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 (a) fallacy of Four Terms (Quaternio terminorum); (b) of Undistributed Middle; (c) of Illicit process of the major or the minor term; (d&#8202;) of Negative Premises.

Of other classifications of Fallacies in general the most famous are those of Francis Bacon and J. S. Mill. Bacon (Novum organum, Aph. i. 33, 38 sqq.) divided fallacies into four Idola (Idols, i.e. False Appearances), which summarize the various kinds of mistakes to which the human intellect is prone (see ). With these should be compared the Offendicula of Roger Bacon, contained in the Opus maius, pt. i. (see ). J. S. Mill discussed the subject in book v. of his Logic, and Jeremy Bentham’s Book of Fallacies (1824) contains valuable remarks.

FALLIÈRES, CLÉMENT ARMAND (1841–), president of the French republic, was born at Mézin in the department of Lot-et-Garonne, where his father was clerk of the peace. He studied law and became an advocate at Nérac, beginning his public career there as municipal councillor (1868), afterwards mayor (1871), and as councillor-general of the department of Lot-et-Garonne (1871). Being an ardent Republican, he lost this position in May 1873 upon the fall of Thiers, but in February 1876 was elected deputy for Nérac. In the chamber he sat with the Republican Left, signed the protestation of the 18th of May 1877, and was re-elected in October by his constituency. In 1880 he became under-secretary of state in the department of the interior in the Jules Ferry ministry (May 1880 to November 1881). From the 7th of August 1882 to the 20th of February 1883 he was minister of the interior, and for a month (from the 29th of January 1883) was premier. His ministry had to face the question of the expulsion of the pretenders to the throne of France, owing to the proclamation by Prince Jérome Napoleon (January 1883), and M. Fallières, who was ill at the time, was not able to face the storm of opposition, and resigned when the senate rejected his project. In the following November, however, he was chosen as minister of public instruction by Jules Ferry, and carried out various reforms in the school system. He resigned with the ministry in March 1885. Again becoming minister of the interior in the Rouvier cabinet in May 1887, he exchanged his portfolio in December for that of justice. He returned to the ministry of the interior in February 1889, and finally took the department of justice from March 1890 to February 1892. In June 1890 his department (Lot-et-Garonne) elected him to the senate by 417 votes to 23. There M. Fallières remained somewhat apart from party struggles, although maintaining his influence among the Republicans. In March 1899 he was elected president of the senate, and retained that position until January 1906, when he was chosen by a union of the groups of the Left in both chambers as candidate for the presidency of the republic. He was elected on the first ballot by 449 votes against 371 for his opponent, Paul Doumer.

FALL-LINE, in American geology, a line marking the junction between the hard rocks of the Appalachian Mountains and the softer deposits of the coastal plain. The pre-Cambrian and metamorphic rocks of the mountain mass form a continuous ledge parallel to the east coast, where they are subject to denudation and form a series of “falls” and rapids in the river courses all along this line. The relief of the land below the falls is very slight, and this low country rarely rises to a height of 200 ft., so that the rivers are navigable up to the falls, while the falls themselves are a valuable source of power. A line of cities may be traced upon the map whose position will thus be readily understood in relation to the economic importance of the fall-line. They are Trenton on the Delaware, Philadelphia on the Schuylkill, Georgetown on the Potomac, Richmond on the James, and Augusta on the Savannah. It will be readily understood that the softer and more recent rocks of the coastal plain have been more easily washed away, while the harder rocks of the mountains, owing to differential denudation, are left standing high above them, and that the trend of the edge of this great lenticular mass of ancient rock is roughly parallel to that of the Appalachian system.

FALLMERAYER, JAKOB PHILIPP (1790–1861), German traveller and historical investigator, best known for his opinions in regard to the ethnology of the modern Greeks, was born, the son of a poor peasant, at Tschötsch, near Brixen in Tirol, on the 10th of December 1790. In 1809 he absconded from the cathedral choir school at Brixen and made his way to Salzburg, where he supported himself by private teaching while he studied theology, the Semitic languages, and history. After a year’s study he sought to assure to himself the peace and quiet necessary for a student’s life by entering the abbey of Kremsmünster, but difficulties put in his way by the Bavarian officials prevented the accomplishment of this intention. At the university of Landshut, to which he removed in 1812, he first applied himself to jurisprudence, but soon devoted his attention exclusively to history and philology. His immediate necessities were provided for by a rich patron. During the Napoleonic wars he joined the Bavarian infantry as a subaltern in 1813, fought at Hanau (30th October 1813), and served throughout the campaign in France. He remained in the army of occupation on the banks of the Rhine until Waterloo, when he spent six months at Orleans as adjutant to General von Spreti. Two years of garrison life at Lindau on Lake Constance after the peace were spent in the study of modern Greek, Persian and Turkish.

Resigning his commission in 1818, he was successively engaged as teacher in the gymnasium at Augsburg and in the progymnasium and lyceum at Landshut. In 1827 he won the gold medal offered by the university of Copenhagen with his Geschichte des Kaisertums von Trapezunt, based on patient investigation of Greek and oriental MSS. at Venice and Vienna. The strictures on priestcraft contained in the preface to this book gave offence to the authorities, and his position was not improved by the liberal views expressed in his Geschichte der Halbinsel Morea während des Mittelalters (Stuttgart, 1830–1836, 2 pts.). The three years from 1831 to 1834 he spent in travel with the Russian count Ostermann Tolstoy, visiting Egypt, Palestine, Syria, Cyprus, Rhodes, Constantinople, Greece and Naples. On his return he was elected in 1835 a member of the Royal Bavarian Academy of Sciences, but he soon after left the country again on account of political troubles, and spent the greater part of the next four years in travel, spending the winter of 1839–1840 with Count Tolstoy at Geneva. Constantinople, Trebizond, Athos, Macedonia, Thessaly and Greece were visited by him during 1840–1841; and after some years’ residence in Munich he returned in 1847 to the East, and travelled in Palestine, Syria and Asia Minor. The authorities continued to regard him with suspicion, and university students were forbidden to attend the lectures he delivered at Munich. He entered, however, into friendly relations with the crown prince Maximilian, but this intimacy was destroyed by the events following on 1848. At that period he was appointed professor of history in the Munich University, and made a member of the national congress at Frankfort-on-Main. He there joined the left or opposition party, and in the following year he accompanied the rump-parliament to Stuttgart, a course of action which led to his expulsion from his professorate. During the winter of 1849–1850 he was an exile in Switzerland, but the amnesty of April 1850 enabled him to return to Munich. He died on the 26th of April 1861.

His contributions to the medieval history of Greece are of great value, and though his theory that the Greeks of the present day are of Albanian and Slav descent, with hardly a drop of true Greek blood in their veins, has not been accepted in its entirety by other investigators, it has served to modify the opinions of even his greatest opponents. A criticism of his views will be found in Hopf’s Geschichte Griechenlands (reprinted from Ersch and Gruber’s Encykl.) and in Finlay’s History of Greece in the Middle Ages. Another theory which he propounded and defended with great vigour was that the capture of Constantinople by Russia was inevitable, and would lead to the absorption by the Russian empire of the whole of the Balkan and Grecian