a separate form-with what advantage, the reader of course will judge. The well-instructed student of mathematics, of logic, of the nature and theory of language, and of what is called moral evidence, will be apt to remark at the close of the work, that it makes no specific addition to the amount of his knowledge. But if the views presented even to him be admitted to be correct as far as they go; if some thoughts are here conveniently brought together which must at least be sought for in widely-scattered sources; if they have the good effect of awakening the attention of the less profound to important points connected with the subject before him, hitherto overlooked; if they suggest or stimulate inquiries worthy of continuance,—the publication will not be in vain. Much use has been made of the sentiments of others, so as to form a sort of philosophical discussion in which many authors are made to speak for themselves. But an ample apology for this, if one be necessary, will be found in the words of Dr. Law in his preface to the translation of Dr. King's Essay on the Origin of Evil: "A writer often does more good by showing the use of some of those many volumes which we have already, than by offering new ones, though this be of much less advantage to his own character. I determined therefore not to say anything myself where I could bring another conveniently to say it for me; and transcribed only so much from others as was judged absolutely necessary to give the reader a short view of thể subject, and by that sketch to induce those who have leisure, opportunity, and inclination to go further and consult the originals, and to afford some present satisfaction to those who have not. "But how judiciously this is performed, the notes themselves must testify." CONTENTS. Mathematical reasoning sets out from definitions These definitions settle the meaning of terms These terms, signs of ideas of figure and quantity— ideas originating in sensible impressions Mathematical reasoning supported by diagrams, or Mr. Whewell's language on experience as the source of mathematical conceptions, criticised Page. The connexion between language and reasoning in Approach to mathematical exactness in metaphysical Distinction between mathematics which commence, and inquiries which end, with definitions |