TWO:In 1720 Colin Maclaurin, the successor of James Gregory in the mathematical chair at Edinburgh, published his "Geometrical Organica," a treatise on curves; in 1742 his admirable treatise on Fluxions; and in 1748 his treatise on Algebra. Dr. Robert Simson, professor of mathematics at Glasgow, published a restoration of the "Loci" of Apollonius, and an English translation of Euclid, which continued down to a late period in use, both in Scotland and England. In 1717 James Stirling published a Latin treatise on lines of the third order, and another on Fluxions, called "Methodus Differentialis," in 1730. William Emerson, a mathematician and mechanist, wrote on fluxions, trigonometry, mechanics, navigation, algebra, optics, astronomy, geography, dialling, etc., but a considerable portion was only in part published during this period. Thomas Simpson, a weaver, of Market Bosworth, at the age of seven-and-twenty suddenly discovered himself as an extraordinary mathematician, and went on till his death, in 1761, publishing works on fluxions, the nature and laws of chance, on mixed mathematics, on the doctrine of annuities and reversions, on algebra, elementary geometry, trigonometry, etc. James Ferguson, also, the son of a day-labourer, in Banffshire, studied mathematics whilst tending sheep, and published a number of works on the phenomena of the harvest moon, astronomy, mechanics, hydrostatics,[154] pneumatics, and optics. Ferguson had a remarkably lucid and demonstrative style, both in writing and lecturing, and his example excited a keen spirit of inquiry amongst the working classes, so that he is said to have diffused the knowledge of physical science amongst the class from which he sprang more than any other man.We have already observed that Scepticism among the ancients was often cultivated in connexion with some positive doctrine which it indirectly served to recommend. In the case of its last supporters, this was the study of medicine on an empirical as opposed to a deductive method. The Sceptical contention is that we cannot go beyond appearances; the empirical contention is, that all knowledge comes to us from experience, and that this only shows us how phenomena are related to one another, not how they are related to their underlying causes, whether efficient or final. These allied points of view have been brought into still more intimate association by modern thought, which, as will be shown in the concluding chapter, has sprung from a modified form of the ancient Scepticism, powerfully aided by a simultaneous development of physical science. At the same time, the new school have succeeded in shaking off the narrowness and timidity of their predecessors, who were still so far under the influence of the old dogmatists as to believe that there was an inherent opposition between observation and reasoning in the methods of discovery, between facts and explanations in the truths of science, and between antecedence and causation in the realities of Nature. In this respect, astronomy has done more for the right adjustment of our conceptions than any190 other branch of knowledge; and it is remarkable that Sextus Empiricus, the last eminent representative of ancient Scepticism, and the only one (unless Cicero is to be called a Sceptic) whose writings are still extant, should expressly except astronomy from the destructive criticism to which he subjects the whole range of studies included in what we should call the university curriculum of his time.301 We need not enter into an analysis of the ponderous compilation referred to; for nearly every point of interest which it comprises has already been touched on in the course of our investigation; and Sextus differs only from his predecessors by adding the arguments of the New Academy to those of Protagoras and Pyrrho, thus completing the Sceptical cycle. It will be enough to notice the singular circumstance that so copious and careful an enumeration of the grounds which it was possible to urge against dogmatismincluding, as we have seen, many still employed for the same or other purposes,should have omitted the two most powerful solvents of any. These were left for the exquisite critical acumen of Hume to discover. They relate to the conception of causation, and to the conception of our own personality as an indivisible, continuously existing substance, being attempts to show that both involve assumptions of an illegitimate character. Sextus comes up to the very verge of Humes objection to the former when he observes that causation implies relation, which can only exist in thought;302 but he does not ask how we come to think such a relation, still less does he connect it with the perception of phenomenal antecedence; and his attacks on the various mental faculties assumed by psychologists pass over the fundamental postulate of personal identity, thus leaving Descartes what seemed a safe foundation whereon to rebuild the edifice of metaphysical philosophy.
