On Syllogism.

Written by georgeboole | Published 2023/10/31
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TLDRThese 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.via the TL;DR App

The Calculus of Logic by George Boole, is part of the HackerNoon Books Series. You can jump to any chapter in this book here. On Syllogism.

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 symboly will lead us to an equation expressive of the conclusion.

the elimination of y gives

the interpretation of which is


the elimination of y gives

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 y let either equation be transformed by solution as in (19). The first gives

the interpretation of which is

No Zs are Xs.

Had we directly eliminated y, we should have had

the reduced solution of which is


in which w is an arbitrary elective symbol. This exactly agrees with the former result.

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.


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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

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Written by georgeboole | George Boole: Self-taught English mathematician and first math professor at Queen's College, Cork.
Published by HackerNoon on 2023/10/31