What is known about Anaximenes' philosophy is what was preserved by later philosophers, particularly Aristotle and Theophrastus.[7] According to their writings, each philosopher of the Milesian School was a material monist who sought to discover the arche (Ancient Greek: ἀήρή, lit. 'beginning, origin'), or the one, underlying basis of all things.[8] This is generally understood in the context of a substance, though scholars have argued that this may be anachronistic by imposing the Aristotelian notion of substance theory on earlier philosophy.[3]Anaximenes argued that the arche is air.[10] He described several basic elements that he considered to be manifestations of air, sorting them from least dense to most dense: fire, air, wind, clouds, water, earth, and stones. Philosophers have concluded that Anaximenes seems to have based his conclusions on naturally observable phenomena in the water cycle: the processes of rarefaction and condensation. He proposed that each substance is created by condensation to increase the density of air or by rarefaction to decrease it.[11][12][13] The rarefaction process described by Anaximenes is often compared to felting.[14]

Temperature was of particular importance to Anaximenes' philosophy, and he developed an early concept of the connection between temperature and density. He believed that expanded air was thinner and therefore hotter while compressed air was thicker and therefore colder—although modern science has found the opposite to be true. He derived this belief from the fact that one's breath is warm when the mouth is wide while it is cold when the air is compressed through the lips.[15][16]

Anaximenes further applied his concept of air as the arche to other questions.[17] He believed in the physis, or natural world, rather than the theo, or divine world.[18] Anaximenes considered air to be divine in a sense, but he did not associate it with deities or personification.[19][20] He presented air as the first cause that propelled living systems, giving no indication that air itself was caused by anything.[19][13] Anaximenes also likened the soul to air, describing it as something that is driven by breath and wills humans to act as they do.[21] These beliefs draw a connection between the soul and the physical world, as they suggest that they are made of the same material, air.[22] From this, Anaximenes suggested that everything, whether it be an individual soul or the entire world, operates under the same principles in which things are held together and guided by the air.[16] In Ancient Greek, the words for wind and for soul shared a common origin.[20][23]

Anaximenes' philosophy was centered on a theory of change through ongoing cycles, defined by the movement of air.[24][17]These cycles consisted of opposite forces interacting with and superseding one another. This is most prominently indicated in the weather and the seasons, which alternate between hot and cold, dry and wet, or light and dark.[24] Anaximenes did not believe that any substance could be created or destroyed, only that it could be changed from one form to another.[25] From this belief, he proposed a model in which the qualitative traits of a substance are determined by quantitative factors.[15][17]