Boole's mathematical system of Logic appear to develop themselves as most plain and evident consequences of the self-same process of substitution, when applied to the Primary Laws of Thought. Should my notion be true, a vast mass of technicalities may be swept from our logical text-books, and yet the small remaining part of logical doctrine will prove far more useful than all the learning of the Schoolmen. CONTENTS. MATHEMATICAL AXIOMS OF EQUALITY GENERAL FORMULA OF MATHEMATICAL INFERENCE SUBSTITUTION OF EQUALS OR SIMILARS GENERAL FORMULA OF LOGICAL INFERENCE EXAMPLES OF LOGICAL SUBSTITUTION, NEGATIVE TERMS AND MOODS OF THE SYLLOGISM THE CONTRAPOSITIVE PROPOSITION THE INDIRECT METHOD OF INFERENCE MR. MILL ON THE QUANTIFICATION OF THE PREDICATE DR. THOMSON'S SYLLOGISM OF ANALOGY THE LOGICAL AND MATHEMATICAL CANONS. BACON'S REMARKS ON THEIR ANALOGY бо THE SUBSTITUTION OF SIMILARS, THE TRUE PRINCIPLE OF REASONING. ARISTOTLE is, perhaps, the greatest of human authors, but we may apply to him the words of Bacon, "Let great authors have their due, as Time, the author of authors, be not deprived of his due, which is farther and farther to discover truth." Aristotle has had his due in the obedience of more than twenty centuries, and Time must not be deprived of his due. Men, whose birthright is the increasing result of reason, are not to be bound for ever by the dictum of a thinker who lived but a little after the dawn of scientific thought. We are not to be persuaded any longer to look upon the highest of the sciences as a dead science. Logic is the science of the laws of thought itself, and there is no sphere of observation and reflection which is more peculiarly open to any inquirer, than B the inquirer's own mind as engaged in the process of reasoning. It is from reflection on the operations of his own mind that Aristotle must have drawn the materials of his memorable Analytics. But Bentham's mind, as he himself remarked, was equally open to Bentham, and it would be slavery indeed if any dictum of the first of logicians were to deprive all his successors of the liberty of inquiry. 1 2. It may be said, perhaps, that the weaker cannot possibly push beyond the stronger, and it is willingly allowed that among us moderns can few or none be found to equal in individual strength of intellect the great men of old. But Time is on our side. Though we reverence them as the ancients, they really lived in the childhood of the human race, and these times are, as Bacon would have said, the ancient times. We enjoy not only the best 1 "Essay on Logic," Bentham's works, vol. viii. p. 218. 2 "De antiquitate autem, opinio quam homines de ipsa fovent, negligens omnino est, et vix verbo ipsi congrua. Mundi enim senium et grandævitas pro antiquitate vere habenda sunt; quæ temporibus nostris tribui debent, non juniori ætati mundi, qualis apud antiquos fuit. Illa enim ætas respectu nostri, antiqua et major; respectu mundi ipsius, nova et minor fuit. Atque revera quemadmodum majorem rerum humanarum notitiam, et maturius judicium, ab homine sene expectamus, quam a juvene, propter experientiam, et rerum quas vidit et audivit, et cogitavit, varietatem et copiam; eodem modo et à nostra ætate (si vires suas nosset, et |