(Ἀναξιμένης), who is usually placed third in the series of Ionian philosophers, was born at Miletus, like Thales and Anaximander, with both of whom he had personal intercourse : for besides the common tradition which makes him a disciple of the latter, Diogenes Laertius quotes at length two letters said to have been written to Pythagoras by Anaximenes; in one of which he gives an account of the death of Thales, speaking of him with reverence, as the first of philosophers, and as having been his own teacher. In the other, he congratulates Pythagoras on his removal to Crotona from Samos, while he was himself at the mercy of the tyrants of Miletus, and was looking forward with fear to the approaching war with the Persians, in which he foresaw that the Ionians must be subdued. (D. L. 2.3, &c.)

There is no safe testimony as to the exact periods of the birth and death of Anaximenes : but since there is sufficient evidence that he was the teacher of Anaxagoras, B. C. 480, and he was in repute in B. C. 544, he must have lived to a great age. (Strab. xiv. p.645; Cic. de Nat. Deor. 1.11 ; Origen, vol. iv. p. 238.) The question is discussed by Clinton in the Philological Museum. (Vol. i. p. 86, &c.)

Like the other early Greek philosophers, he employed himself in speculating upon the origin, and accounting for the phenomena, of the universe: and as Thales held water to be the material cause out of which the world was made, so Anaximenes considered air to be the first cause of all things, the primary form, as it were, of matter, into which the other elements of the universe were resolvable. (Aristot. Met. 1.3.) For both philosophers seem to have thought it possible to simplify physical science by tracing all material things up to a single element: while Anaximander, on the contrary, regarded the substance out of which the universe was formed as a mixture of all elements and qualities. The process by which, according to Anaximenes, finite things were formed from the infinite air, was that of compression and rarefaction produced by motion which had existed from all eternity : thus the earth was created out of air made dense, and from the earth the sun and the other heavenly bodies. (Plut. apud Euseb. Praep. Evang. 1.8.) According to the same theory, heat and cold were produced by different degrees of density of the primal element : the clouds were formed by the thickening of the air; and the earth was kept in its place by the support of the air beneath it and by the flatness of its shape. (Plut. de Pr. Frig. 7, de Plac. Ph. 3.4; Aristot. Met. 2.13.)

Hence it appears that Anaximenes, like his predecessors, held the eternity of matter : nor indeed does he seem to have believed in the existence of anything immaterial; for even the human soul, according to his theory, is, like the body, formed of air (Plut. de Plac. Ph. 1.3); and he saw no necessity for supposing an Agent in the work of creation, since he held that motion was a natural and necessary law of the universe. It is therefore not unreasonable in Plutarch to blame him, as well as Anaximander, for assigning only the material, and no efficient, cause of the world in his philosophical system. (Plut. l.c.)