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Like most of the scientific beliefs of Cuvier’s day, the idea that extinction didn’t exist was derived not only from scientific authority but also from religious authority. Religious authorities’ logic was that God wouldn’t wipe out his own creations, as doing so would be counterproductive to maintaining the connections between all forms of life on Earth, from the ocean to the earth and to the sky.

In 1795, Georges Cuvier did some of his anatomical studies on animals at the National Museum in Paris. There, he embarked on a groundbreaking quest to disprove the idea that extinction was impossible. Using his knowledge of the anatomy of animals, he was able to recreate the entire bodily structures of extinct animals. According to some legends, Cuvier could accomplish this feat even with a couple of bone pieces.

At the time Cuvier presented his 1796 paper on living and fossil elephants, it was still widely believed that no species of animal had ever become extinct. Authorities such as Buffon had claimed that fossils found in Europe of animals such as the woolly rhinoceros and the mammoth were remains of animals still living in the tropics (i.e. rhinoceros and elephants), which had shifted out of Europe and Asia as the earth became cooler.

Thereafter, Cuvier performed a pioneering research study on some elephant fossils excavated around Paris. The bones he studied, however, were remarkably different from the bones of elephants currently thriving in India and Africa. This discovery led Cuvier to denounce the idea that fossils came from those that are currently living. The idea that these bones belonged to elephants living - but hiding - somewhere on Earth seemed ridiculous to Cuvier because it would be nearly impossible to miss them due to their enormous size. He later performed more research studies on fossils of large animals and came to the same conclusion that the fossils simply didn’t match any living today. Ultimately, his findings drove Cuvier to the proposition that the abrupt changes the Earth underwent over a long period of time caused some species to go extinct.

Cuvier’s theory on extinction has met opposition from other notable natural scientists like Darwin and Charles Lyell. Unlike Cuvier, they didn’t believe that extinction was a sudden process; they believed that like the Earth, animals collectively undergo gradual change as a species. This differed widely from Cuvier’s theory, which seemed to propose that animal extinction was catastrophic.

However, Cuvier’s theory of extinction is still justified in the case of mass extinctions that occurred in the last 600 million years, when approximately half of all living species went completely extinct within a short geological span of two million years, due in part by volcanic eruptions, asteroids, and rapid fluctuations in sea level. At this time, new species rose and others fell, precipitating the arrival of human beings.

Cuvier's early work demonstrated conclusively that extinction was indeed a credible natural global process. Cuvier's thinking on extinctions was influenced by his extensive readings in Greek and Latin literature; he gathered every ancient report known in his day relating to discoveries of petrified bones of remarkable size in the Mediterranean region.

Influence on Cuvier's theory of extinction was his collection of specimens from the New World, many of them obtained from Native Americans. He also maintained an archive of Native American observations, legends, and interpretations of immense fossilized skeletal remains, sent to him by informants and friends in the Americas. He was impressed that most of the Native American accounts identified the enormous bones, teeth, and tusks as animals of the deep past that had been destroyed by catastrophe.

Comparative anatomy and classification[edit]
At the Paris Museum, Cuvier furthered his studies on the anatomical classification of animals. He believed that classification should be based on how organs collectively function, a concept he called functional integration. Cuvier also reinforced the idea of subordinating less vital body parts to more critical organ systems as part of anatomical classification. He published these ideas in his book called Animal distribué d'après son organisation, pour servir de base à l'histoire naturelle des animaux et d'introduction à l'anatomie comparée, or The Animal Kingdom Arranged after its Organization; Forming a Natural History of Animals, and an Introduction to Comparative Anatomy) in 1817.

'''Cuvier believed function played a bigger role than form in the fields of comparative anatomy and taxonomy. This emphasis is evident in his guiding hypothesis of the conditions of existence, from which flowed his two rules of anatomy: the principle of the correlation of parts and the principle of the subordination of characters. The hypothesis of the conditions of existence states that, "'''As nothing may exist which does not include the conditions which made its existence possible, the different parts of each creature must be coordinated in such a way as to make possible the whole organism, not only in itself but in its relationship to those which surround it." The application of the idea of the conditions of existence to anatomy led to Cuvier's principle of the correlation of parts, which argues that the harmonious cooperation of organs is the condition of existence for the organism, and that this mutual dependence of the organs means that the presence of a single organ necessarily implies the existence of all of the other organs to which it is functionally related. Cuvier uses respiration as an example of this principle: respiration, he says, relies on circulation to bring the blood into contact with respiratory tissues. The circulation of the blood, in turn, depends on the heart's pumping action, which itself relies on contractions made possible by the nervous fluid. Finally, the nervous fluid is a product of the circulation of the blood. Each component of this system thus cannot exist without the others.

in the idea of the principles of the correlation of parts and of the conditions of existence. The former principle accounts for the connection between organ function and its practical use for an organism to survive. The latter principle emphasizes the animal’s physiological function in relation to its surrounding environment. These findings were published in his scientific readings, including Leçons d'anatomie comparée (Lessons on Comparative Anatomy) and in Le Règne Animal (The Animal Kingdom) in the early 19th century and 1817 respectively.

Ultimately, Cuvier developed four embranchements, or branches, through which he classified animals based on his taxonomical and anatomical studies. He later performed groundbreaking work in classifying animals in vertebrate and invertebrate groups by subdividing each category. For instance, he proposed that the invertebrates could be segmented into three individual categories, including Mollusca, Radiata, and Articulata. He also articulated that species cannot move across these categories, a theory called transmutation. He reasoned that organisms cannot acquire or change their physical traits over time and still retain optimal survival. As a result, he often conflicted with Geoffroy Saint-Hilaire and Jean-Baptiste Lamarck’s theories of transmutation.

In 1798 Cuvier published his first independent work, the Tableau élémentaire de l'histoire naturelle des animaux, which was an abridgment of his course of lectures at the École du Pantheon and may be regarded as the foundation and first statement of his natural classification of the animal kingdom.

In 1800 he published the Leçons d'anatomie comparée, assisted by A. M. C. Duméril for the first two volumes and Georges Louis Duvernoy for the three later ones.