Arche (Ancient Greek: ἀρχή) is a Greek word with primary senses "beginning", "origin" or "source of action". (εξ’ ἀρχής: from the beginning, οr εξ’ ἀρχής λόγος: the original argument), and later first principle or element, first so used by Anaximander (Simplicius in Ph. 150.23), principles of knowledge (ἀρχαί) (Aristot. Metaph. 995b8). By extension, it might mean "first place, power", "method of government", "empire, realm", "authorities" (in plural: ἀρχαί), "command". The first principle or element corresponds to the "ultimate underlying substance" and "ultimate undemonstrable principle". In the philosophical language of the archaic period (8th-6th century BC), arche (or archai) designates the source, origin or root of things that exist. In ancient Greek philosophy, Aristotle foregrounded the meaning of arche as the element or principle of a thing, which although undemonstrable and intangible in itself, provides the conditions of the possibility of that thing.
In the mythical Greek cosmogony of Hesiod (8th-7th century BC), the origin of the world is Chaos, considered as a divine primordial condition, from which everything else appeared. In the creation "chaos" is a gaping-void, but later the word is used to describe the space between the earth and the sky, after their separation. "Chaos" might mean infinite space, or a formless matter which can be differentiated. The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality. The conception of the "divine" as an origin influenced the first Greek philosophers.
In the mythological cosmogonies of the Near East, the universe is formless and empty and the only existing thing prior to creation was the water abyss. In the Babylonian creation story, Enuma Elish the primordial world is described as a "watery chaos" from which everything else appeared. Something similar is described in Book of Genesis where the spirit of God is moving upon the dark face of the waters.
In the Hindu cosmology, which is similar to the Vedic cosmology, in the beginning there was nothing in the Universe but darkness. The self-manifested being created the primordial waters and established his seed into it. This turned into a golden egg (Hiranyagarbha) from which everything else appeared.
Arche in Ancient Greek philosophy
The heritage of Greek mythology already embodied the desire to articulate reality as a whole and this universalizing impulse was fundamental for the first projects of speculative theorizing. It appears that the order of "being" was first imaginatively visualised before it was abstractly thought. In the ancient Greek philosophy, arche is the element and the first principle of existing things. This is considered as a permanent substance or nature (physis) either one or more which is conserved in the generation of rest of it. From this all things first come to be and into this they're resolved in a final state. This source of entity is always preserved. (Aristotle-Metaph.A, 983, b6ff). Anaximander was the first philosopher that used arche for that which writers from Aristotle onwards called "the substratum" (Simplicius Phys. 150, 22). The Greek philosophers ascribed to arche divine attributes. It is the divine horizon of substance that encompasses and values all things.
Thales of Miletus (7th-6th century BC), the father of philosophy, claimed that the first principle of all things is water, and considered it as a substance that contains in it motion and change. His theory was supported by the observation of moisture throughout the world and coincided with his theory that the earth floated on water. His ideas were influenced by the Near-Eastern mythological cosmogony and probably by the Homeric statement that the surrounding Oceanus (ocean) is the source of all springs and rivers.
Thales' theory was refuted by his successor and esteemed pupil, Anaximander. Anaximander noted that water couldn't be the arche, because it couldn't give rise to its opposite, fire. Anaximander claimed that none of the elements (earth, fire, air, water) can be arche for the same reason. Instead, he proposed the existence of the apeiron, an indefinite substance from which all things are born and to which all things will return. Apeiron (endless or boundless) is something completely indefinite and Anaximander was probably influenced by the original chaos of Hesiod (yawning abyss). He probably intended it to mean primarily "indefinite in kind" but assumed it additionally to be "of unlimited extent and duration". The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious conception of immortality and Anaximander's description was in terms appropriate to this conception. This arche is called "eternal and ageless". (Hippolitus I,6,I;DK B2)
Anaximenes, Anaximander's pupil, advanced yet another theory. He returns to the elemental theory, but this time posits air, rather than water, as the arche and ascribes to it divine attributes. He was the first recorded philosopher who provided a theory of change and supported it with observation. Using two contrary processes of rarefaction and condensation (thinning or thickening), he explains how air is part of a series of changes. Rarefied air becomes fire, condensed it becomes first wind, then cloud, water, earth, and stone in order. The arche is technically what underlies all of reality/appearances.