Atomism

Atomism is a natural philosophy that developed in several ancient traditions. In the Western tradition, it dates back to Leucippus and his student Democritus in the fifth century BC.^[1] These atomists theorized that the natural world consists of two fundamental and opposite, indivisible bodies – atoms and void (void is mere nothing, or the body's negation). Atoms are intrinsically unchangeable and move about the void combining into different clusters (and these clusters form differing substances)^[1]. Atoms are reality's very small, indestructible building blocks (Aristotle, Metaphysics, I, 4, 985 b, 10–15). The word atomism derives from the ancient Greek adjective atomos, which literally meant 'uncuttable' (a - tomos (not cuttable) – tomos a conjugate of the Greek verb temnein (to cut)).

Of importance to the philosophical concept of atomism is the historical accident that the particles that chemists and physicists of the early 19th century thought were indivisible, and therefore identified with the uncuttable a-toms of long tradition, were found in the 20th century to be composed of even smaller entities: electrons, neutrons, and protons. Further experiments showed that protons and neutrons are made of fundamental quarks. These particles at present show no experimental evidence of size or substructure.

Thus, as regards quarks, electrons, and other fundamental leptons are concerned, the possibility that they too are composed of smaller particles cannot be ruled out. In the meantime, however, it is these particles (not chemical atoms) which remain the best candidates for the traditional indivisible objects, with which historical atomism has concerned itself.

Traditional atomism in philosophy

The word atom is understood in primarily two distinct ways: firstly, by the physical sciences; secondly, by philosophy. Atomism is traditionally associated with the latter, the traditional argument of which being that atoms are the basic building blocks of all real, knowable matter, and make up absolutely anything that exists. Atoms are the smallest possible division of matter, do not have physical parts, and cannot be split, cut nor in any way further divided; they are either sizeless (point-sized) or they have a tiny size. Those that have a tiny size are called Democritean atoms. This was the perception in Greek theories of atomism. Indian Buddhists, such as Dharmakirti and others, also contributed to well-developed theories of atomism, and which involve momentary (instantaneous) atoms, that flash in and out of existence . The tradition of atomism leads to the position that only atoms exist, and there are no composite objects (objects with parts), which would mean that human bodies, clouds, planets, and whatnot all do not exist. This consequence of atomism was openly discussed by atomists such as Democritus, Hobbes, and perhaps even Kant (there is a debate over whether or not Kant was an atomist) among others, and it is also called mereological nihilism or metaphysical nihilism. In contemporary philosophy, atomism is not as popular as it has been in past times, because many contemporary philosophers are not willing to argue that only atoms exist, wherein there are not any things like trees, etc. Simples theory is a similar theory to atomism, but where unlike mereological nihilism, philosophers do hold that more than just atoms exist (such as cars and trees made up of the atoms).

Greek atomism

Is there an ultimate, indivisible unit of matter?

In the 5th century BC, Leucippus and his pupil Democritus proposed that all matter was composed of small indivisible particles called atoms, in order to reconcile two conflicting schools of thought on the nature of reality. On one side was Heraclitus, who believed that the nature of all existence is change. On the other side was Parmenides, who believed instead that all change is illusion.

Parmenides denied the existence of motion, change and void. He believed all existence to be a single, all-encompassing and unchanging mass (a concept known as monism), and that change and motion were mere illusions. This conclusion, as well as the reasoning that lead to it, may indeed seem baffling to the modern empirical mind, but Parmenides explicitly rejected sensory experience as the path to an understanding of the universe, and instead used purely abstract reasoning. Firstly, he believed there is no such thing as void, equating it with non-being (i.e. "if the void is, then it is not nothing; therefore it is not the void"). This in turn meant that motion is impossible, because there is no void to move into.^{[2] [3]} He also wrote all that is must be an indivisible unity, for if it were manifold, then there would have to be a void that could divide it (and he did not believe the void exists). Finally, he stated that the all encompassing Unity is unchanging, for the Unity already encompasses all that is and can be.^[4]

Democritus accepted most of Parmenides' arguments, except for the idea that change is an illusion. He believed change was real, and if it was not then at least the illusion had to be explained. He thus supported the concept of void, and stated that the universe is made up of many Parmenidean entities that move around in the void.^[2] The void is infinite and provides the space in which the atoms can pack or scatter differently. The different possible packings and scatterings within the void make up the shifting outlines and bulk of the objects that organisms feel, see, eat, hear, smell, and taste. While organisms may feel hot or cold, hot and cold actually have no real existence. They are simply sensations produced in organisms by the different packings and scatterings of the atoms in the void that compose the object that organisms sense as being "hot" or "cold."

The work of Democritus only survives in secondhand reports, some of which are unreliable or conflicting. Much of the best evidence of Democritus' theory of atomism is reported by Aristotle in his discussions of Democritus' and Plato's contrasting views on the types of indivisibles composing the natural world.^[5].

Geometry and atoms

Element	Polyhedron		Number of Faces	Number of Triangles
Fire	Tetrahedron (Animation)		4	24
Air	Octahedron (Animation)		8	48
Water	Icosahedron (Animation)		20	120
Earth	Cube (Animation)		6	24
Geometrical Simple Bodies According to Plato

Plato (c. 427—c. 347 BC) objected to the mechanistic purposelessness of the atomism of Democritus. He argued that atoms just crashing into other atoms could never produce the beauty and form of the world. In the Timaeus, (28B – 29A) Plato insisted that the cosmos was not eternal but was created, although its creator framed it after an eternal, unchanging model.

One part of that creation were the four simple bodies of fire, air, water, and earth. But Plato did not consider these corpuscles to be the most basic level of reality, for in his view they were made up of an unchanging level of reality, which was mathematical. These simple bodies were geometric solids, the faces of which were, in turn, made up of triangles. The square faces of the cube were each made up of four isosceles right-angled triangles and the triangular faces of the tetrahedron, octahedron, and icosahedron were each made up of six right-angled triangles.

He postulated the geometric structure of the simple bodies of the four elements as summarized in the table to the right. The cube, with its flat base and stability, was assigned to earth; the tetrahedron was assigned to fire because its penetrating points and sharp edges made it mobile. The points and edges of the octahedron and icosahedron were blunter and so these less mobile bodies were assigned to air and water. Since the simple bodies could be decomposed into triangles, and the triangles reassembled into atoms of different elements, Plato's model offered a plausible account of changes among the primary substances. ^{[6] [7]}

The rejection of atoms

Sometime before 330 BC Aristotle asserted that the elements of fire, air, earth, and water were not made of atoms, but were continuous. Aristotle considered the existence of a void, which was required by atomic theories, to violate physical principles. Change took place not by the rearrangement of atoms to make new structures, but by transformation of matter from what it was in potential to a new actuality. (This theory is called hylomorphism.) A piece of wet clay, when acted upon by a potter, takes on its potential to be an actual drinking mug. Aristotle has often been criticized for rejecting atomism, but in ancient Greece the atomic theories of Democritus remained "pure speculations, incapable of being put to any experimental test. Granted that atomism was, in the long run, to prove far more fruitful than any qualitative theory of matter, in the short run the theory that Aristotle proposed must have seemed in some respects more promising"^[8][9].

Later ancient atomism

Epicurus (341–270) studied atomism with Nausiphanes who had been a student of Democritus. Although Epicurus was certain of the existence of atoms and the void, he was less sure we could adequately explain specific natural phenomena such as earthquakes, lightning, comets, or the phases of the Moon (Lloyd 1973, 25–6). Few of Epicurus's writings survive and those that do reflect his interest in applying Democritus's theories to assist people in taking responsibility for themselves and for their own happiness—since he held there are no gods around that can help them.

His ideas are also represented in the derivative works of Democritus's followers, such as Lucretius's On the Nature of Things. These derivative works allow us to work out several segments of his theory on how the universe began its current stage. The atoms and the void are eternal. And after collisions that shatter large objects into smaller objects, the resulting dust, still composed of the same eternal atoms as the prior configurations of the universe, falls into a whirling motion that draws the dust into larger objects again to begin another cycle.

Atomism and ethics

Some later philosophers attributed the idea that man created gods; the gods did not create man to Democritus. For example, Sextus Empiricus noted:

Some people think that we arrived at the idea of gods from the remarkable things that happen in the world. Democritus ... says that the people of ancient times were frightened by happenings in the heavens such as thunder, lightning, ..., and thought that they were caused by gods.^[10]

Three hundred years after Epicurus, Lucretius in his epic poem On the Nature of Things would depict him as the hero who crushed the monster Religion through educating the people in what was possible in the atoms and what was not possible in the atoms. However, Epicurus expressed a non-aggressive attitude characterized by his statement: "The man who best knows how to meet external threats makes into one family all the creatures he can; and those he can not, he at any rate does not treat as aliens; and where he finds even this impossible, he avoids all dealings, and, so far as is advantageous, excludes them from his life." [1]

The exile of atomism

While Aristotelian philosophy eclipsed the importance of the atomists, their work was still preserved and exposited through commentaries on the works of Aristotle. In the 2nd century, Galen (A.D. 129–216) presented extensive discussions of the Greek atomists, especially Epicurus, in his Aristotle commentaries. According to historian of atomism Joshua Gregory, there was no serious work done with atomism from the time of Galen until Gassendi and Descartes resurrected it in the 17th century; "the gap between these two 'modern naturalists' and the ancient Atomists marked "the exile of the atom" and "it is universally admitted that the Middle Ages had abandoned Atomism, and virtually lost it." However, scholars still had Aristotle's critiques of atomism, and it seems unlikely that all ideas of atomism could have been lost in the West. In the Medieval universities there were rare expressions of atomistic philosophy. For example, in the fourteenth century Nicholas of Autrecourt considered that matter, space, and time were all made up of indivisible atoms, points, and instants and that all generation and corruption took place by the rearrangement of material atoms. The similarities of his ideas with those of al-Ghazali suggest that Nicholas may have been familiar with Ghazali's work, perhaps through Averroes' refutation of it (Marmara, 1973–74).

Still, "the exile of the atom" is an appropriate description of the interim between the ancient Greeks and the revival of Western atomism in the 16th century, in view of atomism's success elsewhere during that time. If the atom was in exile from the west, it was in India and Islam that atomistic traditions continued.

Indian atomism

The Indian atomistic position, like many movements in Indian Philosophy and Mathematics, starts with an argument from Linguistics. The Vedic etymologist and grammarian Yaska (ca. 7th c. BC) in his Nirukta, in dealing with models for how linguistic structures get to have their meanings, takes the atomistic position that words are the "primary" carrier of meaning – i.e. words have a preferred ontological status in defining meaning. This position was to be the subject of a fierce debate in the Indian tradition from the early Christian era till the 18th century, involving different philosophers from the Nyaya, Mimamsa and Buddhist schools.

In the pratishakhya text (ca. 2nd c. BCE), the gist of the controversy was stated cryptically in the sutra form as "saMhitA pada-prakr^tiH".^[11] According to the atomist view, the words (pada) would be the primary elements (prakrti) out of which the sentence is constructed, while the holistic view considers the sentence as the primary entity, originally "given" in its context of utterance, and the words are arrived at only through analysis and abstraction.^[12]

These two positions came to be called a-kShaNDa-pakSha (indivisibility or sentence-holism), a position developed later by Bhartrihari (c. 500 AD), vs. kShaNDa-pakSha (atomism), a position adopted by the Mimamsa and Nyaya schools (Note: kShanDa = fragmented; "a-kShanDa" = whole).

Between the 5th and 3rd century BC, the atom (anu or aṇor) is mentioned in the Bhagavad Gita (Chapter 8, Verse 9):

kaviḿ purāṇam anuśāsitāram aṇor aṇīyāḿsam anusmared yaḥ sarvasya dhātāram acintya-rūpam āditya-varṇaḿ tamasaḥ parastāt
One meditates on the omniscient, primordial, the controller, smaller than the atom, yet the maintainer of everything; whose form is inconceivable, resplendent like the sun and totally transcendental to material nature

The ancient "shAshvata-vAda" doctrine of eternalism, which held that elements are eternal, is also suggestive of a possible starting point for atomism (Gangopadhyaya 1981).

There has been some debate among scholars as to the origin of Indian atomism; the general consensus is that the Indian and Greek versions of atomism developed independently. However, there is some doubt on this, given the similarities between Indian atomism and Greek atomism and the proximity of India to scholastic Europe, as well as the account, related by Diogenes Laertius, of Democritus "making acquaintance with the Gymnosophists in India".^[13] The atomist position had transcended language into epistemology by the time that Nyaya–Vaisesika, Buddhist and Jaina theology were developing mature philosophical positions.

Will Durant wrote in Our Oriental Heritage:

"Two systems of Indian thought propound physical theories suggestively similar to those of Greece. Kanada, founder of the Vaisheshika philosophy, held that the world was composed of atoms as many in kind as the various elements. The Jains more nearly approximated to Democritus by teaching that all atoms were of the same kind, producing different effects by diverse modes of combinations. Kanada believed light and heat to be varieties of the same substance; Udayana taught that all heat comes from the sun; and Vachaspati, like Newton, interpreted light as composed of minute particles emitted by substances and striking the eye."

Indian atomism in the Middle Ages was still mostly philosophical and/or religious in intent, though it was also scientific. Because the "infallible Vedas", the oldest Hindu texts, do not mention atoms (though they do mention elements), atomism was not orthodox in many schools of Hindu philosophy, although accommodationist interpretations or assumptions of lost text justified the use of atomism for non-orthodox schools of Hindu thought. The Buddhist and Jaina schools of atomism however, were more willing to accept the ideas of atomism.

Nyaya–Vaisesika school

The Nyaya–Vaisesika school developed one of the earliest forms of atomism; scholars date the Nyaya and Vaisesika texts from the 6th century BC to the 1st century BC. Like the Buddhist atomists, the Vaisesika had a pseudo-Aristotelian theory of atomism. They posited the four elemental atom types, but in Vaisesika physics atoms had 24 different possible qualities, divided between general extensive properties and specific (intensive) properties. Like the Jaina school, the Nyaya–Vaisesika atomists had elaborate theories of how atoms combine. In both Jaina and Vaisesika atomism, atoms first combine in pairs (dyads), and then group into trios of pairs (triads), which are the smallest visible units of matter.^[14]

Buddhist school

The Buddhist atomists had very qualitative, Aristotelian-style atomic theory. According to ancient Buddhist atomism, which probably began developing before the 4th century BC, there are four kinds of atoms, corresponding to the standard elements. Each of these elements has a specific property, such as solidity or motion, and performs a specific function in mixtures, such as providing support or causing growth. Like the Hindu Jains, the Buddhists were able to integrate a theory of atomism with their theological presuppositions. Later Indian Buddhist philosophers, such as Dharmakirti and Dignāga, considered atoms to be point-sized, durationless, and made of energy.

Jaina school

The most elaborate and well-preserved Indian theory of atomism comes from the philosophy of the Jaina school, dating back to at least the first century BC. Some of the Jaina texts that refer to matter and atoms are Panchastikayasara, Kalpasutra, Tattvaarthasutra and Pannavana Suttam. The Jains envisioned the world as consisting wholly of atoms, except for souls. Paramāņus or atoms were considered as the basic building blocks of all matter. Their concept of atoms was very similar to classical atomism, differing primarily in the specific properties of atoms. Each atom, according to Jaina philosophy, has one kind of taste, one smell, one color, and two kinds of touch, though it is unclear what was meant by "kind of touch". Atoms can exist in one of two states: subtle, in which case they can fit in infinitesimally small spaces, and gross, in which case they have extension and occupy a finite space. Certain characteristics of Paramāņu correspond with that sub-atomic particles. For example Paramāņu is characterized by continuous motion either in a straight line or in case of attractions from other Paramāņus, it follows a curved path. This corresponds with the description of orbit of electrons across the Nucleus. Ultimate particles are also described as particles with positive (Snigdha i.e. smooth charge) and negative (Rūksa – rough) charges that provide them the binding force. Although atoms are made of the same basic substance, they can combine based on their eternal properties to produce any of six "aggregates", which seem to correspond with the Greek concept of "elements": earth, water, shadow, sense objects, karmic matter, and unfit matter. To the Jains, karma was real, but was a naturalistic, mechanistic phenomenon caused by buildups of subtle karmic matter within the soul. They also had detailed theories of how atoms could combine, react, vibrate, move, and perform other actions, all of which were thoroughly deterministic.

Islamic atomism

Atomistic philosophies are found very early in Islamic philosophy, and represent a synthesis of the Greek and Indian ideas. Like both the Greek and Indian versions, Islamic atomism was a charged topic that had the potential for conflict with the prevalent religious orthodoxy, but it was instead more often favoured by orthodox Islamic theologians. It was such a fertile and flexible idea that, as in Greece and India, it flourished in some leading schools of Islamic thought.

Asharite atomism

The most successful form of Islamic atomism was in the Asharite school of Islamic theology, most notably in the work of the theologian al-Ghazali (1058–1111). In Asharite atomism, atoms are the only perpetual, material things in existence, and all else in the world is "accidental" meaning something that lasts for only an instant. Nothing accidental can be the cause of anything else, except perception, as it exists for a moment. Contingent events are not subject to natural physical causes, but are the direct result of God's constant intervention, without which nothing could happen. Thus nature is completely dependent on God, which meshes with other Asharite Islamic ideas on causation, or the lack thereof (Gardet 2001). Al-Ghazali also used the theory to support his theory of occasionalism. In a sense, the Asharite theory of atomism has far more in common with Indian atomism than it does with Greek atomism.^[15]

Averroism

Other traditions in Islam rejected the atomism of the Asharites and expounded on many Greek texts, especially those of Aristotle. An active school of philosophers in Spain, including the noted commentator Averroes (AD 1126–1198) explicitly rejected the thought of al-Ghazali and turned to an extensive evaluation of the thought of Aristotle. Averroes commented in detail on most of the works of Aristotle and his commentaries did much to guide the interpretation of Aristotle in later Jewish and Christian scholastic thought.

Atomic renaissance

With few exceptions, much of the curriculum in the universities of Europe was based on Aristotle for most of the Middle Ages (Kargon 1966). Scholasticism was standard science in the time of Issac Newton, but in the 17th century, a renewed interest in Epicurian atomism and Corpuscularianism as a hybrid or an alternative to Aristotelian physics had begun to mount outside the classroom. The main figures in the rebirth of atomism were René Descartes, Pierre Gassendi, and Robert Boyle, as well as other notable figures.

One of the first groups of atomists in England was a cadre of amateur scientists known as the Northumberland circle, led by Henry Percy (1585–1632), the 9th Earl of Northumberland. Although they published little of account, they helped to disseminate atomistic ideas among the burgeoning scientific culture of England, and may have been particularly influential to Francis Bacon, who became an atomist around 1605, though he later rejected some of the claims of atomism. Though they revived the classical form of atomism, this group was among the scientific avant-garde: the Northumberland circle contained nearly half of the confirmed Copernicans prior to 1610 (the year of Galileo's The Starry Messenger). Other influential atomists of late 16th and early 17th centuries include Giordano Bruno, Thomas Hobbes (who also changed his stance on atomism late in his career), and Thomas Hariot. A number of different atomistic theories were blossoming in France at this time, as well (Clericuzio 2000).

Galileo Galilei (1564–1642) was an advocate of atomism in his 1612, Discourse on Floating Bodies (Redondi 1969). In The Assayer, Galileo offered a more complete physical system based on a corpuscular theory of matter, in which all phenomena—with the exception of sound—are produced by "matter in motion". Galileo identified some basic problems with Aristotelian physics through his experiments. He utilized a theory of atomism as a partial replacement, but he was never unequivocally committed to it. For example, his experiments with falling bodies and inclined planes led him to the concepts of circular inertial motion and accelerating free-fall. The current Aristotelian theories of impetus and terrestrial motion were inadequate to explain these. While atomism did not explain the law of fall either, it was a more promising framework in which to develop an explanation because motion was conserved in ancient atomism (unlike Aristotelian physics).

Descartes' mechanical philosophy of corpuscularism had much in common with atomism, and is considered, in some senses, to be a different version of it. Descartes (1596–1650) thought everything physical in the universe to be made of tiny vortexes of matter. Like the ancient atomists, Descartes claimed that sensations, such as taste or temperature, are caused by the shape and size of tiny pieces of matter. The main difference between atomism and Descartes' concept was the existence of the void. For him, there could be no vacuum, and all matter was constantly swirling to prevent a void as corpuscles moved through other matter. Another key distinction between Descartes' view and classical atomism is the mind/body duality of Descartes, which allowed for an independent realm of existence for thought, soul, and most importantly, God. Gassendi's concept was closer to classical atomism, but with no atheistic overtone.

Pierre Gassendi (1592–1655) was a Catholic priest from France who was also an avid natural philosopher. He was particularly intrigued by the Greek atomists, so he set out to "purify" atomism from its heretical and atheistic philosophical conclusions (Dijksterhius 1969). Gassendi formulated his atomistic conception of mechanical philosophy partly in response to Descartes; he particularly opposed Descartes' reductionist view that only purely mechanical explanations of physics are valid, as well as the application of geometry to the whole of physics (Clericuzio 2000).

Corpuscularianism

Corpuscularianism is similar to atomism, except that where atoms were supposed to be indivisible, corpuscles could in principle be divided. In this manner, for example, it was theorized that mercury could penetrate into metals and modify their inner structure, a step on the way towards transmutative production of gold. Corpuscularianism was associated by its leading proponents with the idea that some of the properties that objects appear to have are artifacts of the perceiving mind: 'secondary' qualities as distinguished from 'primary' qualities.^[16] Corpuscularianism stayed a dominant theory over the next several hundred years and was blended with alchemy by those such as Robert Boyle and Isaac Newton in the 17th century.^[17][18] It was used by Newton, for instance, in his development of the corpuscular theory of light. The form that came to be accepted by most English scientists after Robert Boyle (1627-1692) was an amalgam of the systems of Descartes and Gassendi. In The Sceptical Chymist (1661), Boyle demonstrates problems that arise from chemistry, and offers up atomism as a possible explanation. The unifying principle that would eventually lead to the acceptance of a hybrid corpuscular–atomism was mechanical philosophy, which was became widely accepted by physical sciences.

Atomic theory

By the late 1700s, the useful practices of engineering and technology began to influence philosophical explanations for the composition of matter. Those who speculated on the ultimate nature of matter began to verify their "thought experiments" with some repeatable demonstrations, when they could.

Roger Boscovich provided the first general mathematical theory of atomism, based on the ideas of Newton and Leibniz but transforming them so as to provide a programme for atomic physics. – Lancelot Law Whyte Essay on Atomism, 1961, p 54.

In 1808, John Dalton assimilated the known experimental work of many people to summarize the empirical evidence on the composition of matter. He noticed that distilled water everywhere analyzed to the same elements, hydrogen and oxygen. Similarly, other purified substances decomposed to the same elements in the same proportions by weight.

Therefore we may conclude that the ultimate particles of all homogeneous bodies are perfectly alike in weight, figure, etc. In other words, every particle of water is like every other particle of water; every particle of hydrogen is like every other particle of hydrogen, etc.

Furthermore, he concluded that there was a unique atom for each element, using Lavoisier's definition of an element as a substance that could not be analyzed into something simpler. Thus, Dalton concluded the following.

Chemical analysis and synthesis go no farther than to the separation of particles one from another, and to their reunion. No new creation or destruction of matter is within the reach of chemical agency. We might as well attempt to introduce a new planet into the solar system, or to annihilate one already in existence, as to create or destroy a particle of hydrogen. All the changes we can produce, consist in separating particles that are in a state of cohesion or combination, and joining those that were previously at a distance.

And then he proceeded to give a list of relative weights in the compositions of several common compounds, summarizing: [2]

1st. That water is a binary compound of hydrogen and oxygen, and the relative weights of the two elementary atoms are as 1:7, nearly;

2nd. That ammonia is a binary compound of hydrogen and azote nitrogen, and the relative weights of the two atoms are as 1:5, nearly...

Dalton concluded that the fixed proportions of elements by weight suggested that the atoms of one element combined with only a limited number of atoms of the other elements to form the substances that he listed.

See also

• Becoming (philosophy)
• History of chemistry
• Infinite divisibility
• Ontological pluralism
• Physical ontology

External links

• Dictionary of the History of Ideas: Atomism: Antiquity to the Seventeenth Century
• Dictionary of the History of Ideas: Atomism in the Seventeenth Century
• Jonathan Schaffer, "Is There a Fundamental Level?" Nous 37 (2003): 498-517.[3] Article by a philosopher who opposes atomism
• Article on traditional Greek atomism
• Atomism from the 17th to the 20th Century at Stanford Encyclopedia of Philosophy

Notes

References

• Clericuzio, Antonio. Elements, Principles, and Corpuscles; a study of atomism and chemistry in the seventeenth century. Dordrecht; Boston: Kluwer Academic Publishers, 2000.
• Cornford, Francis MacDonald. Plato's Cosmology: The Timaeus of Plato. New York: Liberal Arts Press, 1957.
• Dijksterhuis, E. The Mechanization of the World Picture. Trans. by C. Dikshoorn. New York: Oxford University Press, 1969. ISBN 0-691-02396-4
• Firth, Raymond. Religion: A Humanist Interpretation. Routledge, 1996. ISBN 0-415-12897-8.
• Gangopadhyaya, Mrinalkanti. Indian Atomism: history and sources. Atlantic Highlands, New Jersey: Humanities Press, 1981. ISBN 0-391-02177-X
• Gardet, L. "djuz'" in Encyclopaedia of Islam CD-ROM Edition, v. 1.1. Leiden: Brill, 2001.
• Gregory, Joshua C. A Short History of Atomism. London: A. and C. Black, Ltd, 1981.
• Kargon, Robert Hugh. Atomism in England from Hariot to Newton. Oxford: Clarendon Press, 1966.
• Lloyd, G. E. R. Aristotle: The Growth and Structure of his Thought. Cambridge: Cambridge University Press, 1968. ISBN 0-521-09456-9
• Lloyd, G. E. R. Greek Science After Aristotle. New York: W. W. Norton, 1973. ISBN 0-393-00780-4
• Marmara, Michael E. "Causation in Islamic Thought." Dictionary of the History of Ideas. New York: Charles Scribner's Sons, 1973-74. online at the of Virginia Electronic Text Center.
• Redondi, Pietro. Galileo Heretic. Translated by Raymond Rosenthal. Princeton, NJ: Princeton University Press, 1987. ISBN 0-691-02426-X
• McEvilley, Thomas (2002). The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies. New York: Allworth Communications Inc. ISBN 1581152035.