Most systems of atomism depict the action between atoms in terms of collision—i.e., as actual contact. In Newton’s theory of gravitation, however, action between bodies is supposed to be action at a distance—which means that the body in question acts everywhere in space. As its action is the expression of its existence, it is difficult to confine its existence to the limited space that it is supposed to occupy according to its precise shape and size. There is, therefore, no reason for a sharp distinction between occupied and empty space. Consequently, the mind finds it natural to consider the atoms not as extended particles but as point-centres of force. This conception was worked out by the Dalmatian scientist R.G. Boscovich (1711–87), who attempted to account for all known physical effects in terms of action at a distance between point-particles, dynamic centres of force.

Atoms as psychophysical monads

The idea of applying the atomistic conceptions not only to material but also to psychical phenomena is as old as atomism itself. Democritus spoke of the atoms of the soul. According to the principles of his doctrine, these atoms can differ only quantitatively from those of the body: they are smoother, rounder, and finer. This makes it easy for them to move into all parts of the body. Basically, however, the atoms of the soul are no less material than other atoms.

In Leibniz’s monadology the situation is quite different. Leibniz did not first conceive of material atoms and then only later interpret the soul in terms of these atoms; from the beginning, he conceived of his “atoms,” the monads, in terms of an analogy with the soul. A monad is much more a spiritual than a material substance. Monads have no extension; they are centres of action but not, first of all, in the physical sense. Each of the monads is gifted with some degree of perception; each mirrors the universe in its own way. Monads differ from each other, however, in the degree of perception of which they are capable.

Number of atoms

As has already been mentioned, Democritus introduced the hypothesis that the atoms are infinite in number. Although one may question whether the term infinite has to be taken in its strict sense, there is no doubt that by using this term Democritus wanted not merely to express the triviality that, on account of their smallness, there has to be an enormous quantity of atoms. Democritus also had a strong rational argument for postulating a strictly infinite quantity of atoms: only thus could he exclude the existence of atoms that specifically differ from each other.

When in modern science the problem of the number of atoms arises, the situation is quite different from that of the Greek atomists. There is now much more detailed information about the properties of the atoms and of the elementary particles, and there is also in astrophysical cosmology some information about the universe as a whole. Consequently, the attempt to calculate the total number of atoms that exist is not entirely impossible, although it remains a highly speculative matter. In a time (around 1930) when all chemical atoms were supposed to be composed of electrons and protons, the pioneering joint-relativity-quantum astrophysicist A.S. Eddington calculated the number of these elementary particles to be 2 × 136 × 2²⁵⁶, or approximately 10⁷⁹, arguing that, since matter curves space, this is just the number of particles required barely to close the universe up into a hypersphere and to fill up all possible existence states.

The existence of the void

To Democritus the existence of the void was a necessary element in atomistic theory. Without the void the atoms could not be separated from each other and could not move. In the 17th century Descartes rejected the existence of the void, whereas Newton’s conception of action at a distance was in perfect harmony with the acceptance of the void and the drawing of a sharp distinction between occupied and nonoccupied space. The success of the Newtonian law of gravitation was one of the reasons that atomic theories came to prevail in the 18th century. Even with respect to the phenomena of light, the corpuscular and hence atomic theory of Newton, which held that light is made of tiny particles, was adopted almost universally, in spite of Huygens’s brilliant development of the wave hypothesis.

When, at the beginning of the 19th century, the corpuscular theory of light in its turn was abandoned in favour of the wave theory, the case for the existence of the void had to be reopened, for the proponents of the wave theory did not think in terms of action at a distance; the propagation of waves seemed to presuppose instead a medium not only with geometrical properties but with physical ones as well. At first the physical properties of the medium, the ether, were described in the language of mechanics; later they were described in that of the electromagnetic field theory of J.C. Maxwell. Yet, to a certain extent, the old dichotomy between occupied and nonoccupied space continued to exist. According to the ether theory, the atoms moved without difficulty in the ether, whereas the ether pervaded all physical bodies.

In contemporary science this dichotomy has lost its sharpness, owing to the fact that the distinction between material phenomena, which were supposed to be discontinuous, and the phenomena of light, which were supposed to be continuous, appears to be only a relative one. In conclusion, it can be claimed that, although modern theories still speak of space and even of “empty” space, this “emptiness” is not absolute: space has come to be regarded as the seat of the electromagnetic field, and it certainly is not the void in the sense in which the term was used by Democritus.

Atoms in external aggregation versus in internal relationship

In most forms of atomism it is a matter of principle that any combination of atoms into a greater unity can only be an aggregate of these atoms. The atoms remain intrinsically unchanged and retain their identity. The classical atomic theory of chemistry was based upon the same principle: the union of the atoms into the molecules of a compound was conceived as a simple juxtaposition. Each chemical formula (e.g., H₂O, H₂SO₄, NaCl, etc.) reflects this principle through the tacit implication that each atom is still an H, O, or S, etc., even when in combination to form a molecule.

Chemistry had twofold reasons for adopting this principle. One reason was observational, the other philosophical. The fact that some of the properties of a chemical compound could, by simple juxtaposition, be derived from those of the elements (the molecular weight, for example, equals the simple sum of the respective atomic weights) was a strong factual argument in favour of the principle. Many properties of the components, however, could not be determined in this way. In fact, most chemical properties of compounds differed considerably from those of the composing elements. Consequently, the principle of juxtaposition could not be based on factual data alone. It was in need of a more general support. This support was offered by the philosophical idea that inspired all atomism—namely, that if complex phenomena cannot be explained in terms of aggregates of more elementary factors, they cannot be explained at all.

For the evaluation of this idea, the development of the scientific atomic theory is highly interesting, especially with respect to the interpretation of the concept of an aggregate. Is the only interpretation of this concept that of an assemblage in which the components preserve their individuality—like, for instance, a heap of stones? Modern atomic theory offers an answer to this question. This theory still adheres to the basic principle that a complex structure has to be explained in terms of aggregates of more elementary factors, but it interprets the term aggregate in such a way that it is not limited to a mere juxtaposition of the components. In modern theories atomic and molecular structures are characterized as associations of many interacting entities that lose their own identity. The resulting aggregate originates from the converging contributions of all of its components. Yet, it forms a new entity, which in its turn controls the behaviour of its components. Instead of mere juxtaposition of components, there is an internal relationship between them. Or, expressed in another way: in order to know the properties of the components, one has to study not only the isolated components but also the structures into which they enter. To a certain extent modern atomic theory has bridged the gap between atomistic and holistic thought.