When many things are thought of in one way, which way is neither governed nor modified by the difference between one thing and another, there is a common form of thought about distinct matter& Thus arithmetic is a formal science with reference to concrete magnitude : that 8 and 4 make the same as 4 and 8 is a form, a law of thought, which is not affected by the objects counted being yards rather than sheep, or pints rather than men. Pass into algebra, and the difference which are formal in arithmetic become only material : thus 8 +4=4 + 8 is but one material Instance of the form a + b=b + a. Are we there. fore to say that arithmetic and algebra are parts of logic ? Certainly not : logio deals with the pure form of thought, divested of every possible distinction of matter. There is a form of thought iu the above which is not even confined to number, and not even confined to magnitude : namely, that the manner in which we think of part and whole, in every possible case in which these words can apply, is wholly independent of the order in which the parts are considered as coming together. For example, the notions animal and rational are joined together in the mind when ws think of man, but by a mode of junction very different from that called addition in arithmetic. Never theless, it matters nothing as to the notion arrived at whether we think of animal as subsequently limited by the notion rational, or of rptiona/ as subsequently limited by the notion animal. The pure form of thought is that win& belongs equally to the last instance and to 8+ 4 = 4 + 8 ; different matters, different modes of junction, under the common law that order of junction is indifferent.
We now set down the titles of various works of recent publication, and not difficult to obtain, being works which may all be recommended to the student who wishes to go fully into existing controversies, both as sources in themselves and as guides to others.
Paris, 1839-44, 4 vols. 8vo : Barthelemy St. Hilaire, Logique d'Aristote; a translation of the Organon' of Aristotle, with notes. Paris, 1838, 2 'vols. 8vo : Barthelemy St. Hilaire, De Is Logique d'Aristote,' a description of the Organon ' which gained the prize of the Institute. London, 1853, 2 vols. 8vo : O. F. Owen, The Organen of Aristotle,' an English translation. London, 1857, 8vo : J. H. MIlahon, The Metaphysics of Aristotle,' an English translation. Berlin, 1842, 8vo : F. A. Trendelenberg, Elements Logices Aristotelien; extracts from Aristotle, translated in the article Oiroesrosr, and notes. Edin burgh, 1854, I2mo : T. S. Baynes, ' The Port Royal Logic,' a translation from the French, with notes. Paris, 1840, 8vo : J. Tissot, Logique de E. Kant,' a translation highly spoken of. There is an English translation of Kant's Logic, not easily got, by T. Richardson, London, 1819, 8vo, collected with some other translations from Kant, under a title-page of 1836. London, 1851, 2 vols. 8vo (3rd edition, one or more since) : John S. Mill, System of Logic, ratiocinative and inductive, being a connected view of the principles of evidence and the methods of scientific investigation;' a great and widely known work, which takes logic in the fullest extent of meaning : we think Mr. Mill would have
done more justice to himself, and given a better notion of his subject, if he had taken a more descriptive title ; the words which follow " Logic " are of no use, for the book will be " Mill's Logic" all the world over._ With this work, and in reference to a large part of its contents, may be read Dr. Whewell's writings on philosophical method and history, especially London, 1858, 8vo, ' Novum Organum Reno vatum,' and London, 1860, 8vo, The Philosophy of Discovery.' The `Novum Organum' of Bacon himself, not to speak of the recent edition (Longman) of Leslie Ellis and others, which is a magnificent perform ance, may he easily and cheaply obtained in-London, 1853, 8vo, J. Devey, The Physical and Metaphysical Works of Lord Bacon,' Edinburgh, 1850, 8vo : T. S. Baynes,' The New Analytic of Logical Forms,' a prize essay, the first treatise on Sir W. Hamilton's system, with a note by Hamilton himself. Loudon, 1853, 8vo, 2nd edition : • Wm. Hamilton, Discussions on Philosophy, &c.; already mentioned. There is a writing of Sir W. Hamilton which, from its ephemeral character, may be forgotten, but which is very characteristic of the author, and contains logical discussion of permanent value; London and Edinburgh, 1847, 8vo : A Letter to A. De Morgan, Esq., on his claim" to an independent re-discovery of a new Principle in the Theory of Syllogism.' The prospectus of Hamilton's work on logic, which he did not live to complete, attached to this writing and to others, should not be forgotten. • Edinburgh, 1858, 8vo : A. C. Fraser, ' Rational Philosophy in History and in System,' the programme of Sir W. Hamilton a successor, who was further known by-Edinburgh, 1856, 8vo, Essays in Philosophy,' a collection of reviews on philosophical subjects, from the ' North British Review.' Of Whately's Logic, already mentioned, there are many editions ; and the same of Dr. Watts's Logic,• an old and well-known work, which deserved much higher praise than it received.
Oxford, 1856, 8vo, 3rd edition : H. L. Mansol, Artis Logical Rudi ments; an edition of the old and celebrated compendium of Aldrich, with copious English notes ; the easiest and beat way in which a body of discussion on the old logic can be read. Oxford, 1851, Hr L. Manse', Prolegomena Logics,' an inquiry into the. psychological character of logical processes, a most acute work, opposed to all the views of this article. The same writer's article on Metaphysics iu the new edition of the Encyclopndia Britannica (vol. xiv., 1857) will be very useful in conjunction with the ' Prolegomena.' London, 1857, 8vo : W. Thomson, ' An Outline of the Necessary Laws of Thought, a treatise on pure and applied logic ; valuable by thought, brevity, eclectic character, and extent of plan. Oxford, 1850, 8vo : E. Poste, The Logic of Science,' a translation of the Posterior Aualytics of Aris totle, with notes. Oxford, 1848, 8vo : C. P. Chretien, ' An Essay on Logical Method.' Oxford, 1851, 2 vols. (or books) 8vo: W. H. Karslake, Aids to the Study of Logic.' These works are all highly and justly commended by Sir W. Hamilton.