This Online Corrected Edition was created by Kevin C. Klement; this is version 1.0 (January 31, 2010). It is based on the April 1920 so-called “second edition” published by Allen & Unwin, which, by contemporary standards, was simply a second printing of the original 1919 edition but incorporating various, mostly minor, fixes. This edition incorporates fixes from later printings as well, and some new fixes, mentioned below. The pagination of the Allen & Unwin edition is given in red, which is also used for other additions to the text not penned by Russell.
Thanks to members of the Russell-l and HEAPS-l mailing lists for help in checking and proofreading the version, including Adam Killian, Pierre Grenon, David Blitz, Brandon Young, Rosalind Carey, and, especially, John Ongley. A tremendous debt of thanks is owed to Kenneth Blackwell of the Bertrand Russell Archives/Research Centre, McMaster University, for proofreading the bulk of the edition, checking it against Russell’s handwritten manuscript, and providing other valuable advice and assistance. Another large debt of gratitude is owed to Christof Gräber who compared this version to the print versions and showed remarkable aptitude in spotting discrepancies. I take full responsibility for any remaining errors. If you discover any, please email me at klement <at> philos <dot> umass <dot> edu.
The online edition differs from the 1920 Allen & Unwin edition, and reprintings thereof, in certain respects. Some are mere stylistic differences. Others represent corrections based on discrepancies between Russell’s manuscript and the print edition, or fix small grammatical or typographical errors. The stylistic differences are these:
The original uses footnotes, with numbering that begins anew with each page. For this version it was necessary to switch to endnotes at the end of each chapter, numbered sequentially through the chapter. Thus, for example, the footnote listed as note 2 for chapter I of this edition was listed as note 1 on page 5 of the original.
With some exceptions, the Allen & Unwin edition uses vertical fractions, with the numerator over the denominator, in displays, but horizontal fractions of the form “x/y” mid-paragraph. This version uses horizontal fractions everywhere, which is how Russell wrote them.
The following more significant changes and revisions are marked in green in this edition. Most of these result from Ken Blackwell’s comparison with the manuscript. A few were originally noted in an early review of the book by G. A. Pfeiffer (Bulletin of the American Mathematical Society 27:2 (1920), pp. 81–90).
(chapter I, footnote 1) Russell wrote the wrong publication date (1911) for the second volume of Principia Mathematica; this has been fixed to 1912.
(page 21) “… or all that are less than 1000 …” is changed to “… or all that are not less than 1000 …” to match Russell’s manuscript and the obviously intended meaning of the passage. This error was noted by Pfeiffer in 1920 but unfixed in Russell’s lifetime.
(page 43) “… either by limiting the domain to males or by limiting the converse to females” is changed to “… either by limiting the domain to males or by limiting the converse domain to females”, which is how it read in Russell’s manuscript, and seems better to fit the context.
(page 64) “… provided neither m or n is zero.” is fixed to “… provided neither m nor n is zero.” Thanks to John Ongley for spotting this error, which exists even in Russell’s manuscript.
(chapter VIII, note 2) The word “deutschen” in the original’s (and the manuscript’s) “Jahresbericht der deutschen Mathematiker-Vereinigung” has been capitalized.
(page 98) “… of a class α, i.e. its limits or maximum, and then …” is changed to “… of a class α, i.e. its limit or maximum, and then …” to match Russell’s manuscript, and the apparent meaning of the passage.
(page 110) “… the limit of its value for approaches either from …” is changed to “… the limit of its values for approaches either from …”, which matches Russell’s manuscript, and is more appropriate for the meaning of the passage.
(page 113) The ungrammatical “… advantages of this form of definition is that it analyses …” is changed to “… advantage of this form of definition is that it analyses …” to match Russell’s manuscript.
(page 115) “… all terms z such that x has the relation P to x and z has the relation P to y …” is fixed to “… all terms z such that x has the relation P to z and z has the relation P to y …” Russell himself hand-corrected this in his manuscript, but not in a clear way, and at his request, it was changed in the 1967 printing.
(page 124) The words “correlator of α with β, and similarly for every other pair. This requires a”, which constitute exactly one line of Russell’s manuscript, were omitted, thereby amalgamating two sentences into one. The missing words are now restored.
(page 129) The passage “… if x1 is the member of y1, x2 is a member of y2, x3 is a member of y3, and so on; then …” is changed to “… if x1 is the member of γ1, x2 is a member of γ2, x3 is a member of γ3, and so on; then …” to match Russell’s manuscript, and the obviously intended meaning of the passage.
(page 139) The words “and then the idea of the idea of Socrates” although present in Russell’s manuscript, were left out of previous print editions. Note that Russell mentions “all these ideas” in the next sentence.
(page 160) The two footnotes on this page were misplaced. The second, the reference to Principia Mathematica *9, was attached in previous versions to the sentence that now refers to the first footnote in the chapter. That footnote was placed three sentences below. The footnote references have been returned to where they had been placed in Russell’s manuscript.
(page 161) “… the negation of propositions of the type to which x belongs …” is changed to “… the negation of propositions of the type to which φx belongs …” to match Russell’s manuscript. This is another error noted by Pfeiffer.
(page 162) “Suppose we are considering all “men are mortal”: we will …” is changed to “Suppose we are considering “all men are mortal”: we will …” to match the obviously intended meaning of the passage, and the placement of the opening quotation mark in Russell’s manuscript (although he here used single quotation marks, as he did sporadically throughout). Thanks to Christof Gräber for spotting this error.
(page 173) “… as opposed to specific man.” is fixed to “… as opposed to specific men.” Russell sent this change to Unwin in 1937, and it was made in the 1938 printing.
(page 175) The “φ” in “… the process of applying general statements about φx to particular cases …”, present in Russell’s manuscript, was excluded from the Allen & Unwin printings, and has been restored.
(page 176) The “φ” in “… resulting from a propositional function φx by the substitution of …” was excluded from previous published versions, though it does appear in Russell’s manuscript, and seems necessary for the passage to make sense. Thanks to John Ongley for spotting this error, which had also been noted by Pfeiffer.
(pages 186–87) The two occurrences of “φ” in “… extensional functions of a function φx may, for practical purposes, be regarded as functions of the class determined by φx, while intensional functions cannot …” were omitted from previous published versions, but do appear in Russell’s manuscript. Again thanks to John Ongley.
(page 189) The Allen & Unwin printings have the sentence as “How shall we define a “typical” Frenchman?” Here, the closing quotation mark has been moved to make it “How shall we define a “typical Frenchman”?” Although Russell’s manuscript is not entirely clear here, it appears the latter was intended, and it also seems to make more sense in context.
(page 191) “There is a type (r say) …” has been changed to “There is a type (τ say) …” to match Russell’s manuscript, and conventions followed elsewhere in the chapter.
(page 195) “… divided into numbers of separate studies …” has been changed to “… divided into a number of separate studies …” Russell’s manuscript just had “number”, in the singular, without a definite article. Some change was necessary to make the passage grammatical, but the fix adopted here seems more likely what was meant.
(page 197) The passage “the propositional function ‘if all α’s are β and x is an α, then x is a β’ is always true” has been changed to “the propositional function ‘if all α’s are β’s and x is an α, then x is a β’ is always true” to match Russell’s manuscript, as well as to make it consistent with the other paraphrase given earlier in the sentence. Thanks to Christof Gräber for noticing this error.
(page 200) “… without any special word for forms …” is changed to “… without any special words for forms …”, which matches Russell’s manuscript and seems to fit better in the context.
(page 207) The original index listed a reference to Frege on page 10, but in fact, the discussion of Frege occurs on page 11. Here, “10” is crossed out, and “[11]” inserted.
Some very minor corrections to punctuation have been made to the Allen & Unwin 1920 printing, but not marked in green.
Ellipses have been regularized to three closed dots throughout.
(page 53) “We may define two relations …” did not start a new paragraph in previous editions, but does in Russell’s manuscript, and is changed to do so.
(page 53) What appears in the 1920 and later printings as “… is the field of Q. and which is …” is changed to “… is the field of Q, and which is …”
(page 56) “… a relation number is a class of …” is changed to “… a relation-number is a class of …” to match the hyphenation in the rest of the book (and in Russell’s manuscript). A similar change is made in the index.
(page 60) “… and “featherless biped,”—so two …” is changed to “… and “featherless biped”—so two …”
(pages 82–83) One misprint of “progession” for “progression”, and one misprint of “progessions” for “progressions”, have been corrected. (Thanks to Christof Gräber for noticing these errors in the original.)
(page 115) In the Allen & Unwin printing, the “s” in “y’s” in what appears here as “Form all such sections for all y’s …” was italicized along with the “y”. Nothing in Russell’s manuscript suggests it should be italicized, however. (Again thanks to Christof Gräber.)
(page 121) In the Allen & Unwin printing, “Let y be a member of β …” begins a new paragraph, but it does not in Russell’s manuscript, and clearly should not.
(pages 129–130) The phrase “well ordered” has twice been changed to “well-ordered” to match Russell’s manuscript (in the first case) and the rest of the book (in the second).
(page 131) “The way in which the need for this axiom arises may be explained as follows:—One of Peano’s …” is changed to “The way in which the need for this axiom arises may be explained as follows. One of Peano’s …” and has been made to start a new paragraph, as it did in Russell’s manuscript.
(page 137) The accent on “Métaphysique”, included in Russell’s manuscript but left off in print, has been restored.
(page 159) “… or what not,—and clearly …” is changed to “… or what not—and clearly …”
(page 176) Italics have been added to one occurrence of “Waverley” to make it consistent with the others.
(page 185) “… most difficult of fulfilment,—it must …” is changed to “… most difficult of fulfilment—it must …”
(page 197) In the Allen & Unwin printings, “Socrates” was not italicized in “… we may substitute α for men, β for mortals, and x for Socrates, where …” Russell had marked it for italicizing in the manuscript, and it seems natural to do so for the sake of consistency, so it has been italicized.
(page 205) The word “seem” was not italicized in “… a definition which might seem satisfactory for a while …” in the Allen & Unwin editions, but was marked to be in Russell’s manuscript. It is italicized here.
(page 208) Under “Relations” in the index, “similar, 52ff;” has been changed to “similar, 52ff.;” to match the punctuation elsewhere.
There are, however, a number of other places where the previous print editions differ from Russell’s manuscript in minor ways that were left unchanged in this edition. For a detailed listing of the differences between Russell’s manuscript and the print editions, and between the various printings themselves (including the changes from the 1919 to the 1920 printings not documented here), see Kenneth Blackwell, “Variants, Misprints and a Bibliographical Index for Introduction to Mathematical Philosophy”, Russell n.s. 29 (2009): 57–62.
Bertrand Russell’s Introduction to Mathematical Philosophy is in the Public Domain.
This typesetting (including HTML code) and list of changes are licensed under a Creative Commons Attribution—Share Alike 3.0 United States License.