SYLLOGISM. 770 SYLVESTEK. serted to follow upon a single condition (or com- bination of conditions) or (6) alternative con- ditions may be asserted to determine a single consequence (or combination of consequences) ; or (0) an alternative may be presented between a condition with its consequence and another con- dition with its separate consequence. If alter- native consequences are asserted to follow upon a single condition, then it is possible to have a valid conditional syllogism either when a minor premise affirms the condition, warranting as eonclvision the affirmation of the alternative con- sequence; or when a minor premise denies con- junctively ("neither — nor') the alternative con- sequences, warranting as conclusion the denial of the antecedent. If alternative conditions are asserted to determine a single consequence, it is possible to have a valid syllogism when a minor premise either categorically affirms one of the conditions or disjunctively affirms both con- ditions, in either case justif.ying as conclusion the affirmation of the consequent; or when the minor premise categorically denies the consequent, justifying as conclusion the conjunctive denial of the conditions. If the major premise presents an alternative between a condition with its con- sequence and another condition with its separate consequence, a valid syllogism obtains when the minor premise either disjunctively affirms the two conditions, justifying the disjunctive affirma- tion of the two consequences, or when the minor premise conjunctively or disjunctively denies botli eonscquenees. justifying a conjunctive or disjunctive denial respectively of the two ante- cedents. For bibliograpliy, see books mentioned under Logic. See also Fallacy; Dilemma; CONVER.SION ; ObVERSION. SYLPHS (Neo-Lat. siilplw, probably from Gk. ci?.(t>!/, siliiJir. sort of beetle: so called as being a spirit flying in the air). In the fantastic system of the Paracelsists, the elemental spirits of the air, Avho, like the other elemental spirits, hold an intermediate place between immaterial and material beings. They eat. drink, speak, move about, beget children, and aro siibject to in- firmities like men; but, on the other hand, they resemble spirits in being more nimble and swift in their motions, while their bodies are more diaph- anous than those of the human race. They also surpass the latter in their knowledge, both of the present and the future, but have no soul ; and w'hen they die, nothing is left. In common usage, the term 'sylph' has a feminine signification, and is applied to a grace- ful maiden. How this curious change of mean- ing occurred is not quite certain : but it is pos- sibly owing to the popularity of Pope's Fnpe of the Lock, which introduced the term into the world of fashion and literature. Consult: Para- eelsus's Liher de yi/inphis, Sylphis, Pygmwis et Salamandris et Cceteris Spiritibus (Basel ed. of Paracelsus's works, 1590). SYLVANITE. See Tellukium. SYLVES'TER. The name of two popes. Sylvester 1.. Pope .314-335. His reign was the first in the new period of Cliureh freedom under Constantine. In his pontificate the Council of Nica?a was held, which he did not himself at- tend, Init sent two legates to represent liim. Numerous unhistorical legends, especially concern- ing his relations to Constantine, have clustered about liim; concerning them, consult Diil- linger, I'ublcs Respecting the Popes in the Middle Ages (Eng. trans., New York. 1872) ; and see Donation of Constantine. His works are in Migne, Patrologia Latina, viii. — Sylvester II., Pope 9991003, Gerbert by name. He was born at Aurillae, in Auvergne, about 935, and at an early age went to Spain, where he made re- markable progress in scientific studies. He be- came head of the cathedral school at Rheinis, which grew to eminence under his direction. In 9S2 he was made Aliliot of Bobbio on the nomina- tion of Otlio II., but returned to Rheims, of which, by Hugh Capet's wisli, lie was eliosen Archbishop in 991. Four 3'ears later, the deposi- tion of liis predecessor having been declared in- valid, he went to JIagdeburg on Otho III.'s in- vitation, and accompanied him to Italy, where he remained, becoming Archbishop of Kavenna in ^^!i. and reaching the Papal throne in the follow- ing year. He was a strict reformer, and ac- quired the reputation of the most learned man of his age ; he was an adept in mathematics, and in practical mechanics and astronomy, in which his attainments were so amazing to his contem- poraries as to arouse a suspicion that he was in league with the devil. The Gubar numerals, the ancestors of our modern numerals and due to the Western Arabs, owe much of their proiiiincnce, if not their introduction into Europe, to Sylvester. His writings are reprinted in Migne. Patrologia Latina, c.xxxix. ; also by Olleris (Paris. 18(17): his letters, which throw much light upon an obscure period, have been translated into French (Riom, 1847). Con.sult studies of his life and times bv Hock (Vienna, 1837). Axinger (Paris. 1842)'. Tappe (Berlin, 1809), and Scliul- tess (Hamburg, 1891) ; also Schultess, Die Hagcn iiher l^ilvcster II. (ib., 1893), and the book of Didlinger referred to above. — The name was also borne by two antipopes, Sylvester III., wlio con- tested the Papal throne with Benedict IX. in 1044, and Sylvester IV., who was put up by the Imperial party to oppose Paschal II. in 1105. SYLVESTER, .James Joseph (1814-97). One of the foremost English mathematicians of the nineteenth century. He was born in Lon- don, of Jewish parents, and received his early education in a Jewish school. He then attended the Royal Institution school in Liverpool, and thence proceeded to Saint .John's. Cambridge (1831). As a Jew he was barred from taking a degree, and it was not until the passing of the Tests Act that he obtained his B.A. at Cam- bridge (1872). He studied at the Inner Temple after leaving Cambridge, and was called to the bar in 1S50. Sylvesterwas appointed professor of nat- ural philosophy at LTniversity College. London, in 1837. and was elected fellow of the Ro^yal Society in 1839. In 1841 he was appointed professor of mathematics in the University of Virginia, but 60on after (1845) returned to England, where he took up the work of an actuary. In 1855 he be- came professor of mathematics at the Royal Mili- tarv' Academy at Woolwich, where he remained for 15 years. In 1877 he became the first pro- fessor of mathematics at .Johns Hopkins Uni- versity, which position he held for seven years, returning to England to accept the Savilian pro- fessorship of geometry at Oxford. He founded
