A term deriving from the Greek ἄτομον, meaning indivisible, and usually applied to systems maintaining that everything is composed of unchanging and indivisible elements or atoms, whose movements and arrangements account for the changing appearances of reality. In a broader sense, the term is applied also to any systematic explanation that attempts to reduce complex phenomena to invariant unit factors. Thus one may speak of logical
atomism, as elaborated in the philosophy of Bertrand russell, which regards the logical proposition as an ultimate unit; psychological atomism, which attempts to reduce all mental phenomena to combinations of simple elements, along lines proposed by J. locke, D. hume and the advocates of associationism; and biological atomism, which attempts to explain vital phenomena in terms of discrete units such as genes, cells, etc. (see mechanism, biological). The historically more important type of atomism may be described as physical atomism to distinguish it from these other forms. From its beginnings in Greek philosophy it has consistently lent its support to the philosophies of materialism and mechanism and has been used by proponents of atheism to combat belief in the world of spirit. Physical atomism is not to be completely identified with materialism, however, for many thinkers have subscribed to atomistic hypotheses without regarding atoms as the sole reality and while admitting the existence of spiritual entities. Again, physical atomism permits of many different views regarding the nature of the ultimate units, ranging from the mathematical points of the Pythagoreans, the force centers of R. Boscovich and the monads of G. W. Leibniz to the solid particles of Democritus and the qualitatively similar parts (Gr. ὁμοιομερ[symbol omitted]) of Anaxagoras. Yet most forms of atomism
maintain that there is a quantitative limit to the division of bodies, that small ultimate units exist and that all large-scale phenomena are to be accounted for in terms of these.
This article treats physical atomism chronologically under the headings of Greek atomism, other early forms, medieval conceptions, developments from the Renaissance to the 17th century, the classical atomism of the 18th and 19th centuries and the status of atomism in the 20th century.
The first atomistic theories to arise among the Greeks were speculative in nature. The forerunners of Greek atomist concepts are to be found among the Milesian naturalists, such as Thales, Anaximenes and heraclitus, who successively conceived water, air and fire as the primary matter of which all things are made. The solutions these thinkers proffered to the problem of change prompted parmenides, a philosopher of the Eleatic school in Italy, to argue that change itself is an illusion: in his view, being is one and unchangeable, for apart from it, there is only nothing. The metaphysical speculations of Parmenides gave birth to the first atomist school at Abdera in Thrace, where atomism was proposed by Leucippus (fl. 450 b.c.) and his pupil democritus. Democritus argued against Parmenides, that being is not one, but is divided into a number of beings, themselves unchangeable and indivisible, which he called atoms (Gr. ἄτομα). He also conceived of nothing as differently from Parmenides, assigning it a type of reality that he described as the void. By admitting the void Democritus thought he could explain the motion of atoms and through this motion all types of change. He postulated that atoms were infinite in number, qualitatively identical and distinct only in shape and size; he also endowed his atoms with motion, which he conceived as ceaseless and eternal like the atoms themselves (see materialism).
At approximately the same time as Democritus was elaborating his atomic theory, rival theories were being proposed by empedocles and anaxagoras. According to Empedocles, the primordial beings are four qualitatively different elements, namely, fire, air, water and earth; he explained change in terms of the commingling and separation of these four elements, which themselves remain unchanged. Anaxagoras accented Empedocles's notion of commingling, but held that the primitive constituents of matter are an unlimited number of qualitatively different substances, themselves eternal and incorruptible, which he referred to as seeds (Gr. σπέρμaτa). In his view, every composed substance contains all possible kinds of seeds and is named after the type of seed that predominates in it.
In the classical period of Greek philosophy, plato, influenced by the ideas of pythagoras and the Pythagoreans, who held that number is the essence of things and likewise influenced by Democritus, proposed a geometrical theory of the basic particles of the universe. He regarded these as fire, earth, air and water and associated them with the four regular solids, namely, the tetrahedron, the cube, the octahedron and the icosahedron. aristotle, less partial to Democritean ideas than his teacher, explained change by a fourfold causal analysis that placed accent on substance and primary matter as substrates underlying accidental and substantial change respectively (see matter and form). In this context, he adapted Empedocles's theory of the four elements and taught that all bodies are continuous but composed of natural minima, that is, smallest particles of various kinds (see continuum).
Later Greek thought centered on the theories of Democritus and of Aristotle and thereby provided two influential currents that have persisted down to recent times. The notions of Democritus were taken up by epicurus, who reformulated them and used them as a method of inference from the visible to the invisible. The school of epicureanism that he founded kept atomistic notions alive long after the decline of Greek philosophy and can be said to have laid the remote foundations for the atomic theories of modern chemistry. The views of Aristotle, on the other hand, were taken up by his Greek commentators, Alexander of Aphrodisias, Themistius and john philoponus, all of whom contributed to a more systematic explanation of Aristotle's theory of natural minima. They spoke of the smallest particles of particular kinds of matter as ἐλάχιστα, a term with somewhat the same connotation as the modern word molecule. The concept was further developed in the Middle Ages and in the Renaissance; it was eclipsed somewhat with the rise of modern chemistry, only to take on new significance in 20th-century discussions of elementary particles.
Other Early Forms
A type of atomism is also to be found in indian philosophy, where it is associated with the system of Vaisésika Sūtra, attributed to a mythical Kanāda but probably recorded during the first two centuries a.d. Little is known of its origins, although it is possible that it was influenced by Greek thought. Indian atomism is relativistic; both the small (anu ) and the very small (paramānu ) are denied any absolute value. In the system of Vaisésika the very small is described as an elementary form; in an earlier type of atomism associated with jainism, it is regarded as lacking in any forms that would make it perceptible but still as endowed with qualities. Both systems deny the existence of a void and do not regard the atom as the unique principle of reality, admitting that the soul is a spiritual substance and not atomic in character. Where materialism does appear in Indian philosophy, it does not assume an atomistic form.
In Rome, the Greek physician Asclepiades (c. 124–40 b.c.) ascribed diseases to alterations in the size, arrangement and motion of the atoms that make up the human body. More influential was the teaching of the Roman poet and philosopher lucretius, who gave eloquent expression to the ideas of Democritus in his poem De rerum natura. This was a systematic account of an atomist theory of nature, describing in detail the formation of the universe, the origins of life and thought, the nature of human sensation and sexual attraction and the development of human society. Preserved in monastic libraries during the Dark Ages, this became the principal channel through which interest in Greek atomism was preserved to modern times.
Largely because of the materialistic atheism endorsed by Lucretius, Christian writers, such as dionysius of alexandria, attacked the atomists' doctrine as being based on chance and denying a principle of order within the universe (see universe, order of). The Fathers of the Church were likewise unfavorable to atomistic concepts because these seemed to form the basis for a materialistic Epicurean ethics. Through their polemics and through the efforts of encyclopedists such as isidore of seville, basic atomic concepts continued to be discussed. Isidore likened atoms to points, since they were indivisible and distinguished atoms of matter, time, number and language [Etymol., 13.3; Patrologia Latina, ed. J. P. Migne, 217 V., indexes 4 v. (Paris 1878–90) 82: 472–473].
Atomistic theories did not enjoy great popularity during the Middle Ages, the main line of development taking place in a thought context that was predominantly Aristotelian. In the 9th century, an Arab alchemist and physician named Rhazes (al-Rāzī, 865?–924) taught a type of atomism and other Islamic thinkers developed atomic ideas not unlike the earlier Indian concepts (see arabian philosophy). In the 14th century nicholas of autrecourt defended a Democritean type of atomism, speculating over the motions of atoms and their mutual attractions. Some historians list william of conches hugh of saint-victor and adelard of bath as atomists also, but the basis for this ascription is debatable (Van Melsen, Van atomos naar atoom; de geschiedenis van het begrip atoom 77).
The main concern in the Middle Ages regarding theories of matter was one of reconciling how material substance could be composed (compositum ) of primary matter and substantial form and at the same time be a compound (mixtum ) formed from the four elements. The problem this posed is referred to as that of the presence of elements in compounds; this was strenuously debated because of its intimate connection with the problem of the unicity of substantial forms (see forms, unicity and plu rality of). avicenna taught that the essential form of the element remains unchanged in the compound, although the qualities that characterize the element, undergo a remission of intensity. averroËs disagreed with this teaching, maintaining that not only the qualities of the element, but its substantial form also, undergo remission, and thus the element is not present in all its perfection within the compound. St. albert the great minimized the differences between Avicenna and Averroës, while associating the minimum elemental parts present in a compound with the atoms of Democritus (In 1 de gen. 1.12; ed. Borgnet, 4:354b). St. thomas aquinas rejected both Avicenna's view, that the elements are actually present in compounds, and Averroës's view, that they are present only potentially, to propose an intermediate position, namely, that elements are present virtually in compounds, in the sense that their forces or powers (virtutes ) are there conserved. Most other medieval thinkers, as A. Maier has shown, adopted either the Averroist solution (see roger bacon; henry of ghent; peter john olivi; theodoric of freiburg; john of jandun) or that proposed by Aquinas (see peter of auvergne; giles of rome; duns scotus; william of ockham; john buridan; Nicolas Oresme).
The controversy over the presence of elements in compounds was related to Aristotle's theory of natural minima. 14th-century thinkers generally did not identify such minima with atoms, as Albert the Great had been tempted to do. They distinguished between minima inexistentia, that is, as these might exist within a body and minima per se existentia, that is, as these exist when separated from a body. It was generally taught that separated minima could exist, but that minima inexistentia were not present within a body. The elaboration of a theory of natural minima that could be reconciled with atomistic concepts had thus to await the developments of later centuries.
Renaissance to 17th Century
The Italian Averroist movement of the 16th century, in the person of such thinkers as A. nifo, continued to develop Aristotelian doctrine and to apply this to speculation concerning the physical universe. Natural minima were conceived as parts of substance with a more independent existence than heretofore and were ascribed certain functions in physical and chemical processes. A. Achillini (1463–1512) spoke of the minima as reacting upon each other and J. zabarella worked out a more explicit theory concerning the forms of the minima and that of the bodies constituted from them. Perhaps the most complete theory of natural minima that shows affinities with atomic theories was that of J. C. Scaliger, who taught that the minima of different substances vary in size and who used this to explain their different properties, such as density. Scaliger defined chemical composition as "the motion of minima toward mutual contact so that a union is effected."
Other Renaissance thinkers, such as G. bruno and F. bacon, revived the notions of Democritus as transmitted through Lucretius and began to explain physical phenomena in terms of the motion of the ultimate particles of bodies. From about 1550 onward, increased interest manifested itself in Greek atomism and in the relation of atomic concepts to the newly forming sciences of mechanics and chemistry. In 1575 F. Commandino published a translation of the writings of Hero of Alexandria (1st century a.d.), who emphasized the importance of the size and shape of the empty space between the particles of bodies. G. galilei read Democritus and Hero, and used their notions to propose a distinction between primary and secondary qualities: the first are those associated with the motions of atoms and are objectively real; the second are sensations produced in a knowing subject and are merely subjective (see quality).
The first systematic application of atomic notions to chemistry was made by a German physician, D. Sennert (1572–1644), who developed the ideas of Scaliger and attempted to reconcile the minima theory with Democritean concepts. He taught that in chemical compositions the reagents are divided into their smallest parts, which subsequently unite through their minima and then act upon each other through their contrary properties. Perhaps the most influential atomist of the early 17th century was p. gassendi, a French priest and mathematician, who expurgated materialistic connotations from Democritean atomism. According to Gassendi, atoms are not eternal but are created by God; they are not infinite in number; and their motion is not eternal but has been impressed upon them by God for a definite purpose. R. descartes rejected the Democritean concept of the void and conceived all physical processes as taking place in a medium composed of infinitely small particles in motion. Although not an atomist in the strict sense, Descartes contributed to the growth of atomism by his highly influential mechanical philosophy. T. hobbes, the English mechanist, held for the existence of atoms but taught that the spaces between them were filled with some kind of fluid. Rejection of empty space in this and later periods was usually prompted by a philosophical recognition of the impossibility of action at a distance.
The most influential atomists of the later 17th century were R. Boyle, R. Hooke, C. Huygens and I. Newton. Boyle made use of both medieval and modern concepts to clarify the notion of a chemical element. He regarded heat as a type of atomic vibration and explained alteration as well as generation and corruption mechanically, that is, in terms of the motions and rearrangements of atoms. Boyle proposed a complex hierarchy of particles (primary, secondary, etc.), but shared the alchemists' conviction of the unity of matter and the transformability of one type of atoms into another. Hooke suggested that the regular forms of bodies, particularly of crystals, could be explained in terms of arrangements of "globular particles." He taught that all particles are in vibration and explained heat as an oscillatory motion of the smaller particles. Huygens further developed Gassendi's notions while attempting to work out a consistent kinetic theory that would explain the phenomena of gravitation, atmospheric pressure, light and cohesion. Newton also subscribed to the atomistic views of Gassendi, as well as those of Lucretius and attempted to elaborate these quantitatively in terms of his laws of mechanics. He showed that Boyle's law for gases could be derived on the assumption that these consist of hard particles repelling each other inversely as the distance. He also considered both attractive and repulsive forces and used them to replace the hooks postulated in more naïve explanations of atomic combination. From optical studies of the thickness of soap bubbles, he calculated an upper limit of about 10-5 cm for the size of soap particles.
Quantitative atomism thus had its tentative beginnings in the second half of the 17th century. The 18th century saw an accumulation of experimental data and the proposal of theoretical concepts that would lay the groundwork for the full-blown development of classical atomism in the 19th century.
G. W. leibniz, G. vico, E. swedenborg, R. G. Boscovich, J. Priestley, R. J. Haüy and J. L. Proust figured most prominently in this period. At first a materialistic atomist, Leibniz later developed his theory of the monad, which he conceived as a simple substance without extension, shape, position, or movement but with the power of perception. Somewhat similar was the view of Vico, who held that the universe is constituted of point centers of action; unlike Leibniz's "metaphysical points," however, these had location and a tendency to movement and were not endowed with perception. Swedenborg proposed a theory of natural points similar to Vico's to explain all geometrical and mechanical phenomena.
These dynamistic notions reached their culmination in the mathematical theory of atomism proposed by the Jesuit mathematician Boscovich. This theory postulated the existence of a finite number of quasi-material point centers of action, all with identical properties and all obeying an alternately repulsive and attractive force of interaction whose magnitude depended on the distance between each pair. In proposing it, Boscovich substituted a monism of special relations for the earlier dualism of occupied vs. empty space, and gave meaning to the concept of physical structure in terms of a three-dimensional array of point centers. His ideas were viewed favorably by I. kant, who developed a similar theory shortly after Boscovich. Priestley also was aware of Boscovich's theory and called it to the attention of English scientists (see dynamism).
While these theoretical considerations were being proposed, the French chemist Proust was gathering proof that true compounds contain chemical elements in constant proportions. His countryman C. A. Coulomb at about the same time established his law of the attraction and repulsion of electrical charges; and Haüy, a French priest and mineralogist, proposed that a crystal of any type could be subdivided into ultimate solid units of the same shape as the crystal.
Such contributions prepared for the serious experimental work that provided the empirical base for 19th-century theories of classical atomism. Although many distinguished scientists collaborated in this development, J. Dalton, J. L. Gay-Lussac, A. Avogadro, D. I. Mendeleev and M. Faraday may be singled out for comment.
Dalton is generally credited with having placed the atomic theory, for the first time, on an exact quantitative basis. Building on the experimental findings of A. L. Lavoisier and assuming the law of conservation of weight in chemical reactions, he first formulated the law of multiple proportions. With its aid and using measurements of the weights in which chemical elements combine, he was able to calculate the relative weights of their constituent atoms; in this way he reasoned to the existence of about 20 kinds of atoms or elements. Gay-Lussac, experimenting with gases entering into chemical combination, concluded that gases combine in very simple ratios by volume; in his analysis, the law of combining volumes was more accurate than the law of combining weights proposed by Dalton. The oversimplified conceptual schemes used by both Dalton and Gay-Lussac in analyzing their data thereupon led Avogadro to adumbrate the distinction between atoms and molecules. Avogadro assumed that the constituent molecules of any simple gas are made up of half-molecules or third-molecules, etc., later identified with atoms and proposed as a hypothesis that the number of integral molecules in any gas is always the same for equal volumes, or is always proportional to the volumes. With the aid of this hypothesis, he was able to reconcile apparently contradictory experimental data obtained by Dalton and Gay-Lussac.
Building on the work of Avogadro and of S. Cannizzaro, Mendeleev noted regularities in the properties of the then-known elements, by this time 63 in number. He argued that since the mass of a substance is its most fundamental property, a periodicity of its other properties should be expected when the elements are arranged in the order of their atomic weights. He then proposed conclusions following from the periodic law that would be useful for discovering and correcting data on the elements. Meanwhile, Faraday's work on electrolysis led directly to the conception of units of electricity and to estimates of the value of charge that were later to be identified with the electron.
Despite vocal opposition from the empiricist E. Mach and from the energeticist W. Ostwald, the cumulative effect of these discoveries convinced most scientists, toward the close of the 19th century, of the atomic structure of matter. Almost all of the data of chemistry were then capable of explanation in terms of atomic concepts. It seemed only a matter of time that the more complex electromagnetic phenomena of physics would yield to their explanatory power.
Such confidence, however, was doomed to be short-lived. The even more rapid development of atomic physics in the first part of the 20th century led quickly to the abandonment of attempts to explain all physical phenomena in terms of the mechanical motion of Democritean atoms. The details of this development are quite complex and are treated elsewhere. For present purposes, it suffices to mention only the major conceptual developments as these are relevant to the present state of atomistic thought.
No sooner had fairly conclusive evidence for the existence of atoms and molecules been made available than a series of investigators, including J. J. Thomson, E. Rutherford, F. W. Aston and G. H. J. Moseley, produced a theory of atomic structure that viewed the atom as composed of subatomic particles. In the process, it was shown that the atom was divisible, that is, that electrons could be removed from it and that its nucleus could be disintegrated. Attempts to explain electromagnetic radiation and absorption in terms of this atomic structure led to the development of the quantum theory but produced no clearcut mechanical conception of the motion of atomic parts. L. de Broglie, noting parallels between the dynamics of bodies and wave propagation, showed how electrons and other subatomic particles also have a wave or undulatory aspect. This led to the introduction of wave mechanics by E. Schrödinger and others, wherein the planetary motion of electrons was replaced by the interference of systems of stationary waves. More elaborate mathematical theories were then developed, which have been subjected to various physical interpretations but provide no easily imaginable picture of the structure of the atom. W. Heisenberg has pointed out how these conceptual advances forced physicists to adopt the uncertainty principle, to abandon their commitment to physical determinism and to seek only statistical laws when investigating the microcosm. In 1958 he suggested that "all particles are basically nothing but different stationary states of one and the same stuff" (The Physicist's Concept of Nature, 46), and urged the return to the Aristotelian concept of potency as an ontological basis for the indeterminism that seems to characterize the realm of the very small (Physics and Philosophy, 41, 53, 59–62, 69–72, 160, 166).
The status of atomism in 20th-century thought must be evaluated in the context of continuing research in the theory of elementary particles. While atomistic concepts have proved most fruitful in exploring the structure of matter, physicists have generally abandoned hope of attaining the indivisibles Democritus regarded as the ultimate building blocks of the universe. Their researches have accented, rather, elements of truth in competing theories, such as those of Aristotle and his medieval commentators. At the same time, philosophers of science have become more critical of conceptual schemes elaborated by physicists and are more prone to question the ontological status of theoretical entities than heretofore.
In light of these trends, atomism has ceased to play the central role in speculation about the physical universe that it played in the 19th century. This notwithstanding, and granted the oversimplifications that it involves when attempting to account for the wealth of detail in the microcosm, it still stands as one of the most fruitful conceptualizations in the history of scientific thought.
See Also: hylosystemism; element; space.
Bibliography: l. l. whyte, Essay on Atomism (New York 1960). a. g. van melsen, From Atomos to Atom, tr. h. j. koren (Pittsburgh 1952; 1960). k. lasswitz, Geschichte der Atomistik vom Mittelalter bis Newton (Hamburg 1890). r. eisler, Wörterbuch der philosophischen Begriffe, 3 v. (4th ed. Berlin 1927–30) 1:132–137. v. e. alfieri, Enciclopedia filosofica, 4 v. (Venice-Rome 1957) 1:447–455. f. c. copleston, History of Philosophy (Westminster, Md 1946—) v.1. s. sambursky, The Physical World of the Greeks, tr. m. dagut (New York 1962). c. bailey, The Greek Atomists and Epicurus (Oxford 1928). a. maier, Die Vorläufer Galileis im 14. Jahrhundert (Rome 1949); An der Grenze von Scholastik und Naturwissenschaft (2d ed. Rome 1952). Readings in the Literature of Science, eds. w. c. and m. d. dampier (Cambridge, Eng. 1924; 1959), classical contributions to atomic theory. l. k. nash, "The Atomic Molecular Theory" in Harvard Case Histories in Experimental Science, ed. j. b. conant, 2 v. (Cambridge, Mass. 1957) 1:215–321. m. boas, "The Establishment of the Mechanical Philosophy," Osiris, 10 (1952) 412–541. c. ning yang, Elementary Particles (Princeton 1962). w. heisenberg, The Physicist's Concept of Nature, tr. a. j. pomerans (New York 1958); Physics and Philosophy (New York 1958). p. soccorsi, Quaestiones scientificae cum philosophia coniunctae: De vi cognitionis humanae in scientia physica (Rome 1958); Quaestiones scientificae cum philosophia coniunctae: De physica quantica (Rome 1956). w. a. wallace, "The Reality of Elementary Particles," American Catholic Philosophical Association. Proceedings of the Annual Meeting, 38 (1964) 154–166.
[w. a. wallace]
Atomism is a doctrine that has a long history in both philosophy and science. For this reason it is not easy to define its content in such a way as to comprehend all the historical variations and especially the historical development of the doctrine. In a very general sense, however, atomism may be defined as the doctrine that material reality is composed of simple and unchangeable minute particles, called atoms. It holds that all observable changes must be reduced to changes in the configuration of these particles. The multiplicity of visible forms in nature must likewise be based upon differences of configuration. The best way to discuss the variations of this general idea of atomism is to follow the historical development, which shows a gradual shift of emphasis from philosophical to scientific considerations. Consequently, the first part of this article, covering the period from the sixth century BCE to the seventeenth century, will be of a philosophical nature because in this period atomism was considered preponderantly from a philosophic point of view. The second part is concerned primarily with science, for it was in the period after the seventeenth century that atomism evolved in a scientific theory.
The Philosophical Period
In Greek philosophy we are already confronted with several types of atomism. Atomism in the strict sense, propounded by Leucippus and Democritus (fifth century BCE), should be looked upon as an attempt to reconcile the data of sense experience with Parmenides' thesis that matter is unchangeable. Parmenides rejected the possibility of change on rational grounds; change seemed to be unintelligible. He was convinced that reality must be one, that it must possess unity, and that, being one reality, it could not change. It may be remarked that this thesis of Parmenides is a presupposition for all rational science. Without fundamental unity, no universal laws are possible; without fundamental immutability, no laws covering past, present, and future can be valid. Yet, it is clear that Parmenides' approach is one-sided. Science may presuppose unity and immutability, but it also presupposes change. Only by studying changes is science able to discover the immutable laws of nature.
Democritus agreed with Parmenides on the unintelligibility and impossibility of qualitative change. He did not agree on the unintelligibility and impossibility of quantitative change. This type of change is subject to mathematical reasoning and therefore is possible. By the same token, Democritus denied qualitative multiplicity, but accepted multiplicity based on purely quantitative differences. Consequently, he accepted a numeric multitude of original beings, the atoms. These atoms did not differ qualitatively; only their sizes and figures differed. The infinite variety of observable things could be explained by the different shapes and sizes of the atoms that constituted them and by the different ways in which the atoms were combined. Observable changes were based upon a change in combinations of the atoms. During such changes, however, the atoms themselves remained intrinsically unchanged. They did not change their nature, or even their size or figure; they were indivisible (hence their name 'άτομος or indivisible).
Other forms of Greek atomism differed from that conceived by Democritus mainly in two points. First, they did not restrict the differences between the atoms to purely quantitative ones, but also accepted differences in quality. There was even a system that assumed as many qualitatively different atoms as there are different observable substances (Anaxagoras, fifth century BCE). Usually, however, only a few kinds of atoms were assumed, based upon the famous doctrine of the four elements: earth, water, air, and fire (Empedocles, fifth century BCE).
The second point of difference concerned the indivisibility of atoms. It is evident that a system that does not accept the indivisibility of atoms cannot properly be called atomism, but since such systems have played an important role in the history of atomism, we must mention them. For Democritus, the indivisibility of atoms was an absolute indivisibility, being the consequence of an absolute immutability. There were systems, however, that considered the indivisibility and immutability as only relative. The "atoms" could be divided, but they then became "atoms" of another substance; they changed their nature. (Here again an exception must be made for atoms as conceived of by Anaxagoras. These could be divided, but remained of the same kind. Hence they received the name of homoiomerics, possessing similar parts.) From the historical viewpoint, the most important system with qualitatively different atoms is that developed by the commentators on Aristotle—Alexander of Aphrodisias (second century CE), Themistius (fourth century) and John Philoponus (sixth century). In their system the atoms are called elachista (very small or smallest), the Greek equivalent of the Latin minima, which in medieval Latin writings indicates the smallest particles.
That these commentators on Aristotle combined the existence of "atoms" with the possibility of their changing their nature is not surprising. Aristotle was not satisfied by Democritus' atomism and was of the opinion that Democritus went only halfway. Atomism certainly opened up the possibility of explaining some changes that occur in nature, but not all. Nor did it account for all variety. Thus, the first task imposed upon Aristotle was a careful and critical reexamination of Parmenides' thesis. The result was his matter-form doctrine, stating that every material being is composed of primary matter and form of being. This composition, however, is not chemical or physical; it goes deeper. The possibility of change presupposes a certain fundamental nonsimplicity, for otherwise it is not possible to account for both aspects that are present in change: the aspect of a certain permanence (matter) and the aspect of something that is really new (form). Matter in the Aristotelian sense is not a substance, but the capacity to receive "forms."
To a certain extent, Democritus followed the same line of thought. Democritus, however, "substantialized" the permanent aspect (the atoms), thus narrowing the possibility of change. For Aristotle the "atoms" too should be subject to change and therefore "composed." Aristotle, however, did not propound a corpuscular theory of his own. Only a few remarks that could have been the starting point are found in a passus (Physics I 4, 187B18–34) in which he criticizes Anaxagoras' theory about the infinite divisibility of material things. Somewhere there must be a limit to divisibility. This limit depends on the specific nature of a thing. It was left to Aristotle's Hellenistic, Arabian, and medieval commentators to develop the casual remarks of their master into the minima naturalia theory, stating that each kind of substance has its specific minima naturalia.
In Greek philosophy there were also transitional theories between qualitative and quantitative forms of atomism. Plato (427–347 BCE), for example, adhered to the doctrine of the four elements; but the differences between the atoms of the respective elements were quantitative. An atom of fire had the form of a tetrahedron; that of air, an octahedron; that of water, an icosahedron; and that of earth, a cube.
When evaluating the importance of Greek atomism in the light of modern atomic theories, it should be borne in mind that in Greek thought philosophy and science still formed a unity. Greek atomism, therefore, was as much inspired by the desire to find a solution to the problem of mutability and plurality in general as by the desire to provide scientific explanations for specific phenomena. Although we meet with some ideas that can rightly be considered as precursors of classical physics and chemistry, the main importance of the old atomistic doctrines to modern science does not lie in these rather primitive scientific anticipations. The greatest achievement of Greek atomism was its general view of nature. The multitude of phenomena must be based upon some unity, and the ever-changing aspects of the phenomena are nevertheless aspects of a fundamentally unchanging world. To this view both the quantitative and the qualitative atomism have contributed—the latter by drawing attention to empirical aspects; the former, to the mathematical.
The history of the two forms of philosophical atomism until the birth of a scientific atomic theory has been rather different. This can easily be explained. Owing to the influence of Plato and Aristotle, Democritus' atomism did not gain preeminence in Greek, Arabian, and medieval thought. Yet that is not the only reason. Much more important is the fact that Democritus' atomism was more or less complete; and his followers, such as Epicurus (341–270 BCE) and the Latin poet Lucretius Carus (96–55 BCE), could confine themselves simply to taking over Democritus' doctrine.
The Aristotelian minima theory, however, existed only in an embryonic state. To Aristotle and his Hellenistic commentators the minima naturalia did not mean much more than a theoretical limit of divisibility; they were potentialities rather than actualities. With Averroes, however, we find an important development. According to him, the minima play an important role during chemical reactions. The Latin Averroists followed up this line of thought. Whereas most of the Latin commentators on Aristotle restricted themselves to a more or less systematic treatment of the minima as theoretical limits of divisibility, such Averroists as Agostino Nifo (1473–1538) attributed to the minima a kind of independent actual existence. The minima were considered as actual building stones of reality. The increase or decrease of a quantity of a substance amounts to the addition or subtraction of a certain number of minima. A chemical reaction takes place among the minima.
The fundamental importance of this view to science will be clear. Because the minima had acquired more physical reality, it became necessary to examine how their properties could be reconciled with the specific sensible properties of different substances. A first attempt to do so is found in Julius Caesar Scaliger (1484–1558). Some properties of matter, such as fineness and coarseness, depend on the minima themselves, while others depend on the manner in which the minima configurated. Rain, snow, and hail are composed of the same minima; but their densities are different because the minima of these three substances are at smaller or greater distances from one another. As to the chemical reaction, Scaliger remarked: "Chemical composition is the motion of the minima towards mutual contact so that union is effected" (Exercitationes, p. 345). Like Aristotle, he was convinced that Democritus was wrong. In a chemical compound the particles are not just lying close together; they form a real unity. Scaliger, however, was also convinced that the minima play a role in effecting the composition; and for that reason he was not satisfied with the Aristotelian definition of chemical composition as "the union of the reagents," in which the minima are not mentioned.
To sum up our survey of the development of the minima doctrine, and to prove that the opinions of Nifo and Scaliger were no exceptions, we may quote Francis Toletus (1532–1596), one of the best-known sixteenth-century commentators on Aristotle: "Concerning the manner of chemical composition, the opinions of authors vary, but they all agree in this: the reagent substances are divided into minima. In this division the separated minima of one substance come alongside the minima of the other and act upon each other till a third substance, having the substantial form of the compound is generated" (De Generatione et corruptione I, 10, 19).
The Scientific Period
The seventeenth century is an important period in the history of atomism. Not only did atomism come to occupy a central position in philosophical discussion, but it also became an inspiring idea for the spiritual fathers of modern science. The philosophic differences between the atomic systems were soon pushed into the background, while the more scientific aspects that were held in common came to the foreground. Daniel Sennert (1572–1657) offers a clear example of this tendency. Basically, his corpuscular theories were derived from the doctrine of minima naturalia, but they also contain typically Democritean ideas. In a sense the same could be said of Scaliger; but the difference is that Scaliger discussed the philosophical controversies between Aristotle and Democritus, whereas Sennert showed a pronounced eclectic tendency. He was interested mainly in a chemical theory, and he found that from a chemical point of view the two theories really amount to the same thing. In order to support this opinion, Sennert refused to accept the interpretation that Democritus meant to deny the qualitative differences of atoms. As a chemist, Sennert was convinced that elementary atoms differ qualitatively. His main contribution to the corpuscular theory lies in the clear distinction that he made between elementary atoms and atoms of compounds (prima mista ). This distinction forced itself upon Sennert through chemical experience. Each chemical substance, elementary or compound, must have its own atoms.
Contrary to Sennert, Pierre Gassendi (1592–1655) faithfully copied Epicurus and therefore Democritus as well. His own contribution consisted of a number of annotations designed to make the original atomic doctrine acceptable to his contemporaries. In order to effect this purpose, two things were necessary. First of all, the atomic system had to be divested of the materialistic interpretation with which it was hereditarily connected. Second, Gassendi had to "adapt" the original atomic theory to the science of his time. Science had reached the stage at which certain definite physical and chemical properties were attributed to the atoms—i.e., the atoms must possess definite natures; they could not be qualitatively equal. For this reason Gassendi stated that from the original atoms certain molecules were formed first; these differed from each other and were the seeds of different things.
While Gassendi's system is basically without any trace of originality, the corpuscular theory of René Descartes (1596–1650) is original in outline and execution. According to Descartes, matter and extension are identical. This thesis of course excludes the idea of indivisible atoms, but not of smallest particles. To the question of how such particles are separate and distinct from each other, Descartes answered that when a quantity of matter moves together, that quantity forms a unit, distinct from other units that have different motions. Along these lines, Descartes succeeded in devising a corpuscular theory in which the corpuscles were characterized by differences in mass, in amount of motion, and other properties that could be expressed in physical terms and treated mathematically. Descartes's corpuscles were endowed with exactly those properties that could be used in contemporaneous mechanics. As we have seen with Sennert, the seventeenth century was less interested in philosophical considerations than in scientifically fruitful ideas. Therefore, a corpuscular theory was judged, first of all, by this standard; and underlying philosophical discrepancies did not much interest the scientist. This explains why, to their contemporaries, Gassendi and Descartes could stand fraternally united as the renovators of the atomic theory.
Robert Boyle (1627–1691), for example, repeatedly confessed how much both Descartes and Gassendi had inspired him. On the other hand, Boyle was too much a chemist to be satisfied with a general idea of atoms or even with atoms endowed only with mechanical properties. Boyle looked for specific chemical properties. In contrast with mechanics, however, chemistry was not yet sufficiently developed to provide the theoretical framework necessary for a satisfactory chemical atomic theory. Boyle was keenly aware of this situation, as his The Sceptical Chymist (Oxford, 1661) proves. Neither the traditional theory of four elements nor the three-principle theory current among chemists could be of any use to him. Yet he was convinced that the distinction between elements and compounds was a sound one. This distinction therefore governed his own atomic theory. Theoretically, he adhered to the atoms of Democritus; practically, he did not use them. He was convinced that atoms were associated into so-called primary concretions, "which were not easily dissipable into such particles as composed them." Thus the primary concretions were corpuscles with definite qualities; they corresponded to the smallest particles of elements, and consequently Boyle treated them as such. The primary concretions could combine to form compounds of a higher order that may be compared with Sennert's prima mista. Although Sennert's corpuscular theory was based more on the minima theory and Boyle's theory more on the ideas of Gassendi and Descartes, in practice their theories were not very different. Both theories recognized atoms of compounds that are composed of atoms of elements. For Sennert the latter were elements, both theoretically and practically. For Boyle, theoretically they were not elements, but practically they were, because in chemical and physical processes primary concretions are not dissolved.
By combining the relative merits of the minima theory (qualitative atoms) and of Democritus' atomism (open to quantitative treatment), the seventeenth century laid the foundations for the scientific atomic theory of the nineteenth century. The further development of the seventeenth-century atomic theory, however, required better chemical insights, and especially a method of distinguishing elementary from compound substances. This method was found by Antoine Lavoisier (1743–1794), who postulated the conservation of weight as the guiding principle in chemical analysis. For the first time in history, a list of chemical elements could be given, based upon the results of chemical analysis.
The outstanding achievement of John Dalton (1766–1844) was that he connected these chemical results with the atomic theory. His atoms were no longer smallest particles with some general and rather vague physical properties, but atoms endowed with the properties of chemical elements. Dalton himself in A New System of Chemical Philosophy stressed the great importance of "ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one more compound particle" (2nd ed., p. 213).
The fact that Dalton's theory is primarily a chemical theory does not mean that it has no philosophical implications. It is interesting to note that Dalton conceived the union of atoms in a compound as their simple juxtaposition without their undergoing any internal change. On this point the founder of the chemical atomic theory did not differ from the Democritean tradition. On another point, however, he followed the minima tradition. Dalton's atoms were specifically different for every kind of substance. He did not even think of building these atoms from particles without qualities, as Gassendi and Boyle had done.
After Dalton, the development of the atomic theory was very rapid. Jöns Jakob Berzelius (1779–1848) determined the relative atomic weights with surprising accuracy, guided by the hypothesis that under the same pressure and at the same temperature the number of atoms in all gaseous substances is the same. Since hydrogen and oxygen combine in the constant volume proportion of two to one, Berzelius concluded correctly that two atoms of hydrogen combine with one atom of oxygen. Berzelius also gave to chemistry its modern symbols. Amedeo Avogadro (1776–1856) completed the atomic theory by assuming that compound atoms, or molecules, do not necessarily have to be formed out of atoms of different elements; molecules of elements (H2; O2) also exist. According to Avogadro, the law that postulated an equal number of atoms in equal volumes of gas had to be understood as applying to an equal number of molecules. In a short time, the framework for classical chemistry was completed on the basis of Dalton's atomic theory. Chemical reactions were conceived of as a reshuffling of atoms and described by such chemical equations as 2 H2 + O2 → 2 H2O.
An important contribution to the development of the atomic-molecular theory came from physics in the form of the kinetic theory of gases. With the aid of the calculus of probability, James Maxwell and Ludwig Boltzmann succeeded in deriving the behavior of gases, as described in the empirical laws of Boyle and Joseph-Louis Gay-Lussac, from the motions of the molecules.
The discovery of the electron, the electric atom, paved the way for a new theory about the nature of chemical compounds and chemical reactions. According to the new theory, a molecule such as NaCl did not consist of an Na atom and a Cl atom, but of an Na ion and a Cl ion; the Na ion was an Na atom minus an electron, and the Cl ion was a Cl atom plus an electron. Thus the so-called ionic theory revealed the nature of the forces of attraction between the various atoms of a molecule. The Na ion with its positive electric charge was attracted by the Cl ion with its negative charge. As a result of the connection that the theory of electricity established between physics and chemistry, theoretical and experimental materials were available at the beginning of the twentieth century. They led to a new development of the atomic theory that would endeavor to penetrate into the interior of Dalton's atoms.
The atomic model of Niels Bohr (1913) considered every atom as built of a positively charged nucleus around which circled, in fixed orbits as many electrons as were indicated by the charge of the nucleus. This charge corresponded to the place of the element in the periodic system. Bohr's model could explain not only the fundamental chemical properties of the elements, but also such physical properties as the spectrum that is characteristic of each element when it is emitting or absorbing light. Nevertheless, there were also serious difficulties with this model. According to electrodynamics, the moving electrons would ceaselessly emit electromagnetic waves. The atom would not be stable, but would always be losing energy. Hence, the motion of the electrons would gradually decrease and finally cease entirely. In order to save his model, Bohr postulated that emission of energy occurs only when an electron "jumps" from one orbit to another. In other words, the emission of energy is discontinuous. The emitted energy could be only a whole multiple of an elementary quantity of energy.
Thus, following the work of Max Planck, the idea of minima of energy was added to the idea of minima of matter, the traditional basis of atomism. Even light seemed to show an atomistic structure (photon theory). This would have meant a complete victory for the atomistic view if there had not been a complication. This complication was that the reasons which had formerly settled the dispute about the nature of light in favor of Christian Huygens's wave theory against Isaac Newton's corpuscular theory still retained their value. Light showed a dual character. In 1924, it occurred to Louis de Broglie that the same dualism might very well apply to the particles of matter. On the basis of this hypothesis, he could readily explain Bohr's postulate. This resulted in quantum mechanics, a new theory propounded by Erwin Schrödinger and Werner C. Heisenberg, which showed that both the atomic theory and the wave theory were only approximate models and not adequate representations of material reality.
The evolution of the atomic theory in the twentieth century was not limited to these rather startling new theoretical developments; it also gave rise to a new branch of physical science, nuclear physics, which studies the changes that the atomic nucleus is subject to. The first work in this area was in connection with the study of natural radioactivity. It had been observed that through radiation the nucleus of one element changes in charge and mass and thus becomes the nucleus of another element. In 1919 Ernest Rutherford succeeded in effecting an "artificial" transmutation; many others followed. The atoms of chemical elements appeared to be composed like the molecules of chemical compounds. Through nuclear processes a confusingly great number of new elementary particles has been discovered, all of which are subject to transformation under certain conditions. Particles can be changed into other particles and even into radiation. With such transmutations enormous amounts of energy are released.
Thus, twentieth-century science revolutionized many fundamental ideas of the nineteenth century; the atom is not only much more complex than Dalton thought; it is also much more dynamic. Yet Dalton is far from antiquated. Modern chemistry still works along the lines drawn by Dalton and his contemporaries. Can the same be said in relation to his forerunners in the philosophical period of atomism? The answer to this question can be found in the fact that the main mistake of Dalton and other advocates of essentially mechanistic theories lay in the conviction that atoms did not undergo any internal change. Science showed that this assumption was erroneous, but this should not be a de facto statement only. For if we think of the nature of science as experimental, then it is clear that unchangeable atoms would not offer any possibility of being investigated by experimental means. Without change, matter could not respond to experimental questions. Classical science could overlook this simple truth by assuming that it already knew all the relevant features of atoms. This assumption followed from the mechanistic doctrine that, from the seventeenth century onward, formed the philosophical background of the atomic theory and of classical science in general. The mechanistic doctrine points up the fact that classical science originated in a rationalistic climate. The idea of an unchangeable atom endowed with mechanical properties seemed to be in accordance with what an element should be. It satisfied both the imagination and the intellect. The program of science seemed to consist in explaining the forms of nature on the basis of component elements that were already known.
With the development of science, however, increasing knowledge of chemical compounds affected our understanding of elements. The elements, too, became the object of experimental investigation. From this it may be concluded that the mechanistic doctrine was not a real presupposition of the scientific method. In using the experimental method, science presupposed a much more fundamental mutability in nature than traditional mechanism could account for, and the scientific method implied a much more refined view of material reality than the mechanistic interpretations of science suggested. For this reason, the less orthodox forms of atomism were as important to the origin of the scientific atomic theory as were the orthodox. From the point of view of twentieth- and twenty-first-century science, the Greek philosophical discussions about the nature of change remain amazingly modern.
See also Alexander of Aphrodisias; Anaxagoras of Clazomenae; Aristotle; Averroes; Bohr, Niels; Boltzmann, Ludwig; Boyle, Robert; Chemistry, Philosophy of; Descartes, René; Empedocles; Epicurus; Gassendi, Pierre; Heisenberg, Werner; Lavoisier, Antoine; Leucippus and Democritus; Lucretius; Maxwell, James Clerk; Newton, Isaac; Parmenides of Elea; Philosophy of Science, History of; Planck, Max; Plato; Schrödinger, Erwin; Themistius; Toletus, Francis.
Dalton, John. A New System of Chemical Philosophy. London: Bickerstaff, 1808; 2nd ed., 1842.
Dijksterhuis, E. J. The Mechanization of the World Picture. Oxford: Clarendon Press, 1961. Excellent history of science from antiquity to the seventeenth century.
Hooykaas, R. "Elementenlehre und Atomistik im 17. Jahrhundert." In his Die Entfaltung der Wissenschaft, pp. 47–65. Hamburg: Augustin, 1957.
Lasswitz, K. Geschichte der Atomistik vom Mittelalter bis Newton, 2 vols. 2nd ed. Leipzig, 1926. A nineteenth-century classic.
Melsen, A. G. M. van. From Atomos to Atom, the History of the Concept Atom, 2nd ed. New York: Harper and Row, 1960. Includes references for the primary sources.
Nash, Leonard K. The Atomic-Molecular Theory. Cambridge, MA: Harvard University Press, 1950. Discusses the classical chemical theories.
Scaliger, J. C. Exotericarum Exercitationum Libri XV de Subtilitate ad Hier. Frankfurt, 1557; 2nd ed., 1607.
Whittaker, E. History of the Theories of Aether and Electricity, 2 vols. New York: Philosophical Library, 1951 and 1954. For readers with a good background in science.
Whyte, L. L. Essay on Atomism: From Democritus to 1960. Middletown, CT: Wesleyan University Press, 1961. A brief introduction to the idea of atomism and its history.
Yang, Chen Ning. Elementary Particles, a Short History of Some Discoveries in Atomic Physics. Princeton, NJ: Princeton University Press, 1962. Gives a general outline of the research done since 1900.
Andrew G. M. van Melsen. (1967)
Atomism (from Greek átomos: indivisible) considers every substance (including living beings) to be made up of indivisible and extremely small material particles, the atoms. Every sensual quality of perceptible bodies has to be explained by the qualities, configurations, and changes of the atoms composing it, so that the (secondary) qualities of a compound are completely determined by and reducible to the (primary) qualities of its component atoms.
Historically, atomism can be traced back to antiquity, namely to the pre-Socratic philosophers of nature, Leucippus (born c. 480/470 b.c.e.) and Democritus (c. 460–370 b.c.e.). Due to Aristotle's convincing arguments against atomism, and because of its materialistic and atheistic worldview, it was unimportant during the Middle Ages. It was only with the seventeenth century that atomism was transformed into a scientific theory. Pierre Gassendi (1592–1655) revived classical atomism and explained the physical world as being constituted by finitely many atoms, which move in a void and have been endowed by God with a conserving momentum, thus freeing atomism from the stigma of being atheistic. Gassendi already allowed atoms to form compounds, which he called moleculae or corpuscula. The eighteenth and nineteenth centuries then gave rise to chemical atomism, which distinguished element from compound. Although Isaac Newton (1642–1727) had already speculated in detail on the atomic nature of matter and light in his Opticks (1704), physical atomism became widely accepted only after the development of the kinetic theory of gases in the nineteenth century. Atomism strongly supported the deterministic worldview of classical mechanics.
With the discovery of the electron and of radioactive decay, atoms themselves were recognized as composites and not indivisible units. The first atomic models were constructed in analogy to a macroscopic planetary system obeying classical laws of motion (negative electrons circling around a nucleus of neutrons and positively charged protons), but these models proved to be inconsistent. Erwin Schrödinger (1887–1961) and others then applied quantum mechanics to the atom. They substituted the electron orbits with probability distributions (orbitals ), which indicate in which regions of space the electron is most likely to be found. The transition from one state of the atom to another also follows quantum principles, which imply fundamental uncertainties. It has also been shown that two quantum objects that interacted once stay correlated in some of their properties, even if they move away from each other (EPR effect ). Thus, modern atomism with its dynamic view of matter has overcome the mechanistic tendencies of classical atomism and presents material reality as a holistic, fluctuating, and not fully determined net of coherence, which cannot be reconstructed as a set of completely separable massive objects that follow determined trajectories. Consequently, Alfred North Whitehead (1861–1947) suggested that processes ("actual entities") rather than substances are "the final real things of which the world is made up" (Whitehead, p. 18 ).
Thus, contemporary atomism opens new perspectives for the dialogue between science and religion, insofar as nature can be envisioned as being open for divine and human creative action. Living beings, human values, the act of striving for meaning and fulfillment in life, religious beliefs, and science itself are not mere agglomerations and idle enterprises in a mechanical world of swirling atoms, but can be understood as emergent and meaningful phenomena in an evolving process of creation.
See also EPR Paradox; Materialism
gregory, joshua c. a short history of atomism: from democritus to bohr. london: a&c black, 1931.
pais, abraham. inward bound: of matter and forces in the physical world. oxford: clarendon, 1986.
whitehead, alfred north. process and reality: an essay in cosmology, (1929) corrected edition, ed. david ray griffin and donald w. sherburne. new york: free press, 1978.
ATOMISM , theory that physical bodies consist ultimately of minute, irreducible, and homogeneous particles called atoms (Greek atomos/atomon = indivisible). In medieval Arabic and Hebrew works atomism derives from Greek (Democritus, Epicurus) and Indian sources. Common Hebrew terms for the atom are: "ha-ḥelek she-eino mitḥallek" ("indivisible particle") or simply "ḥelek"; "ha-eẓemha-pirdi " ("separate substance") or simply "eẓem"; in Karaite texts also "ḥatikhah" = "juzʾ, " "ḥelek," and "dak" ("minute [body]"). The majority of Jewish thinkers rejected atomism, except for Karaite authors who adhered to the Muʿtazilite system of *Kalām, along with its atomism; e.g., Joseph al-Basir (11th century), his pupil *Jeshua b. Judah, and *Aaron b. Elijah of Nicomedia (14th century; Eẓ Ḥayyim, ed. by F. Delitzch (1841), 12 ff.). Judah Hadassi (12th century) is a prominent exception (Eshkol ha-Kofer (1836), ch. 28, 19b). While propounding a Muʿtazilite-type system, Saadiah Gaon (tenth century) rejected its atomism, and affirmed the virtual infinite divisibility of matter (Beliefs and Opinions, tr. by S. Rosenblatt (1948), 45, 50 ff.). Objections to atomism are also raised by Saadiah's contemporary, the Neo-platonist Isaac b. Joseph *Israeli (Sefer ha-Yesodot, ed. Fried, ch. 2, pp. 43 ff.), and by the later Neoplatonist, Solomon ibn *Gabirol (11th century; Fons Vitae, ed. by C. Baeumker (1895), 52, 57–58). *Maimonides (12th century) followed the physics of Aristotle with its rejection of atomism (Guide of the Perplexed, tr. by Pines, 1 (1963), 51, 112). In a historically significant context, Maimonides criticized the atomism of the later Ashʿarite Kalām, maintaining that its doctrine of constant creation of new atoms by God and rejection of natural causality was induced by preconceived religious opinions concerning creation (ibid., 177 ff., 194 ff.). Aaron b. Elijah defended the Kalām by arguing that atomism is necessitated by reason and is neutral per se with respect to the question of creation, as is evident from its advocacy by Epicurus, who viewed atoms as primordial. Maimonides' strictures were accentuated by later Aristotelians, e.g., *Levi b. Gershom (14th century; Milḥamot Adonai (1560), pt. 6, 1; ch. 3), who also gives a sophisticated explanation of the infinite divisibility of extension (ibid., pt. 6:1, ch. 11). Ḥasdai *Crescas (14th–15th century), a critic of the Aristotelian system, defended the atomistic theory (H.A. Wolfson, Crescas' Critique of Aristotle (1929), 121, 569–70).
C. Bailey, Greek Atomists and Epicurus (1928); I. Efros, Problem of Space in Jewish Mediaeval Philosophy (1917); idem, Ha-Pilosofiyyah ha-Yehudit bi-Ymei ha-Beinayim (1964), index; Guttmann, Philosophies, index; Husik, Philosophy, index; S. Pines, Beitraege zur islamischen Atomenlehre (1936); M. Schreiner, Der Kalām in der juedischen Literatur (1895).