The classic example is that of Euclid's Elements; its hundreds of geometric propositions can be deduced from a set of definitions, postulates, and primitive notions: all three types constitute first principles.
By extension, it may mean "first place", "method of government", "empire, realm", "authorities"[note 2] The concept of an arche was adapted from the earliest cosmogonies of Hesiod and Orphism, through the physical theories of Pre-Socratic philosophy and Plato before being formalized as a part of metaphysics by Aristotle.
[4] 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.
[5] 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.
[7] In the mythical Greek cosmogony of Hesiod (8th to 7th century BC), the origin of the world is Chaos, considered as a divine primordial condition, from which everything else appeared.
[11] The earliest Pre-Socratic philosophers, the Ionian material monists, sought to explain all of nature (physis) in terms of one unifying arche.
[13] Thales of Miletus (7th to 6th century BC), the father of philosophy, claimed that the first principle of all things is water,[14] and considered it as a substance that contains in it motion and change.
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.
[16][17] Apeiron (endless or boundless) is something completely indefinite; and Anaximander was probably influenced by the original chaos of Hesiod (yawning abyss).
He returns to the elemental theory, but this time posits air, rather than water, as the arche and ascribes to it divine attributes.
Using two contrary processes of rarefaction and condensation (thinning or thickening), he explains how air is part of a series of changes.
But Aristotle's references to first principles in this opening passage of the Physics and at the start of other philosophical inquiries imply that it is a primary task of philosophy.
Descartes describes the concept of a first principle in the following excerpt from the preface to the Principles of Philosophy (1644): I should have desired, in the first place, to explain in it what philosophy is, by commencing with the most common matters, as, for example, that the word philosophy signifies the study of wisdom, and that by wisdom is to be understood not merely prudence in the management of affairs, but a perfect knowledge of all that man can know, as well for the conduct of his life as for the preservation of his health and the discovery of all the arts, and that knowledge to subserve these ends must necessarily be deduced from first causes; so that in order to study the acquisition of it (which is properly called [284] philosophizing), we must commence with the investigation of those first causes which are called Principles.
For example, calculation of electronic structure using Schrödinger's equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach.