Anaximenes of Miletus (c 546 BCE) was a younger contemporary of Anaximander and generally regarded as his student. Known as the Third Philosopher of the Milesian School (after Thales and Anaximander) Anaximenes proposed air as the First Cause from which all else comes (differing from Thales, who claimed water was the source of all things, or Anaximander, who cited 'the boundless infinite’). To the Greeks of the time, `air' was comparable to `soul' and, just as one's breath gave an individual life, so air, Anaximenes claimed, gave life to all observable phenomena. He explained the process by which the First Cause creates the observable world in this way:
Air differs in essence in accordance with its rarity or density. When it is thinned it becomes fire, while when it is condensed it becomes wind, then cloud, when still more condensed it becomes water, then earth, then stones. Everything else comes from these. (DK13A5)
To Anaximenes, everything was in a constant state of change owing to the property of air and how it is always in flux. The world itself, he claimed, was created by air through a process he compared to the process of felting, by which wool is compressed to create felt. In this same way was the earth created through compression of air which, through a process of evaporation, gave birth to the stars and the planets. All of life came from this same sort of process, of air being compacted to change itself, or another, into a different thing.
In this way, Anaximenes provided a basis for rational discourse and debate on his claim and laid the groundwork for future scientific inquiry into the nature of existence. His influence is far reaching.
Anaximenes’ theory of successive change of matter by rarefaction and condensation was influential in later theories. It is developed by Heraclitus (DK22B31), and criticized by Parmenides (DK28B8.23-24, 47-48). Anaximenes’ general theory of how the materials of the world arise is adopted by Anaxagoras (DK59B16), even though the latter has a very different theory of matter. Both Melissus (DK30B8.3) and Plato (Timaeus 49b-c) see Anaximenes’ theory as providing a common-sense explanation of change. Diogenes of Apollonia makes air the basis of his explicitly monistic theory. The Hippocratic treatise On Breaths uses air as the central concept in a theory of diseases. By providing cosmological accounts with a theory of change, Anaximenes separated them from the realm of mere speculation and made them, at least in conception, scientific theories capable of testing. (Encyclopedia of Philosophy)
Like Thales and Anaximander before him, Anaximenes sought an underlying reason for existence and natural phenomena without appealing to the tradition of supernatural deities as the First Cause. Even though, like the other Milesians, he is never quoted as teaching atheism, there is nothing theistic in any of the extant fragments of his writings nor in any of the references to him by ancient writers. According to Diogenes Laertius, Anaximenes "wrote in the pure unmixed Ionian dialect. And he lived, according to the statements of Apollodorus, in the sixty-third Olympiad, and died about the time of the taking of Sardis" His influence is especially noticeable in the philosophy of the later writer Heraclitus, as noted above, who developed the concept of Flux as a First Cause in and of itself.
(Citations DK in reference to the Diels/Krantz work The Fragments of the Pre-Socratics, 1967).