After the Greeks had satisfied themselves that they possessed a cosmological theory which answered the demands of reason they turned their investigations to the question of how matter was changed into its innumerable forms. Empedocles had taught that when the primary elements, earth, air, fire, and water, were mixed in variable proportions they yielded different kinds of matter. Leucippus, Democritus, Anaxagoras, and others studied the subject more carefully and developed a novel theory. When matter is divided as far as possible do the ratios of the constituents remain the same? This problem attracted their attention. They also asked themselves whether there was not a simpler conception to explain the basic state of matter. When they began their inquiries, the qualities of matter were believed to reflect their essences. For example, the sweetness of honey and the color of the sky were real things which should be studied in themselves apart from honey and the sky. Democritus thought, however, that such changes of color as the sky undergoes at dawn and sunset would not take place if the colors were real elementary things. While meditating on this the thought arose in their mind: "If we assume matter to be composed of an infinite number of minutest particles or atoms, could we not explain the changes in matter by changes in atomic quantities and orders?" This line of thought resulted in the development of the atomic theory and the origin of the philosophic school of the atomists.
According to Leucippus some of the atoms darting about in the universe collide and thus give rise to new substances. He also believed that the atoms followed whirling or circular paths and that such rotary motions drew in neighboring atoms, and that as these movements continued indefinitely within the atoms the constituents were being constantly rearranged, the lighter elements being grouped around the periphery; the heavier ones around the center. These changes were due to pressure and impact. These conceptions about atoms were carried into cosmological discussions and it was taught that there are various worlds and planets within the boundless universe, each one moving freely according to physical laws, unless fractured by collision with another.
Zeno challenged these doctrines because of the importance attached to the whirling motion. He attempted to show that such atomic motions are impossible. His proofs of the impossibility of atomic motion were designed with the object of sustaining his own theory of an ultimate principle of unity. His mental trend was toward negation. Whenever his rival Parmenides argued affirmatively regarding a scientific principle, Zeno would invariably maintain the negative side of the question.
Zeno's first proof of the impossibility of motion referred to the impossibility of passing through a fixed space. He showed that by dividing a line into an infinite number of parts an infinite number of points would be obtained and these permitted no beginning of motion.
His second proof tried to show the impossibility of passing through space having movable boundaries. The story of Achilles and the tortoise illustrates this. A pursuer in a race at every interval must reach a point from which the pursued starts simultaneously. But the latter is always in advance.
The third, or "resting arrow," argument showed that a moving arrow is at every instant in some one point of its track. Its movement at such instant is then equal to zero. Its track is a group of zeros. No magnitude could be framed from these.
Zeno also anticipated much later philosophical discussions, like Einstein's, relating to the relativity of motion. He took for an example a moving wagon. Its movement would appear different to observers on other moving bodies going in various directions. They would see changes in rates of speed as well as in direction.
Protagoras, at a subsequent date, developed this idea of relativity and showed that things are as they appear to each individual at the moment they are perceived. He summarized his teaching in the aphorism: Man is the measure of all things.
The Skeptics, 200 years later, developed the Protagorean theory of relativity, and by a series of arguments attempted to prove that perceptions change not only with the different species of animate beings, but with many conditions and circumstances. It was also shown that not only man's perceptions are subject to changes, but also his opinions following from his perceptions. Another school taught that to every opinion the opposite can be opposed with equally good reasons.