With the development of a scientific atomic theory, the general philosophical problems gradually disappeared into the background. All attention is focused on the explanation of concrete phenomena. The properties of the atoms are determined in direct relationship with the phenomena to be explained. For this reason the chemical atomic theory of the 19th century supposed that each identified chemical element has its own specific atoms and that each chemical compound has its own molecules (fixed combinations of atoms). What particles act as unchanged and undivided units depends upon what kind of process is involved. Some phenomena, such as evaporation, are explained by a process in which the molecules remain unchanged and identical. In chemical reactions, however, the molecules lose their identity. Their structures are broken up, and the composing atoms, while retaining their own identity, are rearranged into new molecules. With nuclear reactions a new level is reached, on which the atoms themselves are no longer considered as indivisible: more elementary particles than the atoms appear in the explanations of nuclear reactions.

Atoms as lumpish corpuscles

As corpuscles (minute particles), atoms can either be endowed with intrinsic qualities or be inherently qualityless.

The most striking basic differences in the material world, which lead to a first classification of substances in nature, are those between solids, liquids, gases, and fire. These differences are an observed datum that must be accounted for by every scientific theory of nature. It was, therefore, only natural that one of the first attempts to explain the phenomena of nature was based upon these differences and proclaimed that there are four qualitatively different primitive constituents of everything—namely, the four elements: earth, water, air, and fire (Empedocles, 5th century bce). This theory dominated physics and chemistry until the 17th century.

Although the theory of the four elements is not necessarily an atomistic theory, it obviously lends itself to interpretation in atomistic terms—namely, when the elements are conceived as smallest parts that are immutable. In this case, all observable changes are reduced to the separation and commingling of the primitive elementary substances. Thus, Parmenides’ thesis that being is immutable is maintained, whereas the absolute unity of being is abandoned. Yet, the fact that the infinite variety of forms and changes in nature is reduced to just one type of process between only four elementary kinds of atoms shows its affinity with the thesis of the unity of all being.

Notwithstanding the great disparity between the theory of the four elements and modern chemistry, it is clear that modern chemistry falls into the same class of atomic theories as that of Empedocles. There are differences, of course, but these will be deferred for later discussion.

More removed from the original thesis of Parmenides was the theory of his contemporary Anaxagoras of Clazomenae, which assumed as many qualitatively different “atoms” as there are different qualitied substances in nature. Inasmuch as these atoms, which Anaxagoras called “seeds,” are eternal and incorruptible, this theory still contains an idea borrowed from Parmenides. A special feature of Anaxagoras’s theory is that every substance contains all possible kinds of seeds and is named after the kind of seed that predominates in it. Since the substance also contains other kinds of seeds, it can change into something else by the separation of its seeds.

Another interesting form of atomism with inherently qualitied atoms, also based on the doctrine of the four elements, was proposed by Plato. On mathematical grounds he determined the exact forms that the smallest parts of the elements must have. Fire has the form of a tetrahedron, air of an octahedron, water of an icosahedron, and earth of a cube. Inasmuch as he characterized the atoms of the four elements by different mathematical forms, Plato’s conception can be considered as a transition between the qualitative and quantitative types of atomism.

The most significant system of atomism in ancient philosophy was that of Democritus (5th century bce). Democritus agreed with Parmenides on the impossibility of qualitative change but did not agree with him on that of quantitative change. This type of change, he maintained, is subject to mathematical reasoning and therefore possible. By the same token, Democritus also denied the qualitative multiplicity of visible forms but accepted a multiplicity based on purely quantitative differences. In order to reduce the observable qualitative differences to quantitative differences, Democritus postulated the existence of invisible atoms, characterized only by quantitative properties: size, shape, and motion. Observed qualitative changes are based upon changes in the combination of the atoms, which themselves remain intrinsically unchanged. Thus Democritus arrived at a position that was defined above as atomism in the strict sense. In order to make the motion of atoms possible, this atomism had to accept the existence of the void (empty space) as a real entity in which the atoms can move and rearrange themselves. By accepting the void and by admitting a plurality of beings, even an infinite number of them, Democritus seemed to abandon—even more than Empedocles did—the unity of being. Nevertheless, there are sound reasons to maintain that, in spite of this doctrine of the void, Democritus’s theory remained close to Parmenides’ thesis of the unity of being, for Democritus’s atoms were conceived in such a way that almost no differences can be assigned to them. First of all, there are no qualitative differences; the atoms differ only in shape and size. Second, the latter difference is characterized by continuity; there are no privileged shapes and no privileged sizes. All shapes and sizes exist, but they could be placed in a row in such a manner that there would be no observable difference between successive shapes and sizes. Thus, not even the differences in shape and size seem to offer any ground explaining why atoms should be different. By accepting an infinite number of atoms, Democritus retained as much as possible the principle that being is one. With respect to the acceptance of the void, it must be stressed that the void in the eyes of Democritus is more nonbeing than being. Thus, even this acceptance does not seriously contradict the unity of being.

Atoms as sheer extension

Democritus declared quantitative differences to be intelligible because they are subject to mathematical reasoning. Precisely this relationship between quantitative differences and mathematics made it impossible for Descartes (17th century) to think along the atomistic lines of Democritus. If the only thing that is clearly understandable in matter is mathematical proportions, then matter and spatial extension are the same—a conclusion that Descartes did not hesitate to draw. Consequently, he rejected not only the idea of indivisible atoms but also that of the void. In his eyes the concept “void” is a contradiction in terms. Where there is space, there is by definition extension and, therefore, matter.

Yet, however strange it may seem in view of his identification of matter with extension, Descartes offered nonetheless a fully developed theory of smallest particles. To the questions that arise immediately as to how these particles are separated and distinct from each other, Descartes answered that a body or a piece of matter is all of that which moves together. In the beginning of the world all matter was divided into particles of equal size. These particles were in constant motion and filled all of space. As, however, there was no empty space for moving particles to move into, they could only move by taking the places vacated by other particles that, however, were themselves in motion. Thus the motion of a single particle involved the motion of an entire closed chain of particles, called a vortex. As a result of the original motion, some particles were gradually ground into a spherical form, and the resulting intermediary space became filled with the surplus splinters or “grindings.” Ultimately, three main types of particles were formed: (1) the splinter materials, which form the finest matter and possess the greatest velocity; (2) the spherical particles, which are less fine and have a smaller velocity; and (3) the biggest particles, which originated from those original particles that were not subject to grinding and became united into larger parts.

Thus Descartes could construct an atomic theory without atoms in the classical sense. Although this theory as such has not been of great value for the scientific atomic theory of modern times, its general tendency has not been without importance. However arbitrarily and speculatively Descartes may have proceeded in the derivation of the different kinds of corpuscles, he finally arrived at corpuscles characterized by differences in mass, velocity, amount of motion, etc.—properties that can be treated mathematically.