A BUDGET OF
PARADOXES

REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM

SECOND EDITION EDITED BY DAVID EUGENE SMITH

WITH A NEW INTRODUCTION BY ERNEST NAGEL

PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY

UNABRIDGED EDITION—TWO VOLUMES BOUND AS ONE

Volume I

DOVER PUBLICATIONS, INC., NEW YORK

PREFACE TO THE FIRST EDITION.

(1872)

It is not without hesitation that I have taken upon myself the editorship of a work left avowedly imperfect by the author, and, from its miscellaneous and discursive character, difficult of completion with due regard to editorial limitations by a less able hand.

Had the author lived to carry out his purpose he would have looked through his Budget again, amplifying and probably rearranging some of its contents. He had collected materials for further illustration of Paradox of the kind treated of in this book; and he meant to write a second part, in which the contradictions and inconsistencies of orthodox learning would have been subjected to the same scrutiny and castigation as heterodox ignorance had already received.

It will be seen that the present volume contains more than the Athenæum Budget. Some of the additions formed a Supplement to the original articles. These supplementary paragraphs were, by the author, placed after those to which they respectively referred, being distinguished from the rest of the text by brackets. I have omitted these brackets as useless, except where they were needed to indicate subsequent writing.

Another and a larger portion of the work consists of discussion of matters of contemporary interest, for the Budget was in some degree a receptacle for the author's thoughts on any literary, scientific, or social question. Having grown thus gradually to its present size, the book as it was left was not quite in a fit condition for publication, but the alterations which have been made are slight and few, being in most cases verbal, and such as the sense absolutely required, or transpositions of sentences to secure coherence with the rest, in places where the author, in his more recent insertion of them, had overlooked the connection in which they stood. In no case has the meaning been in any degree modified or interfered with.

One rather large omission must be mentioned here. It is an account of the quarrel between Sir James South and Mr. Troughton on the mounting, etc. of the equatorial telescope at Campden Hill. At some future time when the affair has passed entirely out of the memory of living Astronomers, the appreciative sketch, which is omitted in this edition of the Budget, will be an interesting piece of history and study of character.^[1]

A very small portion of Mr. James Smith's circle-squaring has been left out, with a still smaller portion of Mr. De Morgan's answers to that Cyclometrical Paradoxer.

In more than one place repetitions, which would have disappeared under the author's revision, have been allowed to remain, because they could not have been taken away without leaving a hiatus, not easy to fill up without damage to the author's meaning.

I give these explanations in obedience to the rules laid down for the guidance of editors at page 15.^[2] If any apology for the fragmentary character of the book be thought necessary, it may be found in the author's own words at page 281 of the second volume.^[3]

The publication of the Budget could not have been delayed without lessening the interest attaching to the writer's thoughts upon questions of our own day. I trust that, incomplete as the work is compared with what it might have been, I shall not be held mistaken in giving it to the world. Rather let me hope that it will be welcomed as an old friend returning under great disadvantages, but bringing a pleasant remembrance of the amusement which its weekly appearance in the Athenæum gave to both writer and reader.

The Paradoxes are dealt with in chronological order. This will be a guide to the reader, and with the alphabetical Index of Names, etc., will, I trust, obviate all difficulty of reference.

Sophia De Morgan.

6 Merton Road, Primrose Hill.

PREFACE TO THE SECOND EDITION.

If Mrs. De Morgan felt called upon to confess her hesitation at taking upon herself the labor of editing these Paradoxes, much more should one who was born two generations later, who lives in another land and who was reared amid different influences, confess to the same feeling when undertaking to revise this curious medley. But when we consider the nature of the work, the fact that its present rarity deprives so many readers of the enjoyment of its delicious satire, and the further fact that allusions that were commonplace a half century ago are now forgotten, it is evident that some one should take up the work and perform it con amore.

Having long been an admirer of De Morgan, having continued his work in the bibliography of early arithmetics, and having worked in his library among the books of which he was so fond, it is possible that the present editor, whatever may be his other shortcomings, may undertake the labor with as much of sympathy as any one who is in a position to perform it. With this thought in mind, two definite rules were laid down at the beginning of the task: (1) That no alteration in the text should be made, save in slightly modernizing spelling and punctuation and in the case of manifest typographical errors; (2) That whenever a note appeared it should show at once its authorship, to the end that the material of the original edition might appear intact.

In considering, however, the unbroken sequence of items that form the Budget, it seems clear that readers would be greatly aided if the various leading topics were separated in some convenient manner. After considerable thought it was decided to insert brief captions from time to time that might aid the eye in selecting the larger subjects of the text. In some parts of the work these could easily be taken from the original folio heads, but usually they had to be written anew. While, therefore, the present editor accepts the responsibility for the captions of the various subdivisions, he has endeavored to insert them in harmony with the original text.

As to the footnotes, the first edition had only a few, some due to De Morgan himself and others to Mrs. De Morgan. In the present edition those due to the former are signed A. De M., and those due to Mrs. De Morgan appear with her initials, S. E. De M. For all other footnotes the present editor is responsible. In preparing them the effort has been made to elucidate the text by supplying such information as the casual reader might wish as he passes over the pages. Hundreds of names are referred to in the text that were more or less known in England half a century ago, but are now forgotten there and were never familiar elsewhere. Many books that were then current have now passed out of memory, and much that agitated England in De