The study of natural reality: Leucippus, Democritus, Epicurus and Plato

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The article below was originally written as an undergraduate assignment for the Greek Open University in 2007, during a period when the author’s academic skills were still developing. Although the quality of this article does not match that of later examples of the same author’s work, it is written in a thorough manner and contains useful information for students and other readers with non-specialised knowledge; therefore, it has been proudly included on this website.

The reader needs to be warned that the original assignment, on which this article was based, was written in Greek and was intended to be read by specialised academics. Despite the author’s best intentions to present his essay in the clearest way possible, some points and arguments might still be lost in translation. The author recommends that readers consult the web for additional information on any unfamiliar words or specialised vocabulary.

The author admits that the bibliography for this article is limited, as required for an undergraduate assignment of this level. The author did not include any additional bibliography during the translation of his work into English due to time and access limitations. It must also be noted that the original bibliography for this article was studied from translated copies in Greek; therefore, the page numbers suggested in the citations below match the page numbers of the translated copies and not the original volumes.

Introduction

This article discusses the views of Leucippus, Democritus, Epicurus and Plato in relation to natural reality. The paper is divided into two chapters. The first section begins with the views of the two Atomic philosophers, Leucippus and Democritus, and their interpretation of the material world based on their Atomic theory. Furthermore, it discusses the expansion of Atomic theory by Epicurus and the differences between his approach and those of the two Atomic philosophers. The second section discusses Plato’s eccentric approach, which explained natural reality in terms of the geometric properties of physical objects. Furthermore, the section compares Plato’s approach with the theories of the Atomic philosophers and Epicurus. A brief, conclusive section is presented at the end of this paper.

1. The basic principles of the Atomic and Epicurean theories

The Atomic philosophers of the 5th century BC developed a theory to explain natural reality, which was revolutionary at the time and can nowadays be seen as the precursor of atomic physics. The pioneer of the Atomic theory was the philosopher Leucippus, for whom there is extremely limited information. He lived during the 5th century BC, and his approach was probably influenced by Zeno (c. 495-430 BC) and his Eleatic School. The work of Leucippus was overshadowed by the work of his student Democritus (c. 460-370 BC), for whom there is adequate historical information. Even today, it is difficult to draw a clear boundary between the theories of Leucippus and Democritus; therefore, the so-called Atomic theory, discussed in the following sections, is understood as a combined theory of both philosophers. The Atomic theory was picked up quite later by the philosopher Epicurus (341-270 BC), who refined it and placed it in a different context. Epicurus recognised the contributions of Democritus, but was bold enough to doubt the contributions and even the existence of Leucippus (Christianidis 2000a, 60).

1.1 Natural reality by the Atomic philosophers

According to the Atomic philosophers, the material world consisted of two elements: a complete element, which was called ‘being’, and a void element, which was called ‘non-being’. Every material object noted in the natural reality was perceived as a composite body of the above two elements. The variations among different natural objects were explained as a relationship of density and dilution between their two main components. All natural objects were formed by the two primary elements and were common in relation to their primary matter; however, natural objects differed in shape, order, and position in space. The ‘being’ element, which formed the material substance of every object, was also called atom (atomon); it was explained as the smallest and undivided material particle found in nature. According to the Atomic theory, the atoms were so small that the human senses were unable to conceive them. Instead, human senses could only perceive the largest atomic compounds, which were visible due to their shapes, but not the atoms themselves. The atoms were described as compact and undivided due to the absence of void in their internal structure; they were understood as innumerable in relation to their count, shape and order; and finally, they were seen as scattered within the infinite void (Kirk et al. 2001, 414-5).

According to the Atomic philosophers, the natural world was not only innumerable but also infinite. Democritus argued that the natural world was formed through the centrifugation of atoms, a process that he described as ‘turbulence’ (Christianidis 2000a, 61). The atom vortex caused collisions, leading to the formation or dissolution of compound elements. This effect took the form of a swirling sphere, externally surrounded by a tight membrane of peripheral atoms. The external membrane attracted other individual atoms, which were then incorporated into the vortex. The cosmic vortex was initially liquid, then solidified, and finally became combustible. According to the general Atomic theory, the formulation of the natural world was the result of the constant motion of atoms within an infinite void. The collision and the unification of atoms were responsible for cosmogony. Furthermore, the motion of atoms was explained as inherent, continuous and eternal, and was not attributed to any external force. This suggestion contrasted with the theory by Anaxagoras (c. 500-428 BC), who had attributed the primordial motion of the universe to the Mind (Kirk et al. 2001, 416-8).

It is possible that the cause for the initial motion of the atoms was their own weight; however, this assumption can neither be attributed to Democritus nor to Leucippus, at least with certainty. The weight of the atoms was understood as the cause that carried them ‘downwards’ towards the centre of the vortex; however, other explanations suggest their motion was due to random collisions (Kirk et al. 2001, 419-20). All the textual sources on the Atomic theory agree that atoms move in a void and that moving atoms undergo constant collisions. Still, the question remains whether there was an external cause that set the atoms in motion for the first time. Ancient textual information on this issue is limited. It appears likely that the only type of movement considered by the Atomic philosophers was the bouncing of atoms, which was understood as a change of course due to collision with another atom. The Roman philosopher Aetius, who lived sometime between the 1st and 2nd centuries AD, mentioned that Democritus discussed an additional type of movement related to the atom’s ‘pulse’. Modern research has shown that this type of movement must be attributed to Epicurus, who used the term ‘pulse’ to describe the invisible oscillations of atoms in composite bodies (Kirk et al. 2001, 421-3).

The description of composite bodies by the Atomic philosophers included the four primal elements of nature, as discussed by earlier Pre-Socratic philosophers: earth, water, fire, and wind (Christianidis 200a, 61). Composite bodies are formed through the entanglement of atoms resulting from collisions. It appears likely that the collisions generated attractive or repulsive forces, leading to the formation of larger material particles. The internal bonds of composite bodies depended on the shape of the atoms that comprise their structure; for example, hook-shaped atoms bonded with other hook-shaped atoms. If this explanation is correct and the bonds among atoms were based solely on their shape, then the textual sources that mention the existence of attraction and repulsion forces in atom cohesion are likely to be false (Kirk et al. 2001, 423-4).

In general, the Atomic philosophers held that all composite bodies were tangible, visible objects of everyday reality. The human senses perceived such objects through the movement of atoms: the images were perceived through the ‘flow’ of atoms transmitted by the material objects to the human sense organs. The term ‘atom flows’ (aporhoes) is also noted in the Theory of the Senses by Empedocles of Akragas (494-434 BC). Democritus modified this theory and, instead of describing the images of objects as ‘flows’, he introduced the term ‘idols’. According to Democritus, an ‘idol’ represented the external image of a material object. This image travelled in the air in the form of a solid ‘imprint’ (entyposis). Once it reached the human sense organs, it generated a conception of the object in the mind. According to Democritus, every human sense functioned through physical contact (Kirk et al. 2001, 426-7).

1.2 Natural reality by Epicurus

The Atomic Theory of Democritus was taken up by Epicurus, who introduced new principles regarding the properties of atoms. In the Epicurean version, the basic principles of the Atomic Theory remained the same: the universe was eternal, infinite and unchangeable, consisting of particles and void. Furthermore, Epicurus admitted the existence of plain and composite material bodies in nature, of which the former coincided with the plain atoms of Democritus and Leucippus. As with the Atomic philosophers, the Epicurean atoms were undivided entities in constant motion within an infinite void. The first innovation by Epicurus was the idea that the motions of all atoms in the void were uniform in speed. Such motions were attributed to internal collisions, which produced bouncing atoms. In general, the basic properties of atoms by Epicurus were the same as those of the Atomic philosophers; however, Epicurus was the first to introduce the concept of atomic weight in the broader theory (Epicurus, First Letter to Herodotus, 39-44).

According to Epicurean cosmology, all worlds were considered infinite. Although some worlds were likely to resemble our own world on Earth, it was quite likely that other worlds had no resemblance to ours. As atoms were eternal and infinite, they could travel towards any of these other worlds (Epicurus, First Letter to Herodotus, 39-45).

The properties of the human senses, as discussed by Epicurus, resembled those discussed by the Atomic philosophers; however, he introduced a revolutionary idea for his time, which was quite close to modern optics and acoustics. According to Epicurus, the senses functioned through the exchange of particles, which were emitted and received simultaneously between objects and the sense organs. Such particles travelled in the air. Human voice, for example, was explained as the result of particle displacement in the air; the sounds were formed inside the human body (Epicurus probably meant the vocal cords) as a process of atomic collision; then, they were transmitted outside the human body through exhaling. Human smell functioned in a similar manner: the nose captured particles that escaped from an external object and were carried into the air (Epicurus, First Letter to Herodotus, 53-54).

Epicurus developed the original Atomic theory regarding the formation of composite bodies and placed less emphasis on the primary atoms. He argued that during the formation of a composite body, primary atoms retained in their original form. During the dissolution of the composite body, however, primary atoms retained their original form up until the moment they re-collided to produce a new composite body. According to this rationale, the essence of composite bodies remained unaltered through time; however, their properties were subject to continuous changes in shape, weight and size. The atoms could never be destroyed and could not be continuously divided in infinity; if this were likely to happen, then the atoms would have resulted in a state of non-being, which Epicurus rejects (Epicurus, First Letter to Herodotus, 55-56).

Another property attributed exclusively to Epicurus was the existence of minimal particles within the internal structure of atoms. Such particles were understood as infinitesimal segments that did not bond with one another because they were static. It must be noted that the Atomic theory suggested that atomic bonds were due to bouncing and collisions, which required some form of initial motion; therefore, static particles were not able to bond with each other (Epicurus, First Letter to Herodotus, 58-59).

In general, the evolution of the Atomic theory by Epicurus incorporated ideas from other pre-Socratic philosophers, particularly from Zeno of Elea (c. 495-430 BC), who suggested that the infinite division of atoms was impossible. What Aristotle described as Zeno’s paradox of Dichotomy in his fifth volume of Physics probably led Leucippus to describe his primary atom as finite. Following the same rationale, Epicurus discussed the presence of minimal particles in the internal structure of an atom, which could not be divided and, therefore, separated from the actual atom. The existence of minimal particles in the atomic structure described by Epicurus aligns with modern observations of neutrons, protons, and electrons; however, modern science has shown that these particles are in constant motion rather than static, as Epicurus originally suggested.

1.3 Different approaches to the Atomic theory

The Atomic theory by Leucippus and Democritus differed from all other theories of their time. Both philosophers introduced an analytical system that explained the material world and its visual realities in a revolutionary way, resembling physics as it is understood today. Furthermore, their approach was purely analytical and independent of religious and social speculations. The Atomic approach also differed from a contemporary cosmological system proposed by Empedocles of Akragas, who followed Plato in several respects. The main point of differentiation between the two theories was the existence of a non-being. In his approach, Democritus rejected the continuous partition (bisection) of natural objects, which led to the final rejection of non-being; this suggestion was later picked up by Epicurus (Vegetti 2001, 107-8).

In relation to cosmology, Democritus suggested that the composite structure of our world was not to be understood as an order imposed by some divine force. By contrast, he saw the formation of the world as a chaotic process, in which the forces of chance and necessity moved the atoms, which then formed the primordial cosmic vortex. Democritus saw that the Mind, which was the divine force in Anaxagoras’ system, had no participation in his cosmic vortex and was totally rejected. Furthermore, Democritus described the timeline of cosmic creation as a linear process, characterised by a beginning and an end. This approach contrasts with previous philosophical analyses, which saw a circular and perpetual repetition of natural phenomena (Vegetti 2001, 110).

Epicurus recognised Democritus's inability to explain the primordial force that set the atoms in motion for the first time. To explain this problem, he introduced the concept of ‘weight’, which allowed atoms to move ‘downwards’. This approach generated another problem: if this were the case, then all atoms would have moved ‘downwards’ in parallel lines at equal speeds without colliding. Therefore, the first collision, which set all atoms in motion, was attributed to a random deviation (parecclisis) during the atoms’ drop. A single deviation was enough to produce the first collision, which led to subsequent collisions and orbital changes, culminating in the final prevalence of complete chaos within the spinning vortex (Vegetti 2001, 112).

Epicurus also argued that composite bodies were the only objects that could be captured by human senses. Furthermore, human sensing was explained as a process of exchange of atoms on the external surfaces of composite bodies, or in other words, as a transmission and reception of particles between the objects and the human sense organs (Long 1987, 75-6). As opposed to Democritus, who suggested an infinite number of shapes and sizes for the atoms, Epicurus saw that such shapes and sizes were finite (Phili 1989-90, 383-4). On the other hand, both philosophers agreed that the worlds were multiple and infinite, some perhaps resembling and others differing from our own world on Earth (Theodoridis 2000, 807). Finally, they both agreed that the atoms in the internal structure of such worlds were by definition finite (Phili 1989-90, 386-7).

Epicurus expanded the Atomic theory and added an idea not previously reported by Leucippus and Democritus: he suggested that the internal structure of atoms was subdivided into minimal parts (minima). As noted above, Democritus described these minimal parts as finite and static; however, Epicurus suggested that differences in size and order among them defined the shape of the entire atom (Long 1987, 67).

Epicurus' Atomic theory was significantly different from Empedocles' of Akragas. According to Empedocles, the world consisted of four primary elements, which he named ‘sperms’. The four ‘sperms’ were fire, air, water and earth (soil), and comprised the original ingredients of cosmic creation. Epicurus rejected Empedocles’ approach, who saw the four ‘sperms’ as primary elements of cosmogony, and instead, he argued that these were composite bodies, which resulted from the unification of different atoms. In fact, Epicurus suggested that the characteristic properties of the four ‘sperms’ were unlikely to be attributed to anything other than composite atoms. Although Empedocles' theory was rejected by Epicurus, it was ultimately adopted by Plato, who incorporated it into his own eccentric approach to natural reality.

2. Plato’s Geometric Theory

In his dialogue Timaeus, Plato explained the mechanical properties of matter through his Geometric theory, which examined the structural properties of regular polyhedra. He admitted the intervention of a divine force in the universe; however, he introduced a second force, to which he attributed the mechanical behaviour of material bodies. This second force was named ‘necessity’ (anage) (Kalfas 1995, 52).

Plato accepted the existence of the four primary ‘sperms’ as introduced by Empedocles; however, he gave them Geometric properties to explain the mathematical rationale behind their interactions. Plato saw that the four ‘sperms’ of Empedocles were the smallest geometrical entities in nature; he explained that they were invisible to the human eye, as were the Atoms of Democritus and Leucippus (Kalfas 1995, 53).

In studying the natural world, Plato introduced a form of speculative physics, as opposed to the evidential physics followed nowadays. It is important to note that, in all his dialogues, Plato is hesitant about the validity of his speculative reasoning (Kalfas 1995, 54).

2.1 Natural reality in Timaeus

According to Plato, in the early stages of cosmogony, the universe was dominated by a vast, uncontrolled and chaotic material mass. This mass consisted of Empedocles’ four primary elements, which vibrated, moved, collided against each other, and were separated in a random and unclear manner. The state of this material mass resembled the primordial atomic vortex described by Leucippus and Democritus. At a specific moment in time, there was a divine intervention, during which the four ‘sperms’ were re-defined according to a mathematical rationale. These four elements were given three-dimensional forms and symmetrical surfaces derived from two original types of orthogonal triangles: the isosceles and the scalene. In their refined form, the four primary elements were structural composites of the above two types of triangles, yet not of any combinations between them (Plato, Timaeus, 54-55).

Plato suggested that the earth (ge, meaning the soil) had a cubical shape, formed by the unification of twenty-four orthogonal isosceles triangles. Water (ydor) was an icosahedron (a shape with twenty faces), formed by the unification of sixty orthogonal scalene triangles. Air (aer) was an octahedron (shape with eight faces), formed by the unification of forty-eight orthogonal scalene triangles. Finally, fire (pyr) had the shape of a regular tetrahedron, a pyramid formed by the union of twenty-four orthogonal scalene triangles. As all four primary elements descended from two original triangles, Plato concluded that their dissolution into their original components was possible. Furthermore, he suggested that after their dissolution, the original triangles could reform new geometrical structures and produce different elements through the rearrangement of equal numbers of the same triangle types. In other words, a ‘molecule’ of water could dissolve in two ‘molecules’ of air and one ‘molecule’ of fire. The sole exception was the earth ‘molecule’: as this descended from the original isosceles triangle, which did not participate in the production of the other three primary elements, earth ‘molecules’ could dissolve and reform structures of the same triangular nature; hence, earth could only revert into earth (Anapolitanos 1981, 49-51).

Additionally, Plato introduced a fifth geometrical structure, the creation of god rather than the result of necessity, which controlled the context of the four primary elements (Kalfas 1995, 253; Plato, Timaeus, 56). This was a regular dodecahedron (a shape with twelve faces), which not only represented the world but also surrounded and limited the four primary elements of cosmogony (Anapolitanos 1981, 51-2). According to Plato, the world was unique (Kalfas 1995, 253), and his view contrasted with the theory of the Atomic philosophers, who believed that the worlds were innumerable. The existence of a single world in Plato’s system might have been paralleled by the existence of a single god who could have created it. In that sense, the multiplicity of the worlds suggested by the Atomic philosophers could have been rejected by Plato to serve his plan of divine intervention.

It can be argued that Plato’s Geometric theory, with which he explained the properties of the four primary elements, was connected with his broader theory of the Ideas. According to the philosopher, the physical world did not constitute a cognitive discipline. Physical matter was only meant to be captured by the human senses, which, according to Plato, were responsible for the formulation of plain opinion and not the production of real knowledge. However, the matter consisted of composite bodies, all of which comprised four primary elements previously described as invisible. By noting the geometrical modelling of these primary elements and by developing a mathematical theory to describe their properties, Plato promoted the primordial elements of cosmogony as ideal prototypes (Ideas) (Anapolitanos 1981, 49).

The physical properties of the four primary elements were described according to the mechanical properties of the four previously mentioned geometric shapes. The stability of the Earth was attributed to its cubical shape and square faces, which allowed its molecules to stand firmly in place. Fire (pyr) was described as the most agile element due to its pyramidal shape, which only has four faces. Water, which was described as an icosahedron with twenty faces, was explained as the most cumbersome of all elements. Finally, the octahedron structure of air, the ‘molecule’ of which had eight faces, was explained as a semi-agile element that stood between fire and water (Kalfas 1995, 253-7; Plato, Timaeus, 55-58).

The general principle of Plato’s approach was the connection between the agility and the number of faces for each geometrical structure. As fire had the lowest number of faces, it was expected to be the pointiest and sharpest of all elements. In that sense, the physical powers of fire were connected to the sharp shape of its original ‘molecules’, which were able to penetrate and dissolve the other three primary elements. Furthermore, fire had the ability to assimilate all three other elements by ‘trapping’ them inside its pyramidal structure. The process of assimilation and dissolution of the four elements was explained as a war, during which the four primary elements alternated between ‘winners’ and ‘losers’ (Kalfas 1995, 253-7; Plato, Timaeus, 55-58).

2.2 The differences between the Geometric and the Atomic theory

The interpretation of natural reality according to Plato’s Geometric theory followed earlier philosophical ideas discussed by Pythagoras and Empedocles, as well as mathematical theorems discussed by Theaetetus and Euclid. Furthermore, Plato had studied the Atomic theory, from which he borrowed the idea of a minimal, invisible material unit responsible for cosmogony. Plato processed his minimal material units, which were four according to Empedocles, by incorporating the arithmetic and geometric theories of the Pythagoreans. He then concluded that all natural elements participated in the ‘numbers’, meaning his mathematical/geometrical sequence, instead of just imitating it (Phili 2002, 71-2).

Plato opposed the eternal existence and invariability of the atoms, as suggested by the Atomic philosophers. At the same time, he rejected the innumerable count of the atoms and their infinite shapes and sizes; instead, he limited them to four primary elements, which coincided with the four primary ‘sperms’ of Empedocles. He then translated the structure of these four elements into a combination of two primary triangle types. Plato’s four natural elements were never meant to be material objects; they were promoted to spiritual Ideas, which were supposed to be comprehended through the knowledge of geometry and mathematics. The four elements were described as active organisms that transformed into other elements by exchanging triangular faces on their exterior surfaces. Furthermore, Plato’s elements were independent units and were not meant to interact with the void, which, on the other hand, was described as a core universal feature of the Atomic theory. Although the Atomic philosophers rejected the infinite division of the atoms, this specific problem played no part in Plato’s approach. Plato’s primary triangles were not only able to split and merge, but they were also able to assimilate triangles from other material elements (Phili 2002, 72-3).

The basic difference between Plato’s Geometric theory and the theories of Democritus and Empedocles was the amalgamation of mechanical and divine features for the characterisation of material properties. The theories of the Atomic philosophers and Empedocles did not allow for any justification of divine intervention; in Plato, however, god was not only interwoven with the four primary ‘sperms’, but also connected with the fifth element, which surrounded all the rest (Phili 2002, 73-5).

In his analysis, Plato focused on the Epicurean approach, which rejected the existence of infinite matter and, by extension, infinite worlds. The Platonic cosmos was one and unique, just as the god who had arranged the world in an orderly manner (taxis) was one and unique. The notion of taxis (order) in Plato related to the strict definition of matter in geometrical forms with distinct properties (Phili 2002, 73-5). This specific cosmological view contrasts with Empedocles’ approach, which placed matter within an unpredictable system of cosmic chaos.

Finally, Plato’s greatest innovation was the reduction of every single material element to two original triangles, an orthogonal isosceles and an orthogonal scalene. Although Plato’s rationale was based on geometry, it is relatively unclear how he introduced a third triangle into his theory, which he considered perfect. This was the equilateral triangle, a non-orthogonal isosceles triangle with three equal angles and three equal faces. In Plato’s system, the equilateral triangle was used in the formation of the pyramid (fire), the octahedron (air) and the icosahedron (water) (Phili 2002, 75-6). If an equilateral triangle were divided in half, it would produce two equal, orthogonal, scalene triangles. With this in mind, Plato was likely to have considered the equilateral triangle as a unique element in the composition of matter (Phili 2002, 76); however, one cannot miss that his whole scheme of geometric shapes depended solely on a single triangle, namely the orthogonal scalene. This is also the type of triangle which was examined thoroughly by Pythagoras and his school.

If this is so, then one might wonder what the use of the orthogonal isosceles triangle is in Plato’s system. Phili (2002, 75) suggests that this triangle was reserved for the formation of the cube, which represented the earth. In fact, the faces of the cube were formed by the unification of two orthogonal isosceles triangles, which produced a square. On a different approach, however, a square could have also originated from the unification of four equilateral triangles, which were Plato’s perfect geometrical shapes. And if this is so, these four equilateral triangles would have consisted of eight orthogonal scalene triangles. Even Plato’s fifth element, ether, which was described as a dodecahedron with pentagonal faces (Phili 2002, 77), could have been formed by the unification of 60 equilateral triangles, which consisted of 120 orthogonal scalene triangles. The above thoughts lead to an unsolved puzzle: although Plato’s primary triangle was the equilateral, at least as this was presented in Timaeus, why did his system not describe all triangles as composites of Pythagoras’ favourite orthogonal scalene?

Finally, Phili (2002) suggests that the monomer nature of the equilateral triangle, which defined any form of matter in Plato’s scheme, matched the monomer nature of the Atom as this was described by Democritus and Leucippus. The only difference was that Plato’s prefect triangle was not surrounded by void. Furthermore, Plato’s unique and perfect triangle was likely to have incorporated the essence of one unique and perfect god. The divine properties of triangles had been previously suggested by the Pythagoreans and were attributed to the divine nature of number three: as triangles consist of three angles and three faces, they carry divine powers (Phili 2002, 76-8). A personal question for Plato’s scheme, however, would still remain: why not the orthogonal scalene?

Conclusions

The Atomic theory, which was followed by Leucippus, Democritus and Empedocles, regarded natural reality as a chaotic system, in which uncontrolled atoms moved randomly and produced innumerable collisions. The kinetic forces of the atoms were attributed to a combination of chance and necessity. By contrast, Plato introduced a scheme that explained natural reality in terms of mathematics; therefore, he developed a theory in which matter was explained in terms of the properties of specific geometrical shapes. At the same time, Plato introduced god into his Geometric rationale; therefore, he allowed his system to be regulated by a divine mind, ensuring that cosmic order was not disturbed. In other words, in Plato’s scheme, order prevailed against chaos.

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Ancient Sources

Epicurus, First Letter to Herodotus, in Cactus (1994).
Plato, Timaeus, edited and translated by V. Kalfas (1995).