Anaximenes was another resident of Miletus, the last of the Milesian philosophers. He was the student of Anaximander, though he is generally seen as taking a step backward from his great mentor. His one significant accomplishment was that he was the first person to propose a mechanism by which the physis (in his case, a misty air) transforms into the plurality of objects we see around us in the observable world.
Like Anaximander's Unbounded, Anaximenes' aer is unlimited and inexhaustible. Aer, however, is definite. It is something like mist, a breathy thing. Anaximenes arrives at his physis by observing living creatures. What makes a creature alive, he observes, is that it breathes. A breathy thing, which he calls soul, both holds together and guides the living creature. There must be some similar element, he reasons, that performs that same function for the whole cosmos. An argument of this form, which reasons from the human being to the whole cosmos, is often called a microcosm/macrocosm argument. It was used frequently in ancient Greek medicine, but this is its first appearance in natural philosophy.
Most commentators view Anaximenes' choice of aer for physis as a big step backward from Anaximander's Unbounded. After all, the Unbounded had the advantage of being dissociated from the changing elements that it was supposed to explain. But it is not that hard to see why Anaximenes might have believed that his physis was superior to the Unbounded. First of all, aer is not just a theoretical entity; we have a reason to believe it exists, and we can even observe it. In addition, it is not so nebulous and vague a substance, and so we can better understand its connection to the objects around us; we can conceive of how it gave rise to the opposites, whereas with the Unbounded it is difficult to understand how something with no qualities can act as the source of all the qualities in the world. Anaximenes is able to give us an account of how his physis gives rise to the plurality, something that Anaximander, presumably, would have been hard-pressed to do.
Anaximenes is the first to explicitly include the processes by which his physis is transformed into the plurality of observable objects. Like most other processes the Milesians proposed, this one involves the eternal motion of the physis. As aer moves it can either become rarefied or condensed. When rarefied, aer becomes fire. When it condenses just a little it becomes wind. Condense it more and it becomes water, more and it becomes clouds, then earth, and finally, in its most condensed form, stone. In this way, Anaximenes is able to derive all the qualities in the world out of quantity. (By laying out all of these familiar substances in series, Anaximenes makes an important advance: he shows that the elements of the world are not separated by qualitative gaps, but that they instead form a continuity.)
It is tempting to view the process of rarefaction and condensation in the mechanistic terms though which we understand these processes. It is unlikely, though, that Anaximenes' believed his process to involve particles moving further apart and closer together. It is not impossible, though, and if this is the case then he can be viewed as a proto-atomist.
Like a good Milesian, Anaximenes provides us with evidence for the claim that rarefaction and condensation of air can give rise to qualitative changes. In particular, he provides us with evidence that condensation gives rise to coldness, and rarefaction to heat. His first piece of evidence comes from human breath. If we hold our lips far apart and breath out, the resulting breath is hot. If, on the other hand, we purse our lips, forcing the air into a smaller space, the resulting breath is cool. As another confirming instance, Anaximenes points to water, snow, and ice. Water, the most condensed form of the three, is warmest, ice coldest, and snow somewhere in between.