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Agrippa, another sceptic, about a century later than Ænesidemus, also emphasizes the relative and subjective character of our conceptions, the discord among philosophers, their predilection for theories, their reasonings in a circle, and the fact that the syllogism cannot give us certain knowledge, inasmuch as every major premise is the conclusion of a preceding syllogism, and so on ad infinitum (regressus in infinitum).

The last and boldest of the Greek sceptics is SEXTUS EMPIRICUS, a physician of vast learning, who lived at Alexandria about the year 300 A. D., and of whom we have two valuable works: the Pyrrhonic Hypoty poses and the treatise Against the Mathematicians. He turns his attention to science, which, in consequence of its self-evident principles, offers a final refuge to dogmatism and metaphysics, and maintains the uncertainty, not only of grammar, rhetoric, music, astronomy, and the philosophical sciences proper, but also of arithmetic and geometry, in which he discovers the fundamental contradiction that the line is both extended and composed of inextended points. Hence no science is certain ; everything is vague, doubtful, and contradictory, both in theory and in method ; in mathematics as well as in physics, in logic as well as in ethics. True scepticism, like Pyrrho's, does not even grant unconditionally that all sciences are uncertain. The categorical assertion that metaphysics in the Peripatetic sense, i. e., knowledge of things-in-themselves, is impossible, stamps one as a dogmatist and metaphysician. This is, according to the Pyrrhonians, the error in the scepticism of the New Academy, which is but a negative dogmatism. The true sceptic refrains from making any absolute judgment whatsoever. His perfect neutrality (étroxń) enables

1 The Stoics, for example, proved the existence of God by the perfection of the world, and the perfection of the world by the existence of God.

him to realize, if not a state of absolute apathy, at least that repose and moral equilibrium (uerpotábela) in which true happiness consists. The sceptic, like the Stoic and Epicurean, pursues a practical end above everything else, but the way to reach it is to abstain from ontology. His system consists in not having a system ; and should the fancy seize him to advance a dogma, it would be to doubt his own scepticism.

But by doubting its own conclusions, radical scepticism abdicated in favor of Academic probabilism.

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While philosophy was degenerating into barren scepticism, the sciences, which had one by one cut loose from the parent science, copía, made wonderful strides in the Greek islands of the Mediterranean and in Egypt. Mathematics flourished in Egypt at a time when Greece was still steeped in barbarism. Experimental science, it is true, advanced but very slowly. It was, like philosophy, paralyzed by the insane delusion that the senses are deceptive and that reason is incapable of rectifying them. Besides, the natural impatience of the Greeks inclined them to reasoning and a priori speculation rather than to the detailed and painstaking labor involved in observation and experience. But the sciences in which reasoning plays the chief part, mathematics and mathematical physics, the exact sciences, in a word, made rapid strides. They alone escaped the destroy. ing touch of universal scepticism. In spite of the attacks of empiricism, there could be no reasonable doubt of the truth that twice two are four, and that the three angles of a triangle are equal to two right angles.

1 Montucla, Histoire des sciences mathématiques, especially the first two volumes, Paris, 1758; Delambre, Histoire de l'astronomie, 7 vols., Paris, 1817–23; Draper, History of the Intellectual Development in Eu rope, New York, 1863 ; Chasles, Aperçu historique sur l'origine et le développement des méthodes en géométrie, 21 ed., Paris, 1875; (Cantor, Geschichte der Mathematik, I., Leipsic, 1880).

In Sicily, where Pythagorean traditions had been perpetuated, Hicetas and Archimedes of Syracuse taught a system of astronomy (as early as the third century B. C.) that closely resembled the Copernican system. Archimedes gave to physics the method of determining specific weights, invented the sun-glass and the endless screw, and created the science of mechanics by his theory of the lever. At the same time, a fellow-countryman of Pythagoras, Aristarchus of Samos, proposed that the distance between the earth and the sun be measured by the dichotomy of the moon, and, what is more important, - for this method has proved to be impracticable, – attempted to substitute for the geocentric system of Aristotle the hypothesis that the earth revolves around the sun. This theory was accepted and developed by Seleucus of Seleucia in Babylonia, but stamped as impious by the Stoics, and rejected by Ptolemy himself, the most celebrated if not the greatest among the astronomers of Alexandria. It did not succeed in supplanting the old conception until the dawn of modern times, when it was advanced by Copernicus, Kepler, and Galileo.

On the opposite shore of the Mediterranean arose the city of Alexandria which was founded in the second half of the fourth century by the conqueror who gave it his name. Under the Ptolemies this became the educational as well as commercial centre of the world. Here rather than at the schools of Athens are to be found the legitimate spiritual descendants of Plato and Aristotle. Athens had banished the king of science, and its star went down forever. The spirit of the Stagirite descended upon his pupil, and from Alexander to Ptolemy and his successors. The Museum which they founded in the new capital of Egypt was a wonderful institution. Nothing in ancient or modern times can be compared to this attempt to organize science. Here scholars from every nation were entertained at public expense; thousands of students flocked hither from all the surrounding countries. Here the naturalists found a botanical garden, a vast zoological collection, and an anatomical building; the astronomers, an observatory; the littérateurs, grammarians, and philologists, a splendid library, which contained, during the first centuries of our era, 700,000 volumes. Here Euclid wrote (about 290) his Elements of Geometry, his treatises on Harmony, Optics, and Catoptrics; here Eratosthenes, the royal librarian under Ptolenıy Philadelphus, pursued his remarkable astronomical, geographical, and historical labors; here Apollonius of Perga published his treatises on Conic Sections; here Arystillus and Timocharus made the observations which led to the discovery of the precession of the equinoxes by the astronomer Hipparchus; here Ptolemy wrote the Almagest (ueyáan ouvražus), which remained the authoritative system of astronomy until the time of Copernicus, and his Geography, which was used in the schools of Europe for fourteen centuries. Ever since this epoch, the conceptions of the sphericity of the earth, its poles, its axis, the equator, the arctic and antarctic circles, the equinoctial points, the solstices, the inequality of climate on the earth's surface, have been current notions among scientists. The mechanism of the lunar phases was perfectly understood, and careful though not wholly successful calculations were made of intersidereal distances.

On the other hand, literature and art flourished under the careful protection of the Court. Literature and its history, philology and criticism, became sciences. The Hebrew Bible and other books of Oriental origin were translated into Greek. Buddhists and Jews, Greeks and Egyptians, mingled together, bringing with them the most diverse forms of religion. These conditions led to the development of comparative theology, on the one hand, and to the fusion of beliefs or a kind of religious eclecticism, on the other, and paved the way for Catholic unity.

§ 24. Eclecticism? The scientific movement of Alexandria was suddenly checked in the second century by the centralizing power of Rome. From that time on, the Greek genius showed unmistakable signs of decay. Literature and art declined rapidly. Philosophy was suffering from the incurable disease of scepticism. Torn from its native soil, it went to seed. The physical sciences remained stationary after the days of Galen, the physician, and the astronomer Ptolemy. The religion of the fathers became an object of scandal and derision; while ethics, which ought to have taken the place of religion, wavered between the trivialities of Epicureanism and the Utopias of the Stoa; the nearer it seemed to approach its ideal, ataracia, the more the latter seemed to elude its grasp. In this state of senile prostration, Greek thought looked back with longing to the days of its creative force; it cultivated a taste for history and archæology, in a word, for the past. Sceptical even of scepticism and yet unable to produce anything original, it became eclectic and lived on its memories. The ancient schools, each of which but recently possessed a separate principle, a distinguishing characteristic, and an individuality of its own, the Academy, the Lyceum, and the Stoa, after a struggle of three centuries, gradually became reconciled with each other and were eventually fused into a colorless syncretism.

It was, however, not impotence alone that led to such a fusion of elements. As long as Judaism retained its

1 Sources : Suidas, the Treatises of Philo the Jew, Plutarch, and Apuleius; Eusebius, Præp. evangelica, XI., XV., etc.

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