Like Anaxagoras and Empedocles, the atomists wanted to answer the basic post- Eleatic question: if change cannot occur in the real, then how does it occur in the observable world? Also like the previous two philosophers, they answered this question by postulating the existence of certain elements of the cosmos that are real in the Parmenidean sense and by claiming further that through analyzing the arrangement and rearrangement of these basic elements, we can arrive at an account of the visible world without having to admit that there is any change on the level of the real. But whereas the two previous pluralists rejected the Eleatic notion that what exists is one in kind, the atomists retained this contraint. The atomists posit just one kind of real thing — tiny, indivisible atoms, swimming around in a void. This account of reality is by far most sophisticated of all those ventured by the Presocratics, and it even comes alarmingly close to anticipating the modern scientific view of ultimate reality.
The only two known Presocratic atomists were Leucippus and his student Democritus. Unfortunately, we know very little about Leucippus, the founder of atomic theory. Even his place of birth is in dispute, given variously as Miletus, Abdera, and Elea. What we do know with moderate certainty is that Leucippus studied with members of the school of Elea at some point in his life. He was clearly influenced by Zeno as is evidenced by his strong interest in the problems and paradoxes of space. The only other fact we know about this great thinker is that he wrote two books, no parts of which survive. The first of these was called On Mind and the second The Great World System.
Democritus was the student of Leucippus, and he is the figure through whom atomism has been transmitted to later generations. It is not known how much of his theory is simply a repetition of Leucippus's teaching and how much of it is original to him, but it was he who brought atomism to public attention and who made it a matter of philosophical controversy. He born around 460 B.C. in Abdera, Thrace in Northern Greece, and he traveled throughout the ancient world. We are aware of the titles of at least seventy books that he supposedly authored, and these works cover a wide variety of subjects. He wrote in nearly all philosophical areas, including mathematics, natural philosophy, literature, and grammar, and also wrote more popular works, such as accounts of his travels. In addition, he seems to have written on farming, medicine, military science, and even painting. Interestingly, not only did he have something of worth to say on all of these topics, but he even applied atomic theory to most of them. He apparently believed that atomism could be usefully extended to all aspects of the world, including even ethics and politics.
Like Anaxagoras and Empedocles, The Atomists claimed that there was a level of reality that satisfied the Eleatic demands. This level of reality was populated by atoms and the void. Atoms are, literally, indivisible particles, which are so small that they can be split no further. The atoms qualify as Parmenidean Reals in two ways. First, like the four elements and the homeomeric substances, atoms cannot be generated, destroyed, or qualitatively changed. In addition, they have an added level of compliance with the Parmenidean demands: the atoms themselves are one in kind. All atoms are made out of the same material. Reality, then, really is one and continuous in at least a qualitative sense.
Though the atoms are materially homogenous (as well as being uniformly impenetrable and indivisible), they do have some variable properties. They differ from one another in shape, arrangement, position, size, and motion. It is by the arrangement and rearrangement of atoms of different shapes, sizes, and motions that the observable world comes into being.
The boldest aspect of the atomist theory, is that, in addition to positing the atoms as Parmenidean Reals, it also posits a void, which is identified explicitly with non-being. There is an extremely good reason for this move: the Eleatics argued that (1) being cannot admit of a vacuum (i.e. empty space) and (2) without a vacuum there can be no movement. Leucippus was impressed by both of these arguments and was persuaded of their truth. However, he was equally certain of the truth of the claim that movement does in fact exist, since he saw movement all around him. Reasoning with these three premises (i.e. the two Eleatic conclusions, and his own observation that motion must exist) he concluded that there must actually be a vacuum and that this vacuum must be identified with not-being. Though the vacuum is non-being, it is nonetheless real. The atoms exist in this vacuum or void and move about in it, giving rise to the observable world.
The line "is this a dagger which I see before me" is from Macbeth, not Hamlet. C'mon, Sparknotes! I expect better from you.
Is it possible that Parmenides was referring to the object orientation of our thoughts with his famous saying that "what is is and what is not is not"? Consider that when separating an object from its background, we can conceive of the object as something but can not conceive the background as a thing. The object is "what is", while the background is "what is not". This interpretation fits well with several ideas of the time, for example that opposites had a special position in our thought, that the universe is one (Zeno's paradoxes