intellectual riches of the Greeks and Romans, but also the wonderful additions to the physical and mathematical sciences made since the revival of letters. In our time we possess an almost complete comprehension of many parts of physical science which seemed to Socrates, the wisest of men, beyond the powers of the human mind. We have before us an abundance of examples of the modes in which solid and undoubted truths may be attained, and it is absurd to suppose that among such successful exertions of the human intellect we can find no materials for a newer analytic of the mental operations. 3. The mathematics especially present the example of a great branch of abstract science, evolved almost wholly from the mind itself, in which the Greeks indeed excelled, but in which modern knowledge passes almost infinitely beyond their highest efforts. Intellects so lofty and acute as those of Euclid or Diophantus or Archimedes reached but the few first steps on the way to the widening generalizations of modern mathematicians; and what reason is there to suppose experiri et intendere vellet) majora multo quam a priscis temporibus expectari par est ; utpote ætate mundi grandiore, et infinitis experimentis et observationibus aucta et cumulata."-Novum Organum, Lib. i. Aphor. 84. that Aristotle, however great, should at a single bound have reached the highest generalizations of a closely kindred science of human thought? 4. Kant indeed was no intellectual slave, and it might well seem discouraging to logical speculators that he considered logic unimproved in his day since the time of Aristotle, and indeed declared that it could not be improved except in perspicuity. But his opinions have not prevented the improvement of logical doctrine, and are now effectually disproved. A succession of eminent men,-Jeremy Bentham, George Bentham, Sir William Hamilton, Professor De Morgan, Archbishop Thomson, and the late Dr. Boole,-have shown that in the operations and the laws of thought there is a wide and fertile area of investigation. Bentham did more than assert our freedom of inquiry; in his uncouth logical writings are to be found most original hints, and in editing his papers his nephew George Bentham pointed out the all-important key to a thorough logical reform, the quantification of the predicate.1 Sir William Hamilton, Archbishop Thomson, and Professor De Morgan rediscovered and developed the same new idea. Dr. Boole, lastly, employing this fundamental idea as his starting 1 See "Outline of a New System of Logic," by George Bentham, Esq., London, 1827, p. 133 et seq. point, worked out a mathematical system of logical inference of extraordinary originality. 5. Of the logical system of Mr. Boole Professor De Morgan has said in his "Budget of Paradoxes:"1 "I might legitimately have entered it among my paradoxes, or things counter to general opinion: but it is a paradox which, like that of Copernicus, excited admiration from its first appearance. That the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought, and to furnish the grammar and dictionary of an all-containing system of logic, would not have been believed until it was proved. When Hobbes, in the time of the Commonwealth, published his 'Computation or Logique,' he had a remote glimpse of some of the points which are placed in the light of day by Mr. Boole. The unity of the forms of thought in all the applications of reason, however remotely separated, will one day be matter of notoriety and common wonder; and Boole's name will be remembered in connexion with one of the most important steps towards the attainment of this knowledge." 6. I need hardly name Mr. Mill, because he has expressly disputed the utility and even the truthfulness of the reforms which I am considering, and 1 No. xxiii. Athenæum. has evolved most divergent opinions of his own. in a wholly different direction from the eminent men just mentioned. 7. In the lifetime of a generation still living the dull and ancient rule of authority has thus been shaken, and the immediate result is a perfect chaos of diverse and original speculations. Each logician has invented a logic of his own, so marked by peculiarities of his individual mind, and his customary studies, that no reader would at first suppose the same subject to be treated by all. Yet they treat of the same science, and, with the exception of Mr. Mill, they start from almost the same discovery in that science. Modern logic has thus become mystified by the diversity of views, and by the complication and profuseness of the formulæ invented by the different authors named. The quasi-mathematical methods of Dr. Boole especially are so mystical and abstruse, that they appear to pass beyond the comprehension and criticism of most other writers, and are calmly ignored. No inconsiderable part of a lifetime is indeed needed to master thoroughly the genius and tendency of all the recent English writings on Logic, and we can scarcely wonder that the plain and scanty outline of Aldrich, or the sensible but unoriginal elements of Whately, continue to be the guides of a logical student, while the works of De Morgan or of Boole are sealed books. 8. The nature of the great discovery alluded to, the quantification of the predicate, cannot be explained without introducing the technical terms of the science. A proposition, or judgment expressed in words, consists of a predicate or attribute united by a copula to a subject. In this proposition, All metals are elements, the predicate element is asserted of the subject metal, and the force of the assertion consists, as usually considered, in making the class of metals a part of the class of elements. The verb, or copula, are, denotes inclusion of the metals among the elements. But the subject only is quantified; for it is stated that all metals are elements, but it is not stated what proportion of the elements may be metals. Now the quantification of the predicate consists in giving some indication of the quantity or portion of the predicate really involved in the judgment. All metals are some elements is the same proposition thus quantified, and, though the change seems trifling, the consequences are momentous. The proposition no longer asserts |