EXTENSION

As a primitive term, extension can be defined only ostensively, by pointing to a corporeal substance, the parts of which are distinguished by their positions. But extension is synonymous with neither corporeity nor materiality. To be extended is to be dimensively quantified and this results, formally, in the distinction and ordering of material integral parts. The term is more abstract than corporeity and may refer to both natural (or physical) and mathematical quantity, this latter defining sets of properties and relations that have no immediate physical counterpart. A material principle of substance requires dimensive quantity but is ontologically prior to it. Though normally referred to continuous quantity, extension may be said of contiguous parts and even of interrupted segments joined by an intermediary. By analogy, the term may refer to nonquantitative measures as in logic, where, opposed to intension, it signifies the magnitude of a nonnumerable multitude or class. In mathematics, extension shares in the analogy of the term space.

Distinctions. Within scholastic philosophy, one finds a distinction between the order of parts of an extended entity relative to a locating boundary on the one hand, and the order of parts relative to the whole of that entity on the other. The former specifies external or local extension; the latter, a mutual externality of parts, specifies internal or situal extension. [see place; situation (situs).] This distinction emphasizes the factual ordering of dimensive quantity and reflects a controversy. Against the general conviction, some held that extension is primarily a property of occupying space (see F. suÁrez, Disp. meta., 40.4). The general argument has been that an intrinsic distinguishing order of parts must be prior to any principle of external relation. The theological analysis of the doctrine of the eucharist led to this distinction, since there must be some account given of the natural extension of Christ's Body, which is manifestly not circumscribed in the Sacrament.

Dimensive quantity does not necessarily entail external extension. Physical extension is known sensibly by the perception, usually both visual and tactile, of the external dimensive relations that material substances bear toward their environment, and intellectually it is grasped by the measurability and divisibility that it founds. More detailed physical data raise questions about the type of continuity found in nature and the character of the smallest unit with its relations to complex aggregates.

That extension is an objective attribute of material things is an essential element in a realist philosophy, but apart from a rejection of the dynamistic reduction of extension to forces, positions, and motions of unextended points, there is no agreement upon the ultimate physical matrix of extension (e.g., ether, protomatter, or subnuclear particles), nor upon the character of its dividing boundaries. Such knowledge, depending upon a precise understanding of sensible matter, is never more than dialectical, reflecting the state of research at any given time. Recent physical theory tends to support the notion that the universe is an extended plenum determined generally and in its fundamental units by some formal principles of unity and organization.

Other Views. Unable to conceive of material substances as composed ontologically of principles such as primary matter and substantial form, R. descartes (1596–1650) considered body as such, res extensa, a species of substance. He inadequately distinguished substance from its quantitative extension, which he took to be a universal matrix for enfigurement and a requirement for motion. As a result, his philosophy of nature remains ambiguous. Impenetrability or solidity must be attributed by him to some vortex motion in an extended fluid like plenum; yet this plenum is entirely undifferentiable and, in fact, a mathematical construct.

G. W. leibniz (1646–1716) was not more concrete, for he understood extension to be an internal representation to each monad of the order of coexistence of all monads—the unitary, immaterial, simple substances that constituted his universe. The perception of extension was not, therefore, a sensation, but a God-given harmonious adaptation within each monad.

Influenced, most probably, by this position, I. kant (1724–1804) thought extension to be an analytical element of the concept body, hence an a priori form or contribution of the mind itself, which orders the content of sense experience, giving the objects and their extensive relations as man knows them. In effect, Kant identified physical and mathematical extension, since both are traced to the internal form of sensuous intuition. The distinction between a sensed objective property and a conception abstracted from the externality of corporeal substance is therefore lost.

Mathematical Extension. The abstraction of the notion of extension can yield either a mathematical or a physical conception; subsequent applications of the notions, especially to realms beyond direct sensation, thereupon become analogical. The mathematical notion, analogical even within that science, is first seen in Euclidean geometry as an abstraction from physical continua, which in three dimensions yield a homogeneous isotropic space. Chronologically, multidimensional spaces were the next analogues, but the concept of extension did not radically change until the arithmetization of geometry.

The essence of this development was the establishment of a correspondence between sets of numbers and geometric elements, so that continuous extension could be represented by continuous algebraic or numeric functions. Successive generalizations of such functions led to interpretations of extension that are far removed from the notion obtained in abstraction. Thus understood, in terms of the analytic properties of algebraic expressions, extension takes on as many meanings as the formal consistency of the multiple systems permits, including systems not having "smoothness" or perfect continuity. Finally, the whole of geometry and hence the interpretation of mathematical extension was given a further dialectical interpretation in terms of point sets. Extension then became a set of abstract relations, the link with quantity being the foundation of the opposition between the elements or terms of the relations, otherwise known as situs.

See Also: continuum; mathematics, philosophy of.

Bibliography: john of st. thomas, Ars Logica, v.1 of Cursus philosophicus Thomisticus …, ed. b. reiser, 3 v. (Turin 1930–37); Eng. tr. Material Logic: Basic Treatises, tr. y. r. simon et al. (Chicago 1955). l. a. foley, Cosmology: Philosophical and Scientific (Milwaukee 1962). p. borne, "De ente materiale et spirituale sub respectu extensionis et inextensionis," Divus Thomas 42 (1939) 240–253, 349–369, 461–494.

[c. f. weiher]

ex·ten·sion / ikˈstenshən/ • n. 1. a part that is added to something to enlarge or prolong it; a continuation: the railroad's southern extension. ∎  a room or set of rooms added to an existing building. ∎  the action or process of becoming or making something larger: the extension of the president's powers. ∎  an increase in the length of time given to someone to hold office, complete a project, or fulfill an obligation. ∎  Comput. an optional suffix to a file name, typically consisting of a period followed by several characters, indicating the file's content or function.2. (also extension cord) a length of electric cord that permits the use of an appliance at some distance from a fixed socket. ∎  an extra telephone on the same line as the main one.3. [usu. as adj.] instruction by a university or college for students who do not attend full time: extension courses.4. (extensions) lengths of real or artificial hair woven into a person's own hair.5. the action of moving a limb from a bent to a straight position: seizures with sudden rigid extension of the limbs. ∎  the muscle action controlling this: triceps extension. ∎  Ballet the ability of a dancer to raise one leg above the waist, or an instance of this. ∎  Med. the application of traction to a fractured or dislocated limb or to an injured or diseased spinal column to restore it to its normal position. ∎  the lengthening of a horse's stride within a particular gait.6. Physics & Philos. the property of occupying space; spatial magnitude: nature, for Descartes, was pure extension in space.PHRASES: by extension taking the same line of argument further: the disclosures raised serious questions about his credibility and, by extension, the credibility of the company.DERIVATIVES: ex·ten·sion·al / -shənl/ adj.

EXTENSION

An increase in the length of time specified in a contract.

A part constituting an addition or enlargement, as in an annex to a building or an extension to a house. Addition to existing facilities.

An allowance of additional time for the payment of debts. An agreement between a debtor and his or her creditors, by which they allow the debtor further time for the payment of liabilities. A creditor's indulgence by giving a debtor further time to pay an existing debt.

The word extension, when used in its proper and usual sense in connection with a lease, means a prolongation of the previous leasehold estate. The distinction between extension and renewal of lease is chiefly that, in the case of renewal, a new lease is requisite, while, in the case of extension, the same lease continues in force during an additional period upon performance of a stipulated act. An option for renewal implies giving a new lease on the same terms as those of an old lease, while an option for extension contemplates acontinuanceof an old lease for a further period.

Request for additional time to file an income tax return beyond the due date.

extension of a source. In coding theory, the process of encoding several symbols at a time, or the results thereof. If the symbols of a q-ary information source are taken r at a time, and the words of length r are treated (e.g. encoded) as if they were themselves symbols of an alphabet of size q^r, then this compound source is called the rth extension of the original source. See also source coding theorem.

extension A measure of the change in length of a line from its initial unit length. Extension may be positive (elongation) or negative (shortening), depending on whether the length of the line increases or decreases. The simplest type of extension (e) is calculated from: e = (L_f−L₀)/L₀, where L_f is the final length and L₀ the original unit length.