history of logic: The 17th century: …in the otherwise quite traditional Logica Demonstrativa (1697; “Demonstrative Logic”) of the Italian Jesuit Gerolamo Saccheri. Saccheri is better known for his suggestion of the possibility of a non-Euclidean geometry in Euclides ab Omni Naevo Vindicatus (1733; “Euclid Cleared of Every Flaw”). Another incisive traditional logic was that of the…

history of logic: The 17th century: …the Dutch philosopher Arnold Geulincx, Logica fundamentis suis restituta (1662; “Logic Restored to its Fundamentals”). This work attempted to resurrect the rich detail of scholastic logic, including the theory of suppositio and issues of existential import.

history of logic: The 17th century: The Logica Hamburgensis (1638) of Joachim Jung (also called Jungius or Junge) was one replacement for the “Protestant” logic of Melanchthon. Its chief virtue was the care with which late medieval theories and techniques were gathered and presented. Jung devoted considerable attention to valid arguments that…

history of logic: Late medieval logic: …editions, and possibly the huge Logica magna (“Big Logic”) that has sometimes been regarded as a kind of encyclopaedia of the whole of medieval logic.

history of logic: The properties of terms and discussions of fallacies: …were known collectively as the Logica nova (“New Logic”). In a flurry of activity, others in the 12th and 13th centuries produced additional translations of these works and of Greek and Arabic commentaries on them, along with many other philosophical writings and other works from Greek and Arabic sources.

history of logic: Late medieval logic: …works were the very popular Logica parva (“Little Logic”), printed in several early editions, and possibly the huge Logica magna (“Big Logic”) that has sometimes been regarded as a kind of encyclopaedia of the whole of medieval logic.

history of logic: Transmission of Greek logic to the Latin West: …were known collectively as the Logica vetus (“Old Logic”).

Logical Atomism, theory, developed primarily by the British logician Bertrand Russell and the Austrian-born philosopher Ludwig Wittgenstein, proposing that language, like other phenomena, can be analyzed in terms of aggregates of fixed, irreducible units or elements. Logical Atomism supposes that a

realism: Reductionism, error theories, and projectivism: …of this approach is logical behaviourism, which maintains that statements about mental events and states are logically equivalent to statements which, while typically much more complicated, are wholly about observable behaviour in varying kinds of circumstances. Thus, there are no mental facts over and above physical facts. In this sense,…

formal system: …and is more properly called logical calculus; this kind of formulation deals rather with validity and satisfiability than with truth or falsity, which are at the root of formal systems.

connective, in logic, a word or group of words that joins two or more propositions together to form a connective proposition. Commonly used connectives include “but,” “and,” “or,” “if . . . then,” and “if and only if.” The various types of logical connectives include conjunction (“and”),

metalogic: Characterizations of the first-order logic: …of equality as the “logical constants” is assumed to be the correct one. There remains the question, however, of justifying the particular choice of logical constants. One might ask, for example, whether “For most x” or “For finitely many x” should not also be counted as logical constants. Lindström…

logical positivism, a philosophical movement that arose in Vienna in the 1920s and was characterized by the view that scientific knowledge is the only kind of factual knowledge and that all traditional metaphysical doctrines are to be rejected as meaningless. A brief treatment of logical positivism

philosophy of logic: Logic and information: …utilized in semantical discussions than logical equivalence. Hence the transition from one sentence to another logically equivalent one is disregarded for the purposes of meaning concepts. This disregard would be justifiable if one of the most famous theses of Logical Positivists were true in a sufficiently strong sense, viz., that…

history of logic: The 16th century: …consciousness of the importance of logical form (forms of sentences, as well as forms or patterns of arguments). Although the medievals made many distinctions among patterns of sentences and arguments, the modern logical notion of “form” perhaps first crystallized in the work of Sir William Rowan Hamilton and the English…

Rudolf Carnap: Career in the United States of Rudolf Carnap: …of this kind in his Logical Foundations of Probability (1950).

Edmund Husserl: Lecturer at Halle.: …interaction were presented in the Logische Untersuchungen (1900–01; “Logical Investigations”), which employed a method of analysis that Husserl now designated as “phenomenological.” The revolutionary significance of this work was only gradually recognized, for its method could not be subsumed under any of the philosophical orientations well known at that time.…

Hegelianism: Anti-Hegelian criticism: … in his Logische Untersuchungen (1840; Logical Investigations). In Hegel’s view, the passage from Being to Nothing and to Becoming can be posited as a pure beginning “without presuppositions” of logic. In Trendelenburg’s view, however, this passage is vitiated by its spurious dependence upon the surreptitious presupposition of the empirical movement,…

logic: Logical notation: The way in which logical concepts and their interpretations are expressed in natural languages is often very complicated. In order to reach an overview of logical truths and valid inferences, logicians have developed various streamlined notations. Such notations can be thought of as…

logical positivism, a philosophical movement that arose in Vienna in the 1920s and was characterized by the view that scientific knowledge is the only kind of factual knowledge and that all traditional metaphysical doctrines are to be rejected as meaningless. A brief treatment of logical positivism

epistemology: Logical and factual propositions: A logical proposition is any proposition that can be reduced by replacement of its constituent terms to a proposition expressing a logical truth—e.g., to a proposition such as “If p and q, then p.” The proposition “All husbands are married,” for…

metalogic: Semiotic: …logically true sentences having universal logical ranges and factually true sentences having universal logical ranges and factually true ones having more restricted ranges. (Roughly speaking, the logical range of a sentence is the set of all possible worlds in which it is true.)

positivism: Developments in linguistic analysis and their offshoots: …of Carnap, usually designated as logical reconstruction, which builds up an artificial language. In the procedures of ordinary-language analysis, an attempt is made to trace the ways in which people commonly express themselves. In this manner, many of the traditional vexatious philosophical puzzles and perplexities are shown to arise out…

logical relation, those relations between the elements of discourse or thought that constitute its rationality, in the sense either of (1) reasonableness or (2) intelligibility. A statement may be perfectly intelligible without being based upon any good evidence or reason, though of course no

metalogic: Model theory: In model theory one studies the interpretations (models) of theories formalized in the framework of formal logic, especially in that of the first-order predicate calculus with identity—i.e., in elementary logic. A first-order language is

Noam Chomsky: Life and basic ideas: …Modern Hebrew, and especially in The Logical Structure of Linguistic Theory (LSLT), written while he was a junior fellow at Harvard (1951–55) and published in part in 1975, Chomsky adopted aspects of Harris’s approach to the study of language and of Goodman’s views on formal systems and the philosophy of…

constitution theory: …Logische Aufbau der Welt (1928; The Logical Structure of the World: Pseudoproblems in Philosophy, 1967). A scientific concept, such as “atom” or “gene,” is said to be “reduced” when every sentence containing the concept can be transformed into sentences containing concepts that refer only to experiences—which thus constitute the scientific…

Rudolf Carnap: Career in the United States of Rudolf Carnap: …Logische Syntax der Sprache (1934; The Logical Syntax of Language) and Meaning and Necessity (1947). Carnap’s interest in artificial languages included advocacy of international auxiliary languages such as Esperanto and Interlingua to facilitate scholarly communication and to further international understanding.

logic: Logical systems: Logic is often studied by constructing what are commonly called logical systems. A logical system is essentially a way of mechanically listing all the logical truths of some part of logic by means of the application of recursive rules—i.e., rules that can be…

epistemology: Logical and factual propositions: …to a proposition expressing a logical truth—e.g., to a proposition such as “If p and q, then p.” The proposition “All husbands are married,” for example, is logically equivalent to the proposition “If something is married and it is male, then it is married.” In contrast, the semantic and syntactic…

Logician, any member of a school of Chinese philosophers of the Warring States period (475–221 bce). In Chinese the school is called Mingjia (Wade-Giles romanization Ming-chia), the “School of Names,” because one of the problems addressed by the Logicians was the correspondence between name and

logicism, school of mathematical thought introduced by the 19th–20th-century German mathematician Gottlob Frege and the British mathematician Bertrand Russell, which holds that mathematics is actually logic. Logicists contend that all of mathematics can be deduced from pure logic, without the use

Northrop Grumman Corporation: Its wholly owned subsidiary Logicon, Inc., provides information-technology services to U.S. government agencies and commercial customers and management support for U.S. military weapons systems. Its Litton Sector (formerly Litton Industries) is the largest maker of nonnuclear ships for the U.S. Navy and designs, builds, and overhauls surface ships for…

positivism: The verifiability criterion of meaning and its offshoots: …his Logik der Forschung (1935; The Logic of Scientific Discovery), insisted that the meaning criterion should be abandoned and replaced by a criterion of demarcation between empirical (scientific) and transempirical (nonscientific, metaphysical) questions and answers—a criterion that, according to Popper, is to be testability, or, in his own version, falsifiability—i.e.,…

Étienne Bonnot de Condillac: In his works La Logique (1780) and La Langue des calculs (1798; “The Language of Calculation”), Condillac emphasized the importance of language in logical reasoning, stressing the need for a scientifically designed language and for mathematical calculation as its basis. His economic views, which were presented in Le…

Pierre Nicole: Nicole was an influential spokesman from 1655 to 1668 through his writing or editing of most of the Jansenist pamphlets. He was probably the source of the celebrated distinction between the two “questions of fact,” an adroit device allowing him to separate into two parts…

Tractatus Logico-Philosophicus, landmark work by the Austrian-born British philosopher Ludwig Wittgenstein (1889–1951), published in German (as Logisch-philosophische Abhandlung) in 1921 and in English in 1922, that articulates a sophisticated version of the metaphysical theory of logical atomism,

constitution theory: …Logische Aufbau der Welt (1928; The Logical Structure of the World: Pseudoproblems in Philosophy, 1967). A scientific concept, such as “atom” or “gene,” is said to be “reduced” when every sentence containing the concept can be transformed into sentences containing concepts that refer only to experiences—which thus constitute the scientific…

Rudolf Carnap: Career in the United States of Rudolf Carnap: …Logische Syntax der Sprache (1934; The Logical Syntax of Language) and Meaning and Necessity (1947). Carnap’s interest in artificial languages included advocacy of international auxiliary languages such as Esperanto and Interlingua to facilitate scholarly communication and to further international understanding.

Hegelianism: Anti-Hegelian criticism: … in his Logische Untersuchungen (1840; Logical Investigations). In Hegel’s view, the passage from Being to Nothing and to Becoming can be posited as a pure beginning “without presuppositions” of logic. In Trendelenburg’s view, however, this passage is vitiated by its spurious dependence upon the surreptitious presupposition of the empirical movement,…

Edmund Husserl: Lecturer at Halle.: …interaction were presented in the Logische Untersuchungen (1900–01; “Logical Investigations”), which employed a method of analysis that Husserl now designated as “phenomenological.” The revolutionary significance of this work was only gradually recognized, for its method could not be subsumed under any of the philosophical orientations well known at that time.…

population ecology: Logistic population growth: …population growth known as the logistic curve. It is determined by the equation

logistic function, an equation describing growth rates of quantities, such as populations, over time and graphed as an S-shaped, or sigmoid, curve. The equation is applied in many fields, such as biology, sociology, agriculture, and economics. The logistic function is

Kantianism: Epistemological Neo-Kantianism: Logistic Neo-Kantianism, as represented in the most well-known and flourishing school of Kantianism, that at Marburg, originated with Hermann Cohen, successor of Lange, who, in Kants Theorie der Erfahrung (1871; “Kant’s Theory of Experience”), argued that the transcendental subject is not to be regarded as…

logistic regression, in statistics, a method for modeling conditional probabilities with discrete (usually binary) outcomes. In a logistic model (sometimes called a logit model), the probability of a discrete, categorical outcome variable (e.g., “yes/no” or “pass/fail/incomplete”) is modeled on the

logistics: Logistic specialization: For many centuries the soldier was a fighting man and nothing else; he depended on civilians to provide the services that enabled him to live, move, and fight. Even the more technical combat and combat-related skills, such as fortification, siegecraft, and service of…

spiral: The logarithmic, or equiangular, spiral was discovered by the French scientist René Descartes in 1638. In 1692 the Swiss mathematician Jakob Bernoulli named it spira mirabilis (“miracle spiral”) for its mathematical properties; it is carved on his tomb. The general equation of the logarithmic spiral is…

formal system, in logic and mathematics, abstract, theoretical organization of terms and implicit relationships that is used as a tool for the analysis of the concept of deduction. Models—structures that interpret the symbols of a formal system—are often used in conjunction with formal systems.

logistics, in business, the organized movement of materials and, sometimes, people. The term was first associated with the military but gradually spread to cover business activities. Logistics implies that a number of separate activities are coordinated. In 1991 the Council of Logistics Management,

logistics, in military science, all the activities of armed-force units in roles supporting combat units, including transport, supply, signal communication, medical aid, and the like. In the conduct of war, war-making activity behind the cutting edge of combat has always defied simple definition.

logistics: Fundamentals: Eccles, whose Logistics in the National Defense appeared in 1959. Expanding Thorpe’s trinity to five (strategy, tactics, logistics, intelligence, communications), Eccles developed a conceptual framework that envisaged logistics as the military element in the nation’s economy and the economic element in its military operations—that is, as a…

logistics: In 1991 the Council of Logistics Management, a trade organization based in the United States, defined logistics as: “the process of planning, implementing, and controlling the efficient, effective flow and storage of goods, services, and related information from point of origin to point of consumption for the purpose…

history of logic: Leibniz: …development of the logical language LOGLAN and the computer language PROLOG.

Logo, a computer programming language that originated in the late 1960s as a simplified LISP dialect for use in education; Seymour Papert and others used it at the Massachusetts Institute of Technology (MIT) to teach mathematical thinking to schoolchildren. It had a more conventional syntax than

trademark, any visible sign or device used by a business enterprise to identify its goods and distinguish them from those made or carried by others. Trademarks may be words or groups of words, letters, numerals, devices, names, the shape or other presentation of products or their packages, colour

deconstruction: Deconstruction in philosophy: …a manifestation of the “logocentrism” of Western culture—i.e., the general assumption that there is a realm of “truth” existing prior to and independent of its representation by linguistic signs. Logocentrism encourages us to treat linguistic signs as distinct from and inessential to the phenomena they represent, rather than as…

Christian Dotremont: …led to his invention of “logograms,” in which he sought to create a new “visual grammar,” a “poem-landscape.” Binary oppositions abound in his work: mystical-scientific, primal-futuristic, inner-outer, silent-sonic, intellectual-emotional. COBRA also furthered Dotremont’s friendship with the Danish painter Asger Jorn and cemented his links with Scandinavia. In 1951 Dotremont became…

logogram, written or pictorial symbol intended to represent a whole word. Writing systems that make use of logograms include Chinese, Egyptian hieroglyphic writing, and early cuneiform writing systems. No known writing system is totally logographic; all such systems have both logograms and symbols

Antiphon: He was a logographos; i.e., a writer of speeches for other men to deliver in their defense in court, a function that was particularly useful in the climate of accusation and counter-accusation that prevailed in Athens at the conclusion of the Peloponnesian War, between Athens and Sparta.

Chinese languages: Pre-Classical characters: Logographic (i.e., marked by a letter, symbol, or sign used to represent an entire word) is the term that best describes the nature of the Chinese writing system.

Chinese languages: Pre-Classical characters: Logographic (i.e., marked by a letter, symbol, or sign used to represent an entire word) is the term that best describes the nature of the Chinese writing system.

logos, in ancient Greek philosophy and early Christian theology, the divine reason implicit in the cosmos, ordering it and giving it form and meaning. Although the concept is also found in Indian, Egyptian, and Persian philosophical and theological systems, it became particularly significant in

Logone River, principal tributary of the Chari (Shari) River of the Lake Chad Basin, draining northeastern Cameroon and Chad. It is formed by the Mbéré River and its tributary the Vina (Wina, Mba, Bini) of northern Cameroon and by the Pendé of northwestern Central African Republic. The two

speech disorder: Development of speech correction: …speech and voice pathology as logopedics and phoniatrics with its medical orientation subsequently reached many other civilized nations, notably in Japan and on the South American continent. The national organizations in most of these areas are now represented in the International Association of Logopedics and Phoniatrics, which was founded in…

speech disorder: Dysphasia and aphasia: …sometimes excessively and incessantly (logorrhea), although with numerous errors and meaningless clichés, but no longer comprehends what is said to him or her or what he or she tries to read. Those who recover from receptive forms of the disorder are likely to explain that during their aphasia spoken…

logos, in ancient Greek philosophy and early Christian theology, the divine reason implicit in the cosmos, ordering it and giving it form and meaning. Although the concept is also found in Indian, Egyptian, and Persian philosophical and theological systems, it became particularly significant in

Viktor Frankl: …the psychological approach known as logotherapy, widely recognized as the “third school” of Viennese psychotherapy, after the “first school” of Sigmund Freud and the “second school” of Alfred Adler. The basis of Frankl’s theory was that the primary motivation of an individual is the search for meaning in life and…

logothete, in Byzantine government from the 6th to the 14th century, any of several officials who shared a variety of responsibilities ranging from the assessment and collection of taxes to the direction of foreign policy. The logothete of the drome, who was charged with presenting gifts to foreign

Boris Berezovsky: …those contacts to set up LogoVaz, the U.S.S.R.’s first capitalist car dealership. LogoVaz bought cars at the state-set price for cars intended for export and sold them at the much higher price such cars could fetch inside Russia. The profits enabled Berezovsky to expand his interests into oil and banking.…

Angélique Kidjo: …Kidjo left Pili-Pili and recorded Logozo (1991), which featured the American jazz musician Branford Marsalis and the African artists Manu Dibango and Ray Lema. With songs addressing issues of global concern—such as homelessness, the environment, freedom, and integration—Logozo was an international success. Kidjo increased her international appeal through her later

birling, outdoor sport of the North American lumberjack. Its origin can be traced to the spring log drives of eastern Canada and the New England states, particularly the state of Maine, during the early lumbering era in the 19th century, from which it moved westward to the Great Lakes region and

Logroño, city, capital of La Rioja provincia (province) and comunidad autónoma (autonomous community), north-central Spain, lying on the Ebro River. Originated in Roman times, it owed its growth during the Middle Ages to its position on the pilgrim route to Santiago de Compostela as much as to its

La Rioja, comunidad autónoma (autonomous community) and historical region of Spain coextensive with the north-central Spanish provincia (province) of La Rioja (until 1980 called Logroño). La Rioja is bordered by the autonomous communities of the Basque Country to the north, Navarra to the

Aliquippa, city, Beaver county, western Pennsylvania, U.S. It lies along the Ohio River just northwest of Pittsburgh. Settled about 1750 as a post for trade with Delaware, Iroquois, and Shawnee Indians, it was first known as Logstown and was later renamed for “Queen” Aliquippa, probably a Seneca.

Manipur: Relief and drainage: Its main physical feature is Logtak Lake, which covers about 40 square miles (100 square km) and is the source of the Manipur River. The river flows southward through the valley into Myanmar, where it joins the Myittha River, a tributary of the Chindwin.

Sardinian language: Not surprisingly, Logudorese (Logudorian) is the most conservative dialect. The northern form of Logudorese provides the basis for a sardo illustre (a conventionalized literary language that has been used mainly for folk-based verse). Campidanese (Campidanian), centred on Cagliari in the south, was heavily influenced by Catalan and…

Sardinian language: Not surprisingly, Logudorese (Logudorian) is the most conservative dialect. The northern form of Logudorese provides the basis for a sardo illustre (a conventionalized literary language that has been used mainly for folk-based verse). Campidanese (Campidanian), centred on Cagliari in the south, was heavily influenced by Catalan and…

Christopher Logue was an English poet, playwright, journalist, and actor, who was one of the leaders in the movement to bring poetry closer to the popular experience. His own pungent verse has been read to jazz accompaniment, sung, and printed on posters. It is engaged politically and owes much to

logwood, (Haematoxylum campechianum), tree of the pea family (Fabaceae), native to Central America and the West Indies. The wood is heavy and extremely hard. Logwood was once an important source of black dye, which is obtained from the red heartwood and is still used as a source of the histological

logwood: Logwood was once an important source of black dye, which is obtained from the red heartwood and is still used as a source of the histological stain hematoxylin. The plant is also used in certain traditional systems of medicine.

Stern Gang, Zionist extremist organization in Palestine, founded in 1940 by Avraham Stern (1907–42) after a split in the right-wing underground movement Irgun Zvai Leumi. Extremely anti-British, the group repeatedly attacked British personnel in Palestine and even invited aid from the Axis powers.

Guanxiu: …known for his paintings of lohans (arhats). The best known of the lohan paintings that are attributed to him are a series of 16 in the Tokyo National Museum.

Lahore, second largest city of Pakistan and the capital of Punjab province. It lies 811 miles (1,305 km) northeast of Karāchi in the upper Indus plain on the Rāvi River, a tributary of the Indus. Little is known of the history of the settlement prior to the Muslim period. Hindu legend attributes

Al-Luḥayyah, town, western Yemen, on the Red Sea coast. Situated on the coastal plain known as the Tihāmah, it is one of the country’s minor ports. It was founded in the mid-15th century, and tradition connects its origin with a local holy man, Sheikh Salei, around whose dwelling and tomb the town

Richard Wagner: Early life: …attend the first performance of Lohengrin at Weimar, given by his friend Franz Liszt on August 28, 1850.

Lohengrin: …anonymous Middle High German poem, Lohengrin (c. 1275–90), set the story in the historical context of the reign of the German king Henry I the Fowler (876?–936), and its author elaborated the realistic elements of the story at the expense of much romantic material. A contemporary poem known as the…

Lohengrin, the knight of the swan, hero of German versions of a legend widely known in variant forms from the European Middle Ages onward. It seems to bear some relation to the northern European folktale of “The Seven Swans,” but its actual origin is uncertain. The basic story tells of a mysterious

Ram Manohar Lohia was an Indian politician and activist who was a prominent figure in socialist politics and in the movement toward Indian independence. Much of his career was devoted to combating injustice through the development of a distinctly Indian version of socialism. Lohia was born to a

Brahmaputra River: Physiography: …by two mountain streams, the Lohit and the Dibang. Below that confluence, about 900 miles (1,450 km) from the Bay of Bengal, the river becomes known conventionally as the Brahmaputra (“Son of Brahma”). In Assam the river is mighty, even in the dry season, and during the rains its banks…

Elfriede Lohse-Wächtler was a German Expressionist artist associated with the Dresden Sezession artist group and known for her paintings of the city’s disenfranchised population. She suffered from mental illness and fell into obscurity after she was murdered by the Nazis during World War II.

Léopold Senghor: …French parliament passed (1956) the loi cadre, which gave a large measure of self-government to the African territories, Senghor was one of the first to oppose the act, because he felt its emphasis on territorial rather than federal government would result in the proliferation of small, unviable states. To counter…

Falloux Law, (1850) act granting legal status to independent secondary schools in France. It was sponsored by Count Frédéric-Alfred-Pierre de Falloux (1811–86), minister of education in the Second Republic, and one of its main architects was a Roman Catholic bishop, Félix-Antoine-Philibert

Loi-kaw, town, east-central Myanmar (Burma), on the Pilu River, a tributary of the Salween River. Situated in hilly forested country, Loi-kaw has timber and silk-processing industries and is the site of an important hydroelectric power plant. The Loi-kaw Area Irrigation Project is an important

filariasis: Types of filariasis: Loiasis, prevalent in western and central Africa, especially along the Congo River, is caused by Loa loa and transmitted by flies of the genus Chrysops. It is characterized by transient areas of allergic inflammation in the tissues beneath the skin, called calabar swellings; adult worms…

loin: …the butcher’s term for a piece of meat cut from that part of the body. The upper part of a loin of beef is known as the “surloin,” commonly corrupted into “sirloin.” In the plural the word is a term for the lower part of the human body at the…

loin, that part of an animal lying between the upper part of the hipbone and the last of the false ribs on either side of the backbone—hence the butcher’s term for a piece of meat cut from that part of the body. The upper part of a loin of beef is known as the “surloin,” commonly corrupted into

loincloth, usually, a rectangular piece of cloth draped around the hips and groin. One of the earliest forms of clothing, it is derived, perhaps, from a narrow band around the waist from which amuletic and decorative pendants were hung. From about 3000 bce Egyptians wore a loincloth (schenti) of

Loir River, river of northwest-central France, an affluent of the Sarthe River, that rises north of Illiers in Eure-et-Loir département. The Loir flows generally west-southwest, passing through the western extreme of the Little Beauce in its upper course and by Châteaudun. Beyond Vendôme it enters

Centre: Indre, Indre-et-Loire, Loir-et-Cher, Loiret, and Eure-et-Loir. Centre is bounded by the régions of Normandy and Île-de-France to the north, Bourgogne-Franche-Comté to the east, Auvergne-Rhône-Alpes to the southeast, Nouvelle-Aquitaine to the south, and Pays de la Loire

Rhône-Alpes: …encompassed the southeastern départements of Loire, Rhône, Ain, Haute-Savoie, Savoie, Isère, Drôme, and Ardèche. In 2016 the Rhône-Alpes région was joined with the région of Auvergne to form the new administrative entity of