Overview

General Books publication date: 2009 Original publication date: 1881 Original Publisher: Macmillan Subjects: Logic, Symbolic and mathematical Logic Mathematics / Logic Philosophy / General Philosophy / Logic Notes: This is a black and white OCR reprint of the original. It has no illustrations and there may be typos or missing text. When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. Excerpt: CHAPTER III. SYMBOLS OF OPERATIONS (CONTINUED). THE INVERSE OPERATION, -y j OR SYMBOLS OP DIVISION. We have now seen our way clearly enough to the performance, and symbolic expression, of three distinct logical operations upon classes, viz.: -- 1. A direct operation closely analogous to the addition of ordinary arithmetic and algebra, and suitably symbolized by the familiar sign (]). 2. The inverse operation to the above, and therefore closely analogous to subtraction, and which may be suitably symbolized by the sign ( -- ). 3. A direct operation very remotely analogous to multiplication, and which we have seen could (with one restriction in respect of usage) be expressed by the usual signs for that process, viz. (x) or simple juxtaposition of the terms. The question therefore at once suggests itself whether there may not be a fourth operation which shall be the inverse of the third, as the second was of the first. This suggestion, it must be admitted, comes to us rather by way of the symbols than by way of the actual logical process itself. In this it is unlike the first three. As regards them we saw that it was quite impossible to think and speak about classes of objects without having these three operations forced upon our notice: in fact, they are so familiar to us that our trouble arises rather from a confusing redundancy, than from any lack, of phrases to express them. The symbols are therefore an afterthought to express results and operations to w...

Full Product Details

9781375463829

Table of Contents

Reviews

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available