minimal thresholds for the supervenience of form in John
Philoponus concern the inadequacy of material explanation because
changes in the matter do not correlate numerically to--and hence
cannot fully explain--changes in qualities, and not because of
concerns about minimal parts (Berryman 2002).



Scholars have highlighted the importance of Islamic philosophers in
developing what came to be known in medieval Latin philosophy as the
doctrine of *minima naturalia* (Dijksterhuis 1961, 205; Glasner
2001; McGinnis 2015). Giles of Rome particularly developed the notion
of a natural minima in Thomistic thought: the notion of a minimum size
for a given substance was linked in these discussions to the problem
that a given quantity of one element could only be rarefied so far
before it becomes a different element (Duhem 1985, 35-45).



Book 4 of Aristotle's *Meteorology* was sometimes
regarded as inauthentic in the past because of its use of explanations
of the microstructure of matter, explanations that some scholars
argued were too much of a concession in the direction of atomism to be
Aristotle's own. These arguments are no longer widely
accepted.


### 2.4 Diodorus Cronus



Diodorus Cronus (late 4th c. BCE), a member of the supposed
Dialectical School, is reported to have offered new arguments that
there must be partless bodies or magnitudes. Most reports suggest that
his focus was on logical arguments rather than on physical theory: he
used arguments that depend on positing mutually exhaustive
alternatives.



Perhaps drawing on an argument of Aristotle's (*Sens.* 7,
449a20-31]), Diodorus apparently used the idea that there is a
smallest size at which an object at a given distance is visible as the
basis for an argument that there are indivisible magnitudes. His
argument begins from the idea that there is a difference in size
between the smallest size at which a given object is
visible--presumably from a given distance--and the largest
size at which it is invisible. Unless we concede that, at some
magnitude, a body is both invisible and visible (or neither), there
cannot be any other magnitude intermediate between these two
magnitudes. Magnitudes must increase by discrete units.



Sextus Empiricus (*AM* 10.48ff) reports an argument of
Diodorus' also concluding that magnitudes have discrete
intervals. It also denies the existence of moving bodies, insisting
that bodies move neither when they are in the place where they are,
nor when they are in the place where they are not. Since these
alternatives are presented as exhaustive, the conclusion must be that
bodies are never moving. However, rather than assert that everything
is static, Diodorus took the view that bodies must *have moved*
without ever *being* in motion: they are simply at one place at
one moment, and at another place at another moment.



As well as postulating the existence of indivisible smallest bodies
and magnitudes, Diodorus seems to have supposed that there are
indivisible smallest units of time. The argument about motion does not
quite make it explicit that this is what he is committed to, but it is
a reasonable inference: given his insistence that bodies are always at
one place or another at any given time, he might well suppose that
infinite divisibility of time would open up the threatening
possibility of indeterminacy as to whether the change of place has
taken place.



For those who posit indivisibles as a way to escape paradoxes about
infinite divisibility, parallel arguments might equally well have been
applied to the problem of completing tasks in an infinitely divisible
time. Sextus Empiricus reports that the Aristotelian Strato of
Lampsacus (d. 268/70 BCE) argued for time atoms, although this is
contradicted by other sources. Sorabji (1983) suggests that Strato
merely countenanced the *possibility* that time could be
discrete while space and motion are continuous, without endorsing this
position.


### 2.5 Epicurean Atomism



Democritus' atomism was revived in the early Hellenistic period:
Epicurus (341-270 BCE) founded an atomist school in Athens about
306 BCE. The Epicureans formed more of a closed community than other
schools, and promoted a philosophy of a simple, pleasant life lived
with friends. The community included women, and some of its members
raised children. The works of the founder were revered and some of
them were memorized, a practice that was thought to have discouraged
philosophical innovation by later members of the school, although this
view has been challenged (Fish and Sanders 2011).



Epicurus seems to have learned of atomist doctrine through
Democritus' follower Nausiphanes. Because Epicurus made some
significant changes in atomist theory, it is often thought that his
reformulation of the physical theory is an attempt to respond to
Aristotle's criticisms of Democritus. Even more significant,
however, is the increasing centrality of ethical concerns to
Epicurus' atomism, and the importance of the view that belief in
an atomist physical theory helps us live better lives.



Epicurus takes to heart a problem Democritus himself recognized, which
is that atomist theory threatens to undermine itself if it removes any
trust we can place in the evidence of the senses, by claiming that
colors, etc. are unreal. He notoriously said that 'all
perception is true,' apparently distinguishing between the
causal processes which impact our senses, all of which originate with
the films of atoms sloughed off by objects, and the judgments we make
on the basis of them, which may be false. Reasoning to truths about
things that are not apparent--like the existence of
atoms--depends on the evidence of the senses, which is always
true in that it consists of impacts from actually existing films. For
particular phenomena, like meteorological events, Epicurus endorses
the existence of multiple valid explanations, acknowledging that we
may have no evidence for preferring one explanation over another.



It may be that Epicurus was less troubled by any such epistemological
uncertainties because of his emphasis on the value of atomist theory
for teaching us how to live the untroubled and tranquil life. Denying
any divine sanction for morality, and holding that the experience of
pleasure and pain are the source of all value, Epicurus thought we can
learn from atomist philosophy that pursuing natural and necessary
pleasures--rather than the misleading desires inculcated by
society--will make pleasure readily attainable. At the same time,
we will avoid the pains brought on by pursuing unnatural and
unnecessary pleasures. Understanding, on the basis of the atomist
theory, that our fears of the gods and of death are groundless will
free us from our chief mental pains.



Epicurus made significant changes to atomist physical theory. It seems
that Democritus did not distinguish clearly between the physical
uncuttability of atoms and their conceptual indivisibility: this
raises a problem about how atoms can have parts, as evidenced by their
variations in shape or their ability to compose a magnitude, touching
one another in a series on different sides. Epicurus distinguished the
two, holding that uncuttable atoms did have conceptually distinct
parts, but that there was a lowest limit to these. Different solutions
to this problem are found in ancient Indian atomism.



Epicurus' view of the motion of atoms also differs from
Democritus'. Rather than talking of a motion towards the center
of a given cosmos, possibly created by the cosmic vortex, Epicurus
grants to atoms an innate tendency to downward motion through the
infinite cosmos. The downward direction is simply the original
direction of atomic fall. This may be in response to Aristotelian
criticisms that Democritus does not show why atomic motion exists,
merely saying that it is eternal and that it is perpetuated by
collisions. Moreover, although this is not attested in the surviving
writings of Epicurus, authoritative later sources attribute to him the
idea that it belongs to the nature of atoms occasionally to exhibit a
slight, otherwise uncaused swerve from their downward path. This is
thought to explain why atoms have from infinite time entered into
collisions instead of falling in parallel paths: it is also said, by
Lucretius, to enter into the account of action and responsibility.
Scholars have proposed a number of alternative interpretations as to
how this is thought to work.



The epistemological concerns discussed above required a different view
on the nature of composites and macroscopic, perceptible properties.
Epicurus rejected Democritus' eliminativist position that
perceived properties only exist 'by convention' (Sedley
1988; O'Keefe 2005). Epicurus' successor Polystratus
further defended and elaborated a claim about the reality of
properties, including relational properties. Moreover, with the
recovery of new papyrological evidence, controversy has arisen about
the extent to which Epicurus rejected Democritus' attempt to
account for all causal processes by the properties of the atoms and
void alone. Although Epicurus' ideas have long been known from
three surviving letters preserved in the biography by Diogenes
Laertius, no copy of his longer work *On Nature* had been
available. However, following excavation of the Epicurean library at
Herculaneum that was buried by a volcanic eruption, some parts of this
work are being recovered. Many of the scrolls found are badly damaged,
however, and interpretation of this newly recovered material is
ongoing.



The Herculaneum library contains much work of the Epicurean Philodemus
(1st c. BCE). Philodemus wrote extensively, including on the history
of philosophy, ethics, music, poetry, rhetoric and the emotions. He
wrote a treatise on the theory of signs: because they are empiricists,
believing that all knowledge comes from our sense experience, later
Epicureans were concerned about the basis for our knowledge of
imperceptibles like the atoms, and engaged in an extensive debate with
the Stoics about the grounds for inferences to imperceptible
entities.



Although Epicurus' doctrines teach the value of a quiet life in
a specially constructed Epicurean community and decry the search for
fame, atomist theory is also regarded as a cure for the troubles
afflicting others outside the community, and there are certainly
Epicurean texts written for a wider audience. Besides the letters by
Epicurus himself summarizing his doctrines, the Epicurean philosopher
Lucretius (d. c. 50 BCE) wrote a long Latin poem advocating
Epicurus' ideas to Roman audiences (Sedley 1998). Lucretius
makes clear his close allegiance to Epicurus' own views, and
provides more detail on some topics than has survived from
Epicurus' own work, such as an extended account of the origins
of human society and institutions. A less sympathetic contemporary of
Lucretius, Cicero, also wrote a number of Latin works in which an
Epicurean spokesman presents the doctrines of the school.



Diogenes of Oenoanda propagated Epicurean doctrines in Asia Minor,
inscribing them on the wall of a Stoa in his home town so as to
convert passersby to Epicurean theory. Excavation of these since the
nineteenth century has also produced new texts. Smith (1993), in his
latest edition of the text of the inscriptions, dates them to the
early second century CE.


### 2.6 Atomism and Particle Theories in Ancient Greek Sciences



Some figures concerned with the natural sciences, especially medicine,
are thought to have regarded organic bodies as composed of particles.
Galen (2nd c. CE), in *On the Natural Faculties*, divides
medical theorists into two groups, following the division of natural
philosophers. On the one side are continuum theorists, who hold that
all matter is infinitely divisible but that all the matter in things
subject to generation and corruption is susceptible to qualitative
alteration. On the other are those who suppose that matter is composed
of tiny, unchangeable particles separated by void spaces, and explain
qualitative change as produced only in compound bodies, by
rearrangement of the particles alone. In Galen's view,
qualitative alteration is needed to produce the powers whereby
beneficent Nature directs change: Galen credits the first group with
asserting the priority of Nature and its beneficent order, and the
latter with denying this.



Although ancient Greek natural philosophers tend to fall on either
side of Galen's divide (Furley 1987)--continuum theory plus
beneficent teleology, vs. atomism plus blind necessity-- there is
a danger in taking this dichotomy to be exhaustive or exclusive of
possible natural philosophies. Inasmuch as the view Plato develops in
*Timaeus* is atomistic and also endorses teleological
explanation, for example, his position complicates the picture, and
other theories of natural philosophy in the Hellenistic period do not
divide so neatly onto one side or the other. Comparison to other
traditions makes clear that atomism has no necessary affinity to the
absence of divine organization. Galen has polemical interests in
discrediting those who deny the need for qualitatively irreducible
faculties or powers employed by Nature to produce beneficial
results.



A prevailing tendency in modern scholarship to identify particle
theories with 'mechanistic' thinking is not representative
of ancient atomism: the identification of Greek atomism as a precursor
to the New Science was due to the work of 17th century figures like
Pierre Gassendi, Henry More and Robert Boyle. Galen elsewhere
explicitly contrasts atomist thought with the schools who appeal to
explanations from mechanics (Berryman 2002). Galen's
presentation of Greek natural philosophy was important in the later
reception of ideas into Islamic philosophy (Langermann 2009) and the
Renaissance (Copenhaver 1998).



The theories of Heracleides of Pontus (4th c. BCE) and Asclepiades of
Bythnia (2nd c. BCE) are sometimes likened to atomism (Gottschalk
1980; Vallance 1990). Both--a pupil of Plato, and a medical
theorist--are said to have posited the existence of corpuscles
they call *anarmoi onkoi*, likely some kind of partless masses:
the precise meaning is uncertain. Although the theories of Asclepiades
in particular are often assimilated to atomism, it may be that
Galen's characterization of this view is polemical, and that
Asclepiades' particles are capable of division. Galen is the
source for a distinctive argument against the idea that atoms were
alike in substance, based on the Hippocratic idea that organisms
composed of a single substance would not be able to experience
sensations like pain (Leith 2014). Ironically, Galen's theory of
the four elements was sometimes interpreted as an atomist theory by
medieval sources (Langermann 2009).



One of the most prominent writers on mechanics in antiquity, Hero of
Alexandria (1st c. CE), is sometimes regarded, following Hermann
Diels, as an atomist in the Democritean tradition. In the introduction
to his *Pneumatica*, Hero describes matter as made up of
particles with spaces between them. However, Hero's account of
pneumatic effects involving compression of air seems to depend on the
deformation of elastic particles which can be compressed artificially
but will spring back to their original shape quite vehemently. If so,
his account denies a fundamental tenet of classical atomism, that
atoms do not change in their intrinsic properties like shape (Berryman
2011). Pneumatics, because its effects were thought to depend on
forces acting against a void, provided stimulus to discussions of the
possibility of void and why its supposed impossibility would cause
water to move against its natural direction. In late antiquity, John
Philoponus theorized that void must be at least theoretically possible
for these effects to occur (Sedley 1987).


## 3. The Legacy of Ancient Atomism



The conventional division into 'ancient and modern' was
developed in a European context that does not necessarily reflect the
history of other cultures. Without intending to overstate the value or
generality of this division, we might regard three major bodies of
thought as inheriting ideas from the 'ancient' traditions
discussed above: atomism in Islamic *kalam* thought; the
revival of atomism in the European Renaissance and after; and the
continued interest in atomist theories in Indian philosophy through
the early modern period.


### 3.1 Atomism in the Islamic World



Beginning in the late 8th century CE/2nd century AH),
different versions of atomism were adopted and developed by many
adherents of the Islamic schools of *kalam* or theology.
The most important of these early atomist schools were located in
Basra and Baghdad. The philosopher-physician Abu Bakr
al-Razi (d. 313/925) also developed an atomist theory (Pines
1997; Baffioni 1982; Adamson 2014; Koetschet 2019), although adherents
of the philosophical schools known as *falsafa* more commonly
adhered to a philosophical picture based on Neoplatonic continuum
metaphysics. Some medieval Jewish philosophers of the Karaite school,
writing in Arabic and influenced by *kalam* thought,
adopted atomist views (Ben-Shammai, 1985). Critics of
*kalam* atomism include Ibn Sina, the
11th/5th century philosopher known as Avicenna
in the West, and Maimonides (12th/6th C) in his *Guide for the
Perplexed*. Fakhr al-din al-Razi responded to Ibn
Sina's criticisms in the 12th/6th century (Dhanani
2015), and atomist ideas were publicized by the work of al-Iji
(d. 1355 CE) and his student al-Taftazani, which present arguments
from earlier *kalam* and *falsafa* natural philosophy
and were used for teaching purposes (Dhanani 2017).



Although the loss of texts makes it difficult to trace the origins of
atomism in Islamic thought, scholars argue that ancient Greek theories
may have reached the *Mutakallimun* by oral transmission if not
by translation of texts; the indirect transmission may explain some
divergences (Wolfson 1976; Dhanani 1994). Epicurean rather than
Democritean ideas may have been transmitted through doxographies (van
Ess 2018) or from Galen's critiques (Langermann 2009); other
possible routes of transmission that have been explored include the
Greek sceptical tradition and the supposed atomism of the Pythagorean
Ecphantus (Baffioni 1982). Attempts have also been made to link
*kalam* atomism to the Indian tradition (Pines 1997;
Wolfson 1976): echoes include a similar argument that a mountain and a
mustard seed would be equal if bodies were infinitely divisible, and
the fact that perceptible properties are ascribed to atoms, in
contrast to the Greek tradition. Whatever its antecedents, the
development of atomism in an Islamic context--where different
philosophical questions prevailed--led to creative innovations
and a distinctive critical tradition of atomist thought (Rashed
2005).



Unlike Greek atomists, Abu al-Hudhayl--regarded as the founder of
*kalam* atomism--posited that atoms were
indiscernible from one another even in size or shape. Rashed (2005)
argues for the distinctness of al-Hudhayl's atoms from both
ancient Greek or Indian antecedents, since atoms were conceived as
Euclidean points and not as extended material bodies. Rashed stresses
the importance of the conception of atoms as in motion *at an
instant*, connecting it to the development of a notion that bodies
occupying infinitesimal locations could possess motion as a dynamic
property, and to a treatment of mathematical properties that were not
merely regarded as abstracted from bodies, as in the Aristotelian
tradition (Rashed 2005). Al-Nazzan, a prominent early critic of
atomism, tried to solve paradoxes about motion over infinitely
divisible continua with the alternative thesis that motion consisted
in an imperceptible 'leap' from one location to
another.



Because any Islamic metaphysical system was committed to a Creator
God, the ancient Greek use of atomism to solve the problem of change
without something coming from nothing could not be the motivation for
*kalam* atomism. Some scholars believe the created nature
of atoms could have been used as an argument for the existence of God,
since creation implies a Creator (Adamson 2016, 16). Atoms could not
continue existing on their own but were continually recreated by God
at every instant. Al-Razi's atomism, by contrast,
denied that creation from nothing was possible and supposed that atoms
were eternal (Pines 1997, 48). Baffioni (1982) contrasts
al-Razi's physical motivations for adopting atomism
with the 'teleological' atomism of the *kalam*
schools.



Central debates about the viability of atomism in the Islamic world
centred on infinite divisibility, applying paradoxes similar to those
of Zeno to the problem of an ant crawling over a sandal. A problem
about the fact that different particles in a rolling millstone or
wheel must be moving at different speeds, despite the apparent
cohesiveness of the millstone, is found in Islamic discussions. The
insistence within *kalam* atomism on recognizing accidents
that adhere in the whole of composite bodies, and that cannot be
traced back to the properties of individual atoms, may share the
motivation of Epicurus' attempt to avoid the eliminativism of
Democritus' theory. Likewise, epistemological arguments for
preserving confidence in sense perception, even given the possibility
of illusion, may have been formulated to avoid the sceptical potential
inherent in a Democritean approach to perception and empirical
knowledge.



Atoms in Islamic philosophy were typically defined by the occupation
of space and the exclusion of other bodies; by their ability to
receive accidents; and by their ability to be perceived by the senses
of sight and touch, presumably in sufficiently large aggregates. The
assertion of an entailment between materiality and occupying space was
apparently directed against the Peripatetic notion of matter and the
Aristotelian notion of natural place (Dhanani 1994, 88-89). The
spatial extendedness of atoms was also linked to the notion that atoms
served as a unit for measuring extension. Because spherical atoms
packed together would leave a space that is smaller than the
atom--which would be impossible if atoms represented the smallest
possible magnitude--atoms were said to be cubic (Dhanani 1994,
115). Atoms were thought to adhere to one another without the physical
'hooks' proposed by Democritus; even so, it proved
difficult to avoid ascribing subatomic parts to atoms.



As in the Greek tradition, the positing of atoms in Islamic thought
was paired with assertions about the existence of void space, in
opposition to the continuum physics characteristic of most
*falsafa* thought (cf. Pines 1979). Debate over the existence
of void was enriched by the need to explain the operation of so-called
pneumatic devices like the siphon, medical cupping glasses or syringe
(Lugal and Sayili 1951; Koetschet 2019). The supposed impossibility of
void space forming was used to account for observed fluid movements in
pneumatic devices, raising questions about how a metaphysical
impossibility might produce physical motions. Ingenious thought
experiments were developed to test the assumptions at work, asking
what would happen if a single film of atoms were trapped between two
cupping glasses, or comparing the effect of cupping glasses on stone
to their effect on flesh (Dhanani 1994, 77). The fascination with
pneumatic technology in the medieval Islamic world is attested in
surviving texts which detail increasingly complex marvels: trick
fountains, surprise vessels, water clocks with elaborate mechanical
side-shows (Hill 1974, 1979), although the explanation of these
effects did not necessarily involve atomist or particle theories of
matter. 


### 3.2 Ancient Greek Atomism in Later European Philosophy



Aristotelian natural philosophy came to predominate in the medieval
Latin West during the 13th century, and prevailed in the universities
into the seventeenth century. Nonetheless, scholars recognize pockets
of interest in atomist thought in the middle ages, including a 12th
century 'renaissance' of atomism (Pabst 1991, 1994; Grant
1996; Dijksterhuis 1961), and the work of the 14th century
'indivisibilists,' who focused on the mathematics of
motion (Duhem 1985; Murdoch 1982, 1984). Reasons for the renewed
interest in atomist thought have been linked to the vision of a
relatively autonomous nature found in *Timaeus* (Pabst 1994),
and to the need to account for motion of immaterial bodies like angels
(Murdoch 1984). Medical authors and Latin sources were important in
the transmission of ideas from antiquity to the 12th century, for whom
the atomist theories in the Arabic tradition were largely inaccessible
(Pabst 1994, 86). Later medieval Latin philosophers would have access
to ideas from the Islamic atomist tradition through Maimonides'
reports and Ibn Sina's refutations: modern scholarly
opinions differ as to the extent to which Latin theorists were aware
of Islamic atomism, however: recent scholarship has uncovered more
evidence of borrowings from the Islamic world into the 14th century
Latin texts (Murdoch 1974; Sorabji 1982; Freudenthal 2003; Grellard
2009; Robert 2009).



Although 12th century atomists were inspired by Plato,
Calcidius' widely circulated commentary did not include the
passages detailing Plato's geometrical atomism: instead, they
developed particle theories and attempted to reconcile these with the
doctrine of the four elements. An original attempt by Thierry of
Chartes to solve the problem of the different motions of the four
elements--fire and air tending upward, earth and water tending
downward to different degrees--relied on the relative
cohesiveness of different elements to explain the different degrees of
mobility (Pabst 1991). Elemental intertransformation shows that
elements must be composed of atoms of similar substance, but fire
atoms, say, are less entangled with one another and thus more mobile
than other kinds of atoms. Other classic problems, including puzzles
about the different speeds of particles of a rotating wheel, continued
to occupy theorists into the early modern period; this problem was
called *rota Aristotelis* or 'Aristotle's
wheel' because of its appearance in the pseudo-Aristotelian
*Mechanica* (Palmerino 2001).



Renaissance alchemy, as much as the reworking of ancient Greek atomist
theories by adherents of the 'New Science' of the
seventeenth century, proved important sources of inspiration for
corpuscularian theories in the early modern world (Newman 2006). The
Aristotelian notion of *minima naturalia*, and the appeal to
microstructures of matter in explanation of chemical changes in
Aristotle's *Meteorology* IV, meant that consideration of
corpuscularian explanations need not automatically be framed as a
rejection of Aristotle. A useful corrective here to the tendency to
regard early modern atomism as merely reviving ancient Greek theories
is Newman's argument that an 'operational' notion of
minima--the smallest unit that seems to be manifest in the best
explanation of the observed phenomena--emerged from the
alchemical tradition and provided an alternative to the metaphysical
arguments of the ancient Greek atomists (Newman 2006, 2009).



Hero of Alexandria's matter theory has long been considered an
important source for Robert Boyle and other New Scientists of the
seventeenth century (Boas 1949). However, Hero's theory differed
from classical atomism, and drew heavily on the need to explain
pneumatic effects (see section 2.6 above). The evidence of
Sennert's influence on Boyle casts further doubts on the
centrality of ancient Greek atomism to his matter theory. Newman
(2006, 2009) argues that the relevant sense of 'atom'
depended on the incapacity for chemical decomposition, not spatial or
physical indivisibility, a notion grounded in empirical evidence
rather than logical or mathematical reasoning.



Milton (2002) offers a helpful perspective on why ancient Greek
atomism, despite its naturalist worldview, was not especially
conducive to scientific investigation. Features of seventeenth century
New Science that do not fit well with classical atomist theory include
the application of mathematical analysis to motion and the appeal to a
machine model to conceptualize the possibility that complex causal
sequencing could produce regular and determinate results without
ongoing intelligent direction (Berryman 2009). A modern scholarly
tendency to describe Democritean atomism as 'mechanistic'
contributes to a prevailing overestimate of the scientific credentials
of ancient Greek atomism.



Epicurean philosophy played a very different role in the seventeenth
and eighteenth centuries, providing a classical 'cover'
for hedonistic and anti-religious sentiment among intellectuals
attracted by the vision of a tranquil life free of fear of the gods
(Kargon 1966; Wilson 2008). Women philosophers and intellectuals were
unusually prominent amongst the seventeenth century advocates and
translators of Epicurus (Wilson 2008). The Cambridge Platonists may
have fueled the identification of atomism with atheism, because of the
presentation of ancient Greek natural philosophy in Cudworth's
*True Intellectual System of the Universe*. A tendency to
mischaracterize Epicurean philosophy as licentious persisted.



The young Karl Marx wrote his doctoral dissertation on Democritus, a
fact that may have contributed to his sensitivity to materialist
explanations. Given the association with Marx, Soviet-era scholarship
produced important work on Democritus, especially S.I. Luria's
magisterial edition of the fragments.


### 3.3 Early Modern Indian Atomism



The philosophical traditions discussed above continued for over a
millenium in the Indian schools, without the historical discontinuity
caused in Europe and West Asia by the collapse of the Roman Empire and
the rise of Islam. The debate between 'idealist' and
'realist' metaphysics continued, the latter represented by
the Navya-Nyaya school which developed about the fourteenth
century, building on the work of Udayana and Gangesa
(Phillips 1995). Stephen Phillips argues that the 'New
Logic' thought of Navya-Nyaya school proliferated in Indian
culture and law as well as impacting other philosophical schools,
especially after 1500 CE. Although it incorporated
Vaisesika realism, the focus was on epistemology and on
cognitive experience rather than on the atomist metaphysics.



Jonardon Ganeri (2011) has argued for regarding the early modern
period in India as a period of innovation comparable to that in
Europe, although the Indian intellectual world was less concerned to
present itself as a radical break from the past than was true of the
European 'New Science.' Francois Bernier, protege
of the French atomist Pierre Gassendi, travelled to India in 1656 and
found a receptive audience in the Sanskrit scholars trained in the
atomism of the classical period of Indian philosophy (Ganeri 2011).
Jayarama, an early modern Indian atomist working in the
Vaisesika tradition, produced an atomist theory that Ganeri
argues is closer to that of Daniel Sennert than to that of Gassendi
(Ganeri 2011, p. 218). Substantial concessions are made within this
atomist metaphysics towards acknowledging the reality of emergent
properties.