Atomism is the theory that all the objects in the universe are composed of very small particles that were not created and that will have no end. The word atomism derives from the ancient Greek word atomos which meant "that which cannot be cut into smaller pieces." 
If atomism is the idea that anything might ultimately consist of an aggregation of small units that cannot be sub-divided further, then "atomism" might be applied to even the aggregations of society or logic.
Accordingly, the term social atomism is used to denote the point-of-view that individuals rather than social institutions and values are the proper subject of analysis since all properties of institutions and values merely accumulate from the strivings of individuals. 
Similarly, Bertrand Russell developed logical atomism in an attempt to identify the atoms of thought, the pieces of thought that cannot be divided into smaller pieces of thought.
The atoms that chemists and physicists of the early 1800s thought were indivisible turned out to be composed of even smaller entities--electrons, neutrons, and protons. Similarly, experiments showed that protons and neutrons are made of even smaller quarks. So, the trend of empirical evidence for ever-smaller particles inside "atoms" suggests the question: "Is matter infinitely divisible?" Experiment likely can never answer that question; who can say that the experimentalists and the theorists will not contrive some even more powerful means to smash what some previously had thought to be "indivisible" to find that it is composed of even smaller pieces of matter and energy?
How about space and time? In many mathematical descriptions, space and time are infinitely divisible. That is, for example, many classical descriptions of space assume that between any two points of space, there will be another point of space. But some current theorists suggest that even space and time are composed of measurable quanta that "cannot be cut into smaller pieces" to observe.  
The puzzle of similarities and differences
The various arguments of atomism trace the various attempts to understand sufficiently why some things of the world, such as different fires, are so similar in appearance and yet other things, such as dark nights, are so different from their opposites, as fires compared to dark nights.
- Consider how very much one fire is like another fire.
- But notice how opposite in nature all the dark nights are to fire. 
As the solution for that puzzle, Parmenides stated that, despite the appearances of differences, all things are composed of the same solitary, never-created, never-ending, eternal Being--the One--the "it" that is "without beginning and without end." 
This is not an atomism theory, because Parmenides did not speculate on eternal indivisible units that composed the "eternal Being," but Parmenides provided two important features that atomism theories later would employ: 1) asserting that all objects of the physical world consisted of some never-created and never-ending hidden substance and 2) explaining the differences among objects to be the result of different configurations of the never-ending substance hidden inside them.
Are there different elements?
Empedocles about 450 BC looked at the puzzle of similarities and differences and conjectured in a poem also titled "On Nature" that things of similarity, like fires, are composed of the same proportions of the elements fire, air, earth, and water. On the other hand, opposite substances, like fire and dark night, have inverse or otherwise contrasting proportions of the four elements.
And the elemental substances of fire, air, earth, and water are never-created and never-ending. Accordingly, changes in the physical world, such as growth and decay, consist merely of shifts in the combinations of the elements fire, air, earth, and water. 
But Empedocles still had not discovered atomism. For even though Empedocles postulated that there were the four different elements composing the hidden substance of physical objects, he did not discuss the internal structure of these different elements. The four elements fire, air, earth, and water were fluids, not discrete particles.
Is there an ultimate, indivisible unit of matter?
At least as early as 400 BC, Democritus was teaching and writing that the hidden substance in all physical objects consists of different arrangements of 1) atoms and 2) void. Both atoms and the void were never created, and they will be never ending. Democritus became famous for this idea, but he followed closely what his teacher Leucippus taught, and it is not known where Leucippus got the ideas he taught Democritus.
The void is infinite and provides the space in which the atoms can pack or scatter differently. The different possible packings and scatterings within the void make up the shifting outlines and bulk of the objects that we feel, see, eat, hear, smell, and taste. We sense hot and cold, but hot and cold have not real existence. For hot and cold are simply sensations produced in us by the different packings and scatterings of the atoms in the void that compose the object that we sense as being "hot" or "cold."
Democritus also wrote his exposť of nature titled--"On Nature." But very few fragments of Democritus's writings have survived. Nevertheless, there are many derivative works of Democritus's students that scholars say faithfully represent Democritus's writings. Leucretius's On the Nature of Things provides an example. One scholar attributes the large loss of Democritus's writings to the burning of the library at Alexandria in 48 B.C. when Julius Caesar allegedly burned his own ships to prevent his Egyptian enemy from taking them, the flames then leaping from the burning ships to the library in which were Democritus's writings together with many other worthy books of the ancient world. 
Nevertheless, the derivative works by Democritus's students and progeny work out several segments of a theory on how the universe began its current stage. The atoms and the void are eternal. And after collisions that shatter large objects into smaller objects, the resulting dust, still composed of the same eternal atoms as the prior configurations of the universe, falls into a whirling motion that draws the dust into larger objects again to begin another cycle.
Democritus found fault with the philosophers around him who pandered to the unwitting hungers and passions of people that cause them to yearn for an "intelligent designer". Democritus asserted that some things were possible in the universe and somethings were not possible. And he asserted that it was not possible that there could have been an intelligent designer. What would have made the intelligent designer?
The workings of the universe are entirely mechanical, driven by what he called the "vibrations," the velocities and impacts of the constituent atoms*. He explained that things happen because of what he called "necessity," the mechanistic collisions and aggregations of the atoms according to their own "nature." He explained the common person's belief in gods to be the result of animal passions, faulty understanding, and ignorance of how the correlated motions of the atoms caused powerful displays of nature such as thunder, lightning, and earthquakes.
Consequences for guiding one's life
Epicurus studied atomism with Nausiphanes who had been a student of Democritus. But Epicurus was less interested in the part of Democritus's theories that explained wild nature, as in worlds, universes, and earthquakes. Epicurus was more interested in applying Democritus's theories to assist people in taking responsibility for themselves and for their own happiness--since in reality there is no god around that can help them.
By 310 BC, Epicurus argued that, if a person tangled responsibly with the reality that there is no god to help them, there would be three effects on the person's life. First, many obligations of the law, state, and politics are no longer necessary because often the obligations serve no purpose other than to indulge animal passions that are destructive and counter-productive in making people miserable--for no good reason. Second, rather than accepting the law, state, and politics of their parents, wise people should band together and create a more functional society by a social contract of agreement among themselves on what would make things work. Third, since neither god nor any other high moral value existed without people willing it into existence, there was no good reason to work for justice in the society--unless that work gave the activist pleasure or some other real payoff. 
However, Epicurus asked people to notice that it was much more pleasurable to live in a community in which there was harmony, in which there was friendship, in which there was freedom, in which men and women were treated equally, in which people felt that there was fairness, and in which people felt that they had something to look forward to when they thought about the next day, the next month, the next year.
And in attempting to describe the principles that actually worked for people to give them pleasure, value, and hope, Epicurus and his community of Epicureans developed a series of aphorisms for people to revise according to what worked, to discuss when sorting through problems, and to memorize for testing and using in helping each other--because they were alone in the universe even if their animal passions tempted them to wish for gods that could help them.
Epicurus summarized the principles that he and his community discovered in a book of Principal Doctrines. Here are a few samples. 
- Death is nothing to us; for that which has been dissolved into its elements experiences no sensations, and that which has no sensation is nothing to us.
- Some men want fame and status, thinking that they would thus make themselves secure against other men. If the life of such men really were secure, they have attained a natural good; if, however, it is insecure, they have not attained the end which by nature's own prompting they originally sought.
- No pleasure is a bad thing in itself, but the things which produce certain pleasures entail disturbances many times greater than the pleasures themselves.
- It is impossible for someone to dispel his fears about the most important matters if he doesn't know the nature of the universe but still gives some credence to myths. So without the study of nature there is no enjoyment of pure pleasure.
- Injustice is not an evil in itself, but only in consequence of the fear which is associated with the apprehension of being discovered by those appointed to punish such actions.
- Where without any change in circumstances the things held to be just by law are seen not to correspond with the concept of justice in actual practice, such laws are not really just; but wherever the laws have ceased to be advantageous because of a change in circumstances, in that case the laws were for that time just when they were advantageous for the mutual dealings of the citizens, and subsequently ceased to be just when they were no longer advantageous.
For Epicurus, people were driven by passions and hungers they inherited from the past but could not understand. One of the inexplicable passions and hungers was the longing for a creator god to watch over them; but the inherited longing for a creator god to make sense out of the chaos was delusional. Accordingly, in this world that lacks a god that will help, only people banding together in a wise social contract to remove the message of the creator god could make any difference at all. Three hundred years later, Lucretius in his epic poem On the Nature of Things would depict Epicurus as the hero who crushed the monster Religion through educating the people in what was possible in the atoms and what was not possible in the atoms.
However, Epicurus expressed non-aggression to Religion or any other face of violence in the following statement. "The man who best knows how to meet external threats makes into one family all the creatures he can; and those he can not, he at any rate does not treat as aliens; and where he finds even this impossible, he avoids all dealings, and, so far as is advantageous, excludes them from his life." 
Plato objected to the mechanistic purposelessness of the atomism of Democritus. Atoms just crashing into atoms could never produce the beauty and form of the world. In the Timaeus, Plato wrote the following question and answer sometime around 350 BC. 
- Is the world created or uncreated? -- that is the first question.
- Created, I reply, being visible and tangible and having a body, and therefore sensible; and if sensible, then created; and if created, made by a cause, and the cause is the ineffable father of all things, who had before him an eternal archetype.
according to Plato
For Plato, even the Creator used an "eternal archetype" of the Good to form the earth. As part of that creation, the Creator made atoms of fire, air, earth, and water. But the atoms imitated the ideals of the Good and followed the laws of the Creator. Plato even speculated on the specific forms of the atoms according to the table to the right.
That the Creator controlled the atoms that He had created profoundly affected the proper form of human government and society. In the Republic, Plato asserted the philosopher-king should serve as captain and true pilot of the ship of state. The philosopher-king should follow the ideal Good associated with the Creator, should exact obedience from subjects, and should keep people from sinking into the depravity that "democracy" and "liberty" would promote. Plato describes the mechanism of the inherited passions and hungers that the philosopher-king would have to control in the people this way. 
- Then you must further imagine the same thing to happen to the son which has already happened to the father:--he is drawn into a perfectly lawless life, which by his seducers is termed perfect liberty.
Plato taught a point-of-view that attracted kings and tyrants of his day. Plato himself tutored Dionysus II until such time as the young Dionysus exerted the power he had to expel his competitors from the kingdom, including Plato, his teacher.
Sometime before 330 BC Aristotle asserted that the atoms of fire, air, earth, and water actually change when making new combinations to form the objects that we see. But changes in nature exhibit direction and not chaos. To treat this issue of direction in change, Aristotle asserted the principles of "in potency" and "becoming" to deal with what he saw as the primary flaw in Democritus's atomism--Democritus's insufficient explanation for the direction of change among the atoms: 
- when air is produced from water, the same matter has become something different, not by acquiring an addition to it, but has become actually what it was potentially, and, again, water is produced from air in the same way.
Accordingly, Aristotle concluded that every material object in the universe has two essential components: the 1) potential matter and the 2) actual matter. The potential matter consists of the atoms of fire, air, earth, and water that can change from one potential condition to another and can be observed directly. In contrast, the actual matter, such as the statue into which the bronze is cast, can appear or disappear depending on what a sculptor does with the bronze.  Actual matter can be contained in time of the 1) past, time of the 2) future, or 3) both. 
- Of things which do not exist but are contained by time some were, e.g. Homer once was, some will be, e.g. a future event; this depends on the direction in which time contains them; if on both, they have both modes of existence.
Though Aristotle realized that atoms cannot be eternal because they change, he still contended that something had to be eternal. And he concluded that motion must be eternal, but there is a prime mover behind it all. 
- Our present position, then, is this: We have argued that there always was motion and always will be motion throughout all time, and we have explained what is the first principle of this eternal motion: we have explained further which is the primary motion and which is the only motion that can be eternal: and we have pronounced the [prime mover] to be unmoved.
- First of all they should provide against their own enslavement, and in the second place obtain empire for the good of the governed, and not for the sake of exercising a general despotism, and in the third place they should seek to be masters only over those who deserve to be slaves.
Thus, with a philosophy that justified the use of power by an enlightened warrior to plunder the barbarian, Aristotle attracted favor from warriors, and he became tutor to Alexander the Great, who conquered and exacted tribute from more of the world than had any one man up to that time in history.
A different atom for each element
By the late 1700s, the useful practices of engineering and technology began to influence philosophical explanations for the composition of matter. Those who speculated on the ultimate nature of matter began to verify their "thought experiments" with some repeatable demonstrations, when they could.
In 1808, John Dalton assimilated the known experimental work of many people to summarize the empirical evidence on the composition of matter. He noticed that distilled water everywhere analyzed to the same elements, hydrogen and oxygen. Similarly, other purified substances decomposed to the same elements in the same proportions by weight.
- Therefore we may conclude that the ultimate particles of all homogeneous bodies are perfectly alike in weight, figure, &c. In other words, every particle of water is like every other particle of water; every particle of hydrogen is like every other particle of hydrogen, &c.
Furthermore, he concluded that there was a unique atom for each element, using Lavoisier's definition of an element as a substance that could not be analyzed into something simpler. Thus, Dalton concluded the following.
- Chemical analysis and synthesis go no farther than to the separation of particles one from another, and to their reunion. No new creation or destruction of matter is within the reach of chemical agency. We might as well attempt to introduce a new planet into the solar system, or to annihilate one already in existence, as to create or destroy a particle of hydrogen. All the changes we can produce, consist in separating particles that are in a state of cohesion or combination, and joining those that were previously at a distance.
And then he proceeded to give a list of relative weights in the compositions of several common compounds, summarizing: 
- 1st. That water is a binary compound of hydrogen and oxygen, and the relative weights of the two elementary atoms are as 1:7, nearly;
- 2nd. That ammonia is a binary compound of hydrogen and azote [nitrogen], and the relative weights of the two atoms are as 1:5, nearly. . . .
Dalton concluded that the fixed proportions of elements by weight suggested that the atoms of one element combined with only a limited number of atoms of the other elements to form the substances that he listed.
Creationism versus evolution
Many modern creationists, those who believe that some Creator made the universe, see atomism as the root of the evil in which people have attempted repeatedly throughout history to avoid the "moral dictates" of the Creator. They conclude that Democritus, Epicurus, Darwin, and molecular biologists who promote godless evolution are head-strong in denying the pangs of their own conscience and hoping to overthrow God's law to become master of their own destiny. Accordingly, the teaching of evolution to the exclusion of facts supporting creationism is unfair by promoting an anti-religious agenda. 
In contrast, many modern evolutionists state that, though some religious faiths express true values, it is irresponsible to teach a child that morality, ethics, self-sacrifice, or any other important positive value comes from God -- because it is simply not true. And, if the child goes into adulthood believing that moral values come from God, then the young adult will be unprepared to resist effectively the natural temptations that business, politics, and relationships present to cheat, lie, and steal. (Firth 1996:215-216)
- Dictionary of the History of Ideas: Atomism: Antiquity to the Seventeenth Century
- Dictionary of the History of Ideas: Atomism in the Seventeenth Century
- The Atomists: Leucippus and Democritus, C. C. W. Taylor (Translator) (University of Toronto Press 1999) ISBN 0802043909.
- Raymond Firth, Religion: A Humanist Interpretation (Routledge, 1996) ISBN 0415128978.