The Calculus of Logic by George Boole, is part of the HackerNoon Books Series. You can jump to any chapter in this book . On Syllogism. here On Syllogism. The forms of categorical propositions already deduced are the two first of which are similarly convertible into If now the two premises of any syllogism are expressed by equations of the above forms, the elimination of the common symbol will lead us to an equation expressive of the conclusion. y the elimination of gives y the interpretation of which is the elimination of gives y which is interpretable into Some Zs are Xs. It is always necessary that one term of the conclusion should be interpretable by means of the equations of the premises. In the above case both are so. Instead of directly eliminating let either equation be transformed by solution as in (19). The first gives y the interpretation of which is No Zs are Xs. Had we directly eliminated we should have had y, the reduced solution of which is in which is an arbitrary elective symbol. This exactly agrees with the former result. w These examples may suffice to illustrate the employment of the method in particular instances. But its applicability to the demonstration of general theorems is here, as in other cases, a more important feature. I subjoin the results of a recent investigation of the Laws of Syllogism. While those results are characterized by great simplicity and bear, indeed, little trace of their mathematical origin, it would, I conceive, have been very difficult to arrive at them by the examination and comparison of particular cases. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. George Boole (2022). The calculus of logic. Urbana, Illinois: Project Gutenberg. Retrieved October 2022 https://www.gutenberg.org/cache/epub/69512/pg69512-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

Laws of Syllogism deduced from the Elective Calculus.

General Solution of Elective Equations.

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