FIRST NOTIONS OF LOGIC (PREPARATORY TO THE STUDY OF GEOMETRY) BY AUGUSTUS DE MORGAN, OF TRINITY COLLEGE, CAMBRIDGE, PROFESSOR OF MATHEMATICS IN UNIVERSITY COLLEGE, LONDON. The root of all the mischief in the sciences, is this; that falsely magnifying and admiring the powers of the mind, we seek not its real helps.—BACON. LONDON: PRINTED FOR TAYLOR AND WALTON, BOOKSELLERS AND PUBLISHERS TO UNIVERSITY COLLEGE. 28 UPPER GOWER STREET. M.DCCC.XXXIX. ⁂ This Tract contains no more than the author has found, from experience, to be much wanted by students who are commencing with Euclid. It will ultimately form an Appendix to his Treatise on Arithmetic. The author would not, by any means, in presenting the minimum necessary for a particular purpose, be held to imply that he has given enough of the subject for all the ends of education. He has long regretted the neglect of logic; a science, the study of which would shew many of its opponents that the light esteem in which they hold it arises from those habits of inference which thrive best in its absence. He strongly recommends any student to whom this tract may be the first introduction of the subject, to pursue it to a much greater extent. _University College, Jan, 8, 1839._ LONDON:—PRINTED BY JAMES MOYES, Castle Street, Leicester Square. FIRST NOTIONS OF LOGIC. What we here mean by Logic is the examination of that part of reasoning which depends upon the manner in which inferences are formed, and the investigation of general maxims and rules for constructing arguments, so that the conclusion may contain no inaccuracy which was not previously asserted in the premises. It has nothing to do with the truth of the facts, opinions, or presumptions, from which an inference is derived; but simply takes care that the inference shall certainly be true, if the premises be true. Thus, when we say that all men will die, and that all men are rational beings, and thence infer that some rational beings will die, the _logical_ truth of this sentence is the same whether it be true or false that men are mortal and rational. This logical truth depends upon the structure of the sentence, and not on the particular matters spoken of. Thus, Instead of, Write, All men will die. Every A is B. All men are rational beings. Every A is C. Therefore some rational beings will die. Therefore some Cs are Bs.