Archē

« Archē Arch ē , or 'principle', is an ancient Greek philosophical term.

Building on earlier uses, Aristotle established it as a technical term with a number of related meanings, including 'originating source', 'cause', 'principle ofknowledge' and 'basic entity'.

Accordingly, it acquired importance in metaphysics, epistemology and philosophy ofscience, and also in the particular sciences.

According to Aristotle's doctrine of scientific principles, all sciencesand all scientific knowledge are founded on principles ( archai ) of a limited number of determinate kinds.

Arch ē is an ancient Greek term meaning 'rule' (in a political sense) and 'beginning'.

The latter sense was developed inphilosophical contexts to mean 'origin', 'starting point', and 'principle' or 'first principle'.

It derives from the verbarchō , 'to begin', 'to rule'.

Both verbal meanings are found in Homer, although he does not use the noun ' archē ' to mean 'rule'.

In historical and political writings archē means 'sovereignty', 'realm', 'political office', and, in the plural, 'authorities', 'magistrates'.

The history of the noun as a philosophical term is controversial.

Passages like Simplicius,On Aristotle's Physics 24.15 and 150.23 have led many to believe that Anaximander (§2) was the first to use arch ē in a philosophical sense, while according to others these passages simply mean that he was the first to refer to thefirst principle of his system (in Simplicius' vocabulary, the archē ) as apeiron .

Depending on the view taken, the history of archē as a philosophical term begins either in the sixth century BC or much later.

The latter view is probably correct.

Archē is not used in a distinctively philosophical way in the authentic fragments of any Presocratic philosopher before Philolaus and although it carries philosophical weight in his writings (fragments 6, 8, 13) as well as in the Hippocratic medical writings, in Plato (especially Phaedo 101, Phaedrus 245 and Republic 510-11, 533), and possibly in early Greek mathematics, we must look to Aristotle for systematic discussion and use of the term (seeAristotle §6 ).

In Metaphysics V 1 Aristotle says the term arch ē is used in six ways, including the following: 'that from which (as an immanent part) a thing first arises, for example, the foundation of a house'; 'that from which ( not as an immanent part) a thing first arises, and from which the movement or the change naturally first proceeds, as achild comes from the father and the mother'; 'that by whose choice that which is moved is moved and that whichchanges changes, for example, the magistracies in cities, and the arts'; and 'that from which a thing can first beknown; for example, the hypotheses are the origins of demonstrations'.

Aristotle points out that all causes ( aitia ) are archai , as are the nature ( physis ) of a thing, the elements, thought, choice, substance, and 'that for the sake of which'.

In accordance with some of these conceptions of arch ē , Aristotle and his Peripatetic successors refer to the basic principles of the Presocratics (whether they were conceived of as originative substances or asfundamental entities) as archai .

In Physics I, Aristotle develops a more abstract account of physical archai , identifying them as two (matter and form) or three (matter, form and privation) (see Aristotle §8 ).

The Stoics, who were material monists, believed in two archai - a passive principle, matter, and an active principle, god, which like Aristotle's physical archai are best understood as inseparable aspects of substance (see Stoicism §3 ).

It is unclear how, why or in what field the Greeks first conceived of basing proofs on unprovable principles (the fundamental stepin axiomatics).

By the late fifth century BC mathematics had made progress in this direction.

In discussingmathematical method in the Republic , Plato emphasizes the way geometry establishes conclusions on the basis of unproved 'hypotheses' which are considered obvious, but which are not, strictly speaking, known.

(Unfortunately,Plato does not make clear what these 'hypotheses' are.) By contrast, dialectic proceeds from hypotheses to an'unhypothetical' archē which is the basis of certain knowledge.

Influenced to some extent by mathematics, Aristotle asserts in the Posterior Analytics that every science is based on three kinds of archai : definitions ( horismoi ), hypotheses, which seem to posit the existence of the basic entities which the science studies, and commonprinciples ( koina ) or axioms ( axiōmata ) such as the Law of Non-Contradiction, used in more than one science. These kinds of principles correspond approximately, but not perfectly, to the principles on which the geometry ofEuclid's Elements is based: definitions ( horoi ), construction postulates ( aitēmata ) and 'common notions' ( koinai ennoiai ).

The Posterior Analytics develops a general doctrine of scientific archai .

Every science ( epistēm ē ) consists of demonstrations of conclusions from archai .

Aristotle argues that the archai cannot themselves be demonstrated. The archai must satisfy several strict conditions: they must be true, primary, immediate, and prior to the conclusions that follow from them.

Moreover, they must be better known than and causes (that is, aitia : 'grounds', 'explanations') of these conclusions.

'Primary' and 'immediate' here mean 'unprovable' or 'basic'.

By 'better known'and 'prior' Aristotle means better known and prior 'in nature' to the conclusions; that is, more intelligible.

By'causes', Aristotle indicates that scientific archai are causally prior to the facts that follow from them; he is thus committed to believing in a real ordering of facts in which some are more causally basic than others, and to holdingthat scientific knowledge is a matter of knowing the basic facts, knowing that they are basic, and knowing how thederivative facts follow from them.

It follows that scientific archai are basic both ontologically and epistemologically; an archē is an arch ē within the context of a single science.

In general, an arch ē of one science has no status either as arch ē or as conclusion in another science.

In one sense arch ē is a relative term: an arch ē is an arch ē of or for certain other facts or propositions (Aristotle did not always distinguish these from one another).

In anothersense an arch ē is absolute: a fact is basic whether or not anyone happens to recognize it as such.. »