I. Strength and universality of the Greek intellect, 1—Specialisation of individual genius, 2—Pervading sense of harmony and union, 3—Circumstances by which the intellectual character of the Greeks was determined, 3—Philosophy a natural product of the Greek mind, 4—Speculation at first limited to the external world, 4—Important results achieved by the early Greek thinkers, 5—Their conception of a cosmos first made science possible, 6—The alleged influence of Oriental ideas disproved, 6. II. Thales was the first to offer a purely physical explanation of the world, 7—Why he fixed on water as the origin of all things, 8—Great advance made by Anaximander, 9—His conception of the Infinite, 9-Anaximenes mediates between the theories of his two predecessors, 10—The Pythagoreans: their love of antithesis and the importance attributed to number in their system, 11—Connexion between their ethical teaching and the general religious movement of the age, 13—Analogy with the mediaeval spirit, 13. III. Xenophanes: his attacks on the popular religion, 14—Absence of intolerance among the Greeks, 15—Primitive character of the monotheism taught by Xenophanes, 16—Elimination of the religious element from philosophy by Parmenides, 16—His speculative innovations, 17—He discovers the indestructibility of matter, 17—but confuses matter with existence in general, 18—and more particularly with extension, 19—In what sense he can be called a materialist, 19—New arguments brought forward by Zeno in defence of the Eleatic system, 20—The analytical or mediatorial moment of Greek thought, 21—Influence of Parmenides on subsequent systems of philosophy, 22—Diametrically opposite method pursued by Heracleitus, 22—His contempt for the mass of mankind, 22—Doctrine of universal relativity, 23—Fire as the primordial element, 24—The idea of Law first introduced by Heracleitus, 25—Extremes to which his principles were afterwards carried, 25—Polarisation of Greek thought, 26. IV. Historical order of the systems which succeeded and mediated between Parmenides and Heracleitus, 26—Empedocles: poetic and religious character of his philosophy, 27—His inferiority to previous thinkers, 28—Eclectic tendency of his system, 29—In what respects it marks an advance on that of Parmenides, 29—His alleged anticipation of the Darwinian theory, 30—The fixity of species a doctrine held by every ancient philosopher except Anaximander, 31—The theory of knowledge put forward by Empedocles: its objective and materialistic character, 32—How it suggested the Atomic theory, 33—The possibility of a vacuum denied by Parmenides and asserted by Leucippus, 34—The Atomic theory developed and applied by Democritus: encyclopaedic range of his studies, 35—His complete rejection of the supernatural, 36.