ties which were first fully solved by De Morgan. The theory of the purely ' relative ' nature of space, the refusal to distinguish between primary and secondary qualities, seems to reduce all mathematical theorems to the level of empirical propositions. Geometrical properties are inferred from the pro- perties of particular figures. This doctrine, worked out by Hume, led to Kant's famous theory of space and time, in which the reality and a priori necessity of mathematical propositions are made to follow from the assumption that space and time are forms imposed by the mind upon experience instead of being qualities of external and independent objects. Berkeley seems scarcely to appreciate the difficulties of his position ; as, indeed, he represents a brilliant appreciation of one aspect rather than a systematic elaboration. This is equally apparent in his theological application. According to him his theory demonstrates immediately the existence of a divine mind, 'in whom we live, move, and have our being' (Principles, § 61). The existence of such a mind follows, first, as solving the obvious difficulty, that upon his theory evervthing ceases to exist when it ceases to be present to consciousness, to which he replies that it still exists as perceived by the supreme mind ; and, secondly, because ideas being in their nature passive, and what we call causation being merely the arbitrary connection of sign and thing signified, we must assume the existence of a supreme cause which speaks to us through this divine language. Hume implicitly replies by denying the existence of any such idea of power as Berkeley postulates, and argues that the difficulties inherent in Berkeley's matter may be retorted against his mind and spirit. Berkeley replies to this by anticipation that, although we have not properly an 'idea' (in his sense) of spirit, we have a 'notion,' as of that which has ideas and wills and reasons about them, and infer the existence of other spirits from our own.
Berkeley never developed his philosophy beyond these early works. The ' Alciphron ' contains a restatement of the main principles, and an assertion of the ordinary arguments against deists, containing the ethical view of utilitarian theologians with no special originality. The ' Siris ' is a reverie rather than an argument, showing that the speculations of the later Platonists were congenial to his temperament, but not giving a philosophical elaboration of the position. Historically Berkeley, as a link between Locke and Hume, led to scepticism, and was controverted upon that assumption by Reid and his followers. In assaulting matter he seemed to destroy reality. But it is possible, with Professor Fraser, to hold that the real tendency of his works was, as he never doubted, in favour of the doctrine which makes mind the ultimate reality, and thus of the more systematic idealism of later times.
Berkeley's works, as given by Professor Fraser, are : 1. 'Arithmetica abeque Algebra aut Euclide demonstrata ;' 2. 'Miscellanea Mathematica' (published together anonymously at Dublin in 1707). 3. 'Essay towards a New Theory of Vision,' 1709 (a second edition with an appendix in the same year, a third appended to 'Alciphron' in 1732). 4. 'Treatise concerning the Principles of Human Knowledge,' 'Part I.' 1710; translation, 1869. 5. 'Passive Obedience, ... a Discourse delivered at the College Chapel,' 1712 (second edition, 1712; third, 1713). 6. 'Three Dialogues between Hylas and Philonous,' 1713 (second edition, 1725; third and fourth with second and third of the 'Principles,' as above) ; French, 1750 (Amsterdam) ; German (Rostock), 1756 ; German (Leipzig), 1781 (part of an intended version of 'Works'). 7. Essavs in the 'Guardian,' 1713 (Nos. 3, 27, 85, 39, 49, 55, 62, 69, 70, 77, 83, 88, 89, and 126 are ascribed to him from 14 March to 15 Aug. 1713). 8. 'De Motu,' 1721. 9. 'An Essay towards preventing the Ruin of Great Britain,' 1721. 10. 'A Proposal for the better supplying of Churches in our Foreign Plantations ... by a College to be erected in ... Bermuda,' 1725. 11. 'Sermon before the Society for the Propagation of the Gospel,' 1732. 12. 'Alciphron, or the Minute Philosopher,' 1732 (two editions; a third in 1752, collated in 'Works,' vol. ii.); French, 1734; German, 1737. 13. 'Theory of Vision ... vindicated and explained,' 1733 (an annotated edition by V. H. Cowell in 1800). 14. 'The Analyst, or a Discourse addressed to an Infidel Mathematician, &c.,' 1734. 15. 'A Defence of Free-thinking in Mathematics,' 1735. 16. 'Reasons for not Replying to Mr. Walton's Full Answer,' 1735. 17. 'The Querist,' Part I. 1735, Part II. 1736, Part IV. 1737 (second edition with an advertisement by the author, 1750; reprint in Glasgow, 1751. An edition was published in London in 1829. The queries omitted in the first edition are reprinted at the end of the ' Works,' vol. iii.) 18. 'A Discourse addressed to Magistrates,' 1736 and 1738. 19. ' [Siris, a chain of] Philosophical Reflections and Inquiries concerning the Virtues of Tar-water, &c.' (three editions in 1744, others in 1746 and 1748 ; the title ' Siris ' first added in second edition). 20. 'Three
