A Budget of Paradoxes, by Augustus De Morgan
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A Budget of Paradoxes, by Augustus De Morgan
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Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous From the introduction: "If I had before me a fly and an elephant, having never seen more than one such magnitude of either kind; and if the fly were to endeavor to persuade me that he was larger than the elephant, I might by possibility be placed in a difficulty. The apparently little creature might use such arguments about the effect of distance, and might appeal to such laws of sight and hearing as I, if unlearned in those things, might be unable wholly to reject. But if there were a thousand flies, all buzzing, to appearance, about the great creature; and, to a fly, declaring, each one for himself, that he was bigger than the quadruped; and all giving different and frequently contradictory reasons; and each one despising and opposing the reasons of the others—I should feel quite at my ease. I should certainly say, My little friends, the case of each one of you is destroyed by the rest. I intend to show flies in the swarm, with a few larger animals, for reasons to be given. In every age of the world there has been an established system, which has been opposed from time to time by isolated and dissentient reformers. The established system has sometimes fallen, slowly and gradually: it has either been upset by the rising influence of some one man, or it has been sapped by gradual change of opinion in the many. I have insisted on the isolated character of the dissentients, as an element of the a priori probabilities of the case. Show me a schism, especially a growing schism, and it is another thing. The homeopathists, for instance, shall be, if any one so think, as wrong as St. John Long; but an organized opposition, supported by the efforts of many acting in concert, appealing to common arguments and experience, with perpetual succession and a common seal, as the Queen says in the charter, is, be the merit of the schism what it may, a thing wholly different from the case of the isolated opponent in the mode of opposition to it which reason points out. During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true. Even in those sciences which are not yet under the dominion of mathematics, and perhaps never will be, a working copy of the mathematical process has been made. This is not known to the followers of those sciences who are not themselves mathematicians and who very often exalt their horns against the mathematics in consequence. They might as well be squaring the circle, for any sense they show in this particular."
A Budget of Paradoxes, by Augustus De Morgan- Published on: 2015-06-18
- Original language: English
- Dimensions: 9.00" h x 1.14" w x 6.00" l,
- Binding: Paperback
- 504 pages
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5 of 5 people found the following review helpful. Review of "A Budget of Paradoxes" By J. S. Hazelton I first ran across this book in a reference in one of Martin Gardiner's books, and ordered it knowing little about it.Augustus de Morgan was an English mathematician who lived from 1806-1871. He uses the term "paradox" to mean a person who has views or theories contrary to the established system, in a variety of fields, including mathematics, the sciences in general, religion, politics, etc.This book is a single paperback book containing both Volumes 1 and 2. This was originally published as two volumes in 1915. However, the material all dates from the 1860's and earlier, and Volume 1 was apparently published in that time.This book is about people as revealed in their books and letters. In most or all cases, these were books or pamphlets or letters which were in de Morgan's collection. They are taken in chronological order, meaning the subject will jump from geometry to atomic theory to religion and back again. Some are described in a few sentences or paragraphs, some in a page or two, and some run on for multiple pages.One of the more common themes is the squaring of the circle or the related question of the calculation of pi. It might be assumed that de Morgan would go into detail about the methods used, the errors introduced, refutation of the false ideas, etc. But this is a book mainly about people, and so you'll find a discussion of this or that person, and generally what their ideas were, but in most cases, not a detailed analysis of their work or their errors.A general understanding of mathematical and scientific principles is helpful when reading the work, although, as noted, it is not a book of math theorems. Fortunately, most of the French and Latin quotations have been translated by the editors.The value of the work seems to me to be threefold. First, it reviews a great number of works and people, many of which were obscure in their own day, and many of which would be impossible to find today. Secondly, it serves as a window into the 19th century (and earlier) world of math and science, the ways of thinking, and the relationships between different groups. Thirdly, de Morgan does have occasional real gems of humor or wording in his work, and what might be otherwise very dry writing is made considerably more interesting by his sense of humor.
3 of 3 people found the following review helpful. Bibiographical information By Dennis Des Chene The first edition is London: Longmans, Green, 1872. The second is from Open Court, 1915 with a preface by David Eugene Smith. The edition listed here is a mutilated version of 1915 (I think) minus the two prefaces of that edition (by Sophia de Morgan and Smith). Save your money and buy the Dover reprint of 1954, which has a nice preface by Ernst Nagel.
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