Transcriber’s Note:
The cover image was created by the transcriber and is placed in the public domain.
⁂ This Tract contains no more than the author has found, fromexperience, to be much wanted by students who are commencingwith Euclid. It will ultimately form an Appendix to his Treatise onArithmetic.
The author would not, by any means, in presenting the minimumnecessary for a particular purpose, be held to imply that he has givenenough of the subject for all the ends of education. He has long regrettedthe neglect of logic; a science, the study of which would shewmany of its opponents that the light esteem in which they hold it arisesfrom those habits of inference which thrive best in its absence. Hestrongly recommends any student to whom this tract may be the firstintroduction of the subject, to pursue it to a much greater extent.
University College, Jan, 8, 1839.
What we here mean by Logic is the examination of that part ofreasoning which depends upon the manner in which inferences areformed, and the investigation of general maxims and rules for constructingarguments, so that the conclusion may contain no inaccuracywhich was not previously asserted in the premises. It has nothing todo with the truth of the facts, opinions, or presumptions, from which aninference is derived; but simply takes care that the inference shallcertainly be true, if the premises be true. Thus, when we say that allmen will die, and that all men are rational beings, and thence infer thatsome rational beings will die, the logical truth of this sentence is thesame whether it be true or false that men are mortal and rational. Thislogical truth depends upon the structure of the sentence, and not on theparticular 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. |
The second of these is the same proposition, logically considered, as thefirst; the consequence in both is virtually contained in, and r