D ocuments

 

 

RUSSELL’S CORRECTED PAGE PROOFS OF PRINCIPIA MATHEMATICA

 

Bernard Linsky

Philosophy, U. of Alberta

Edmonton, ab, Canada t6g 2e5

bernard.linsky@ualberta.ca

 

Kenneth Blackwell

blackwk@mcmaster.ca

 

 

We report here on the set of complete proofs of Volumes I and II of Whitehead and Russell’s Principia Mathematica newly acquired by the Bertrand Russell Archives. These proof sheets, marked with a number of corrections, were likely bound for Russell by Cambridge University Press, though not exactly the same as the first edition. We assess the information to be gained from the texts and the corrections, most significantly around *110 in Vol. II and the lost dot of the empty relation Λ̇ in Vol. I. Russell’s hand and described in an appendix. We also note several revisions in the first edition that were made after these proofs. We discuss the provenance of the volumes, and Russell’s correspondence about proofs of PM with M. H. Dziewicki, but we find that there is insufficient evidence to determine the chain of possession from Russell to their discovery for sale in Australia in recent years.

 

 

I. Proofreading “PM”

 

espite accounts in his letters at the time of having written sev­eral thousand pages of Principia Mathematica and con­veying them to Cambridge University Press on 19 October 1909,[1]

 Illustration 1. The bound proof volumes. [End P. 142]

almost nothing is known to survive. There are rejected drafts and an [End P. 141] immense index of where propositions were used, but only two and one-half leaves of the manuscript from which type was set. One leaf is with a letter to Lady Ottoline Morrell at the University of Texas,[2] she having ignored Russell’s instruction to destroy the leaf. The other one and one-half leaves are in the Bertrand Russell Archives, where Rus­sell reused the versos for another purpose. They were found among other documents inserted in his copy of the first edition of PM.[3] They are of interest, not for revisions on the leaves or between them and the text of the first edition, but for the printer’s markings of the signature line and the name of a particular compositor. Of proofs at any stage, only a single leaf was known, a proof of the “Additional Errata to Volume I” that appeared in Volume II, page [viii].[4] The proof is marked “1st”, dated 20 November 1911 and initialled “H.S.D.” There had been no hint of the survival of further proofs. Now bound proof sheets of the first two volumes have come to light, providing, among much else, a second stage of the “Additional Errata to Volume i”.[5] The Appendix records and describes all the proof markings and whether the corrections appear in the Errata, the first edition, or the second.

   The acquisition appears to be Russell’s reference copy of the final or (in the case of some sheets) near-final page proofs of the first two volumes.[6] Consider not only the size of the original manuscript but also the multiple stages of proofs: his desk would soon have been awash in manuscript and proofs as the proofreading of the volumes proceeded over a three-year period. The proof sheets were large: 22 × 30 inches[7] for these Imperial Crown Octavo volumes. The paper in the proof volumes and the first edition is identical. The signatures are signed numerically.[8] They were probably proofread unfolded, since [End P. 143] reading a folded sheet would require opening the top and fore-edge of all the leaves with little paper remaining to hold the sheet together.[9] We know the sheets started to arrive regularly in spring 1910[10] until Whitehead stopped the printing a year later, in January 1911. They resumed three to four months later and until Volume II was finished. The proofreading of Volume III was completed in February 1913.[11] Russell evidently discarded the manuscript as it was returned by the Press, and also the intervening stages of proofs. However, rather than keep a perhaps unstable pile of folded sheets by him as he worked on new proofs, he had his set bound. To judge by the cloth and the binding’s quality, the binding could have been done by Cambridge University Press, but the typeface used on the spines, the unbevelled boards and lack of blind-stamped rules, the binding of the endpapers, and red speckling of the edges differentiate the proof bindings from the first edition. The proof volumes are bound identically, but it would make sense for Russell to have had the first set bound in the interval between finishing the proof­reading of Volume I and starting that of Volume II. After Volume I’s appearance from the Press a short time before publication in December 1910,[12] he would no longer have needed a handy copy of its proofs on which to record new errata and for referring to what the authors had passed for the press as he worked on Volume II. The same consideration applies to the binding of the page proofs of Volume II as he worked on Volume III before Volume II was published in April 1912. There was no practical need to bind the proofs of Volume III. The accumulated proofs of that volume were probably discarded when it was published in April 1913.

   Despite the unexpected survival of the bound proofs, the number of stages of proofs is unknown, and would have varied according to whether the revisions required checking. There were always at least two stages. Consider the subject phrases in the right running heads, e.g. “the logical calcu­lus” (p. 93 of the first edition, p. 89 of the second). Although PM’s chapter headings are strong clues to what [End P. 144] should go in the running heads, this one doesn’t mirror any such heading. The compositors[13] would not have decided on the wording, and the authors would have filled in the topic words on the first proofs.[14] If there were lengthy insertions or deletions in the text, they might have had to readjust the running heads. The bound proofs have a fair number of corrections, and we know that as “final revises” the corrections are incomplete (see secs. III–IV below). Whether the authors were sent new proofs again—until everything was confirmed to be correct—is unknown. What is known is that the sheets for each sixteen-page section (or signature or gathering) were printed in their 750 copies (500 for Volumes II and III[15]) so that the limited supply of cold metal type (especially for unusual “sorts”) could be distributed and reused for a new set of sixteen pages.[16] As an example of this approach at the Press, Whitehead in August 1911 pointed out an error in Volume II, *74×12, commenting: “If the sheet is printed off, keep this as an erratum.” We do not know how many sheets were on the go (in varying stages of composition and revision), but it could hardly be less than three. Both men saw proofs. At one point Whitehead wanted Russell “to return my marked proof in time for me to compare them with the revises”.[17] It was Russell’s job to collate the corrections and deal with the Press. Distribution of the type is why PM had to be reset in the early 1920s when demand justified reprinting the work.[18] [End P. 145]

 

 

Illustration 2. Scan of Volume II, p. 66. Two subscripts to a conjunction are replaced here and elsewhere and a footnote deleted. [End P. 146]

 

II. Correction to Volume II, P. 66, in the Proofs

 

The most significant of the corrections in these proofs occurs in Volume II, Part III, titled “Cardinal Arithmetic”, in the Summary of

section B, “Addition, Multiplication and Exponentiation”. Two corrections were made in the text (see Illus. 2) and a footnote deleted.

   The changes occur at the foot of page 66 of the first edition (p. 63 of the second). The paragraph preceding the changes (which is the same in both editions) explains what is intended:

 

    If a and b are mutually exclusive classes, the sum of their cardinal numbers will be the cardinal number of a È b. But in order that a and b may be mutually exclusive, they must have no common members, and this is only significant if they are of the same type. Hence, given two perfectly general classes a and b, we require to find two classes which are mutually exclusive and are respectively similar to a and b ; if these two classes are called a¢ and b¢ , then Nc‘(a¢ È b¢ ) will be the sum of the cardinal numbers of a and b. We take as a¢ and b¢ the two classes*

 

¯L_b ‘‘i ‘‘a and L_a  ¯ ‘‘i ‘‘b

 

* Here L_a and L_b have the meaning defined in *65×01, i.e. L_a=L Ç t‘a.

 

The markings on the proofs are on the last two lines. A long line through the note beginning “*Here ... ” indicates that the note is to be deleted. A line from L_b  in the penultimate line indicates that L_b  is to be replaced by (L Ç b ), and a second line indicates that L_a  is to be replaced by (L Ç a). This change indicates that the notions expressed by L_a and L_b  will not be defined via *65×01 but instead directly expressed by the simpler expressions (L Ç a) and (L Ç b ), respec­tively. This simplification of the notation will be explained below, but first it is important to notice that the changes indicated, in the last two lines, are not the whole of what appears in the first edition, where the paragraph above continues as before to the point of “We take as a¢  and b¢  the two classes ...” (notice that the asterisk indicating a note disappears). In the published first edition we have:

 

... the sum of the cardinal numbers of a and b. We note that (L Ç a) and (L Ç b ) indicate respectively the L’s of the same types as a and b, and accordingly we take as a¢ and b¢ the two classes [End P. 147]

¯(L Ç b )‘‘i ‘‘a and (L Ç a)¯‘‘i ‘‘b ;

 

This shows that these marginal corrections were not the last indication of the changes to be made. Further changes, in particular the addition of the phrase “We note that L Ç a and L Ç b indicate respectively the L’s of the same types as a and b ...”, indicate that the changes marked in these proofs were not the very last before the final printing.

   In the remainder of *110 the change from L_a  to (L Ç a) was made between the proofs and the published first edition in several places, but not in all. Thus *110×01×1×101×11×12×13×115×152×18 were all corrected. Occur­rences of L_b  and L_γ in *110×71 on page 86 were not corrected. This seems to be a result of the length of the lines in which they occur. It would have been impossible to add the spaces needed for the extra symbols given the structure of the lines. There was probably a query from the printer on this that was later discarded.

   The changes on page 66 were not all the changes made before the final version of Volume II was published. For other changes see sec­tions III–IV below. Still other changes in these proofs were made to the erratum lists in the published edition. The bound proofs may contain the corrections that Russell intended to be the last, to be copied over in full to a second set that was returned, sheet by sheet, to the Press prior to the printing of Volume I’s 750 or Volume II’s 500 copies as a sheet’s proofreading was completed and the corrections made.[19]

   The present alteration was intended as a simplification of the notation, al­though it involves changes in the notion of relative types, including the addition of the long “Prefatory Statement of Symbolic Con­ventions”, that were made late in the composition of Volume II. The problem being addressed is to define a notion of the sum of two classes for which the cardinal number of the sum will be the sum of the cardinal numbers. If two classes overlap, say the classes {a, b} and {a, c}, their union {a, b, c} will not do as the sum of the classes, for the cardinal of each of these classes is 2, and the sum of the cardinals, 4, [End P. 148] is not the cardinal of the union of the classes, which is 3. The solution in *110 of PM is to define the sum as a union of two classes, of types close to those of the original classes, but which do not overlap.[20] The two classes are constructed so that each member of a is paired with the unit set of {b } and each member of b is paired with {a}. In modern notation *110×01 would be written:

 

a + b = (b ´{a}) È (a ´{b }).

 

The additional feature of taking the intersections of a and b with L, the empty class (Æ in contemporary notation), is used to make sure that the types of the two summed classes are unchanged. The inter­section of L with a is an empty class, but of the type of classes whose members are in a. An expression like “L” for the empty class will be typically ambiguous. There is an empty class of individuals, an empty class of classes of individuals, and so on, for each type. In the version of PM that is corrected in these proofs the notion of the members of L_a is defined at *65×01 as: L_a =L Ç t‘a. The latter intersected class t‘a is defined in turn at *63×01 by {a}È -{a}, the union of {a} and its complement. In contemporary set theory the complement of a set (everything not a member of the set) is too large to be a set, and will form a proper class. In type theory every class a of a given type t will have a complement—a, the class of everything of type t that is not in a. (It is informative to see that despite the impression of talking about types as somehow metalinguistic, or otherwise inexpressible in the language of PM, there is in fact no problem with defining this notion of the type of a class.) The upshot of this chain of eliminating two definitions, *63×01 and *65×01, is that the notion of the empty class of the type of classes which have a as a member, L_a , is to be replaced by the expression L Ç a, the empty class of the lower type of the members of a—thus saving the two steps of definition. The change does not appear to affect the results about addition that follow.[21] This is precisely the simplification indicated in the corrections to the proofs on page 66 of Volume ii. [End P. 149]

 

III. Additions to the First Edition after These Proofs

 

Two related changes involve material added to the first edition that are not marked in the proofs. This strongly suggests that these were not the last proofs that the authors corrected of the sheets concerned.

The first change is at Volume II, page 68, line 11, where the proofs have:

 

This illustrates what is required generally where typical ambiguity occurs, namely that, though it is often desirable that our symbols should be typically ambiguous, it is always essential to right symbolism that their value should be unique as soon as their type is assigned.

 

This is replaced in the first edition with:

 

It is always essential to right symbolism that the values of typically ambiguous symbols should be unique as soon as their type is assigned. The scope of these definitions and of the corresponding definitions for multiplication and exponentiation (*13×04×05 . *116×03×04) is extended by convention IIT of the prefatory statement.

 

   The second change is at Volume II, page 76, line 4, where this addition is made to the end of the paragraph:

 

Also in connection with these definitions and the corresponding definitions *113×04 and *116×03×04 and in *117×02×03, the convention IIT of the prefatory statement must be noted.

 

There are two concerns about types that effect the discussion in this section related to the “Prefatory Statement of Symbolic Conventions’’ that delayed the appearance of Volume II. The restriction of the theory of cardinal numbers to classes of common types was met with the notion of “homogeneous cardinals” and the notation N₀ in the Introduction to Part III. The “Prefatory Statement” discussed a further restriction on theorems that depend on the existence of a classes of cardinalities that are not assured by the Axiom of Infinity introduced in *120. The “convention IIT” indicates the restriction of propositions and definitions to cases where the assumption is made that the cardinalities are “adequate” to avoid this.

These changes indicate that the adjustment of Volume II to meet with the Axiom of Infinity were still troubling the authors at the very last stages of proof correction. [End P. 150]

 

Illustration 3. Scan of Volume I, p. 34, with a Lambda dot
restoration and an R for x correction over a scribble in pencil. [End P. 151]

 

IV. Corrections to Volume I, P. 34 and *25, in the Proofs

 

A seemingly trivial typographical correction relating to the empty relation Λ̇̇ reflects an important issue about relations and the theory of types, and leads to the discovery of places where the first edition of Volume I of PM was corrected by hand! On page 34 of Volume I (see Illus. 3), a capital Lambda, L, is corrected to a dotted Lambda, Λ̇̇. The list of errata says for page 218, “[owing to brittleness of the type, the same error is liable to occur elsewhere].”[22] It is interesting that this remark does not come as an erratum for the Introduction, at page 34.

   Whitehead noticed an earlier Λ̇̇ discrepancy on page 30 of the Introduction at the same time he noticed the discrepancy in *25:

 

In sheet 16 as printed off there are some very annoying misprints of Λ for Λ̇̇, especially in the Definition, which are not in the 2nd proof. I have written to the Press to ask about it. Also on p 30 of the Introduction Λ comes for Λ̇̇, but I can’t find my proofs of sheets 1 and 2, so am not sure if we or the Press are to blame. Please look it up—this habit of the Press will be disastrous. (ra1 710, 23 Aug. 1910)

 

The Press tell me that the loss of the dots (Λ for Λ̇̇) on pp 241–243 is due to breakage in printing. They will put them in by hand. I think we must ask them to do so in that number—as it involves the definition and general introduction of Λ̇̇.(ra1 710, 26 Aug. [1910])

 

This printing fault shows that, as might be expected, the authors did not routinely subject the printed-off sheets to a close re-examination. Whitehead discovered the fault only because it recurred much later, at this point overlooking the one on page 218. The missing dots were drawn in on pages 30 and 34 (cf. the 2nd ed., pp. 29 and 32). Someone (perhaps Russell) first dotted the Lambdas, and then Russell (definitely) made marginal insertions to restore them, as we see below: [End P. 152]

 

Illustration 4. From Volume I, p. 30, of the PM proofs.

 

It is quite possible that dots broke off different Lambdas at different times in the printing of certain sheets of PM. Perhaps, therefore, no two copies of Volume I of PM are identical. The inking of the restored dots is sometimes greyish, and the dots are often off-centre in the first edition. Cf. under magnification the dot above the L at I: 243: 2 up. In the ra Supporting Library copy, the dot is off-centre to the right, whereas in the line below it the dot is not off-centre. In Russell’s copy (Illus. 5 below), both dots are misshapen, not a perfect circle like the dot above the ∃ on each line.

 

  

Illustration 5. Last three lines, *25×62×63 of Volume I, p. 243, showing two
hand-drawn Lambda dots (first edition, Russell’s library copy).

 

   Whitehead and Russell were acutely aware of the significance of the dot over the Lambda.[23] It is easy for one to think that because classes and relations are extensional, the empty class will be the same as the [End P. 153] empty relation. However, the dot over the Lambda marks the difference between the empty class and the empty relation, between the class that has no members and the empty relation that holds between no pairs of things. These belong to two distinct logical types, as mon­adic and two-place propositional func­tions belong to different types. The warning in the Errata about brittle type was inserted after proofs of the Introduction had been passed by the authors, the respective sheets printed off in their 750 copies, and the dots hand-supplied on the unbound sheets. Following Whitehead’s complaint, stronger dotted Lambdas must have been ordered from the type foundry, or some other adjustment made. No Lambdas were marked for restoration after page 243 of Volume I, including Volume II.

   Norbert Wiener’s famous paper “A Simplification of the Logic of Relations”[24] proposes to represent relations as classes of ordered pairs, those being defined as classes of a certain complex form, <x, y> = {{{x}, L}, {{y}}}, in which L serves as a tag, as in Russell’s new definition of +, in order to introduce an asymmetry that distinguishes the first member of the pair from the second. Ordered pairs, and con­sequently relations, are all of the same types as monadic functions of functions, etc. One consequence that Wiener notes at the end of the paper is that with his definition there is no distinction between the empty class and an empty relation, and so L= Λ̇̇.  

   Wiener, then, was aware of the use of L as a technical device to tag one element of a pair, and to the difference between L and Λ̇̇. This knowledge may have come from some explicit reference to these issues by Russell.

 

V. The Dziewicki Correspondence with Russell

 

Michael Henry Dziewicki (1851–1928) was born in England to a Polish immigrant father and English Quaker mother, studied at Jesuit colleges in France, and moved to Poland in 1880, where he was known as “Michał Henryk”, and married. Dziewicki was associated with the Jagiellonian University as an English instructor, although he wrote on and edited the medieval logician John Wyclif (or Wycliffe) and translated Polish fiction into English. Dziewicki was known for a distinctive and successful approach to teaching English to Poles and in a letter [End P. 154] says that he had tutored Leon Chwistek in English.[25] Twenty-four letters from Dzie­wicki to Russell between 1913 and 1923 are preserved in the Bertrand Russell Archives, and are the basis of our record of him.[26] On 10 May 1915 Russell wrote to Ludwig Wittgenstein,[27] who then was serving on a gunboat on the Vistula river near Kraków,[28] and suggested that Wittgenstein visit him. Russell describes Dziewicki as “a lonely old logician” who has studied Principia Mathematica. Postcards that Dziewicki sent to Wittgenstein describe visits in June of 1915. In a letter after the war (20 Sept. 1919) Dziewicki described Wittgenstein as “a most genial young man”, and (14 Feb. 1923) that they discussed philosophical issues related to time and space and the nature of belief during their visits.[29]

   A study of this correspondence is not strictly inconsistent with the hypoth­esis that the volumes acquired by the Russell Archives are the proofs that Russell sent to Dziewicki in 1913, but there are difficulties in accepting the hypothesis. The correspondence also suggests that there was a circle of logicians and philosophers in Kraków who were influenced by Russell’s works.

   21 February 1913. Dziewicki reports to Russell that:

 

I had got as far as “Implication and Formal Implication” [PoM, Chap. II] in your great work, when the Problems of Philosophy, which I had sent for, arrived. I at once interrupted my work and set to read the smaller book, which I have just finished.

 

In a later letter (1 Feb. 1922), Dziewicki, who is usually precise, states: [End P. 155] “It is now ten years or more since I wrote to you for considerable help in my studies of mathematical logic.” That assistance included sending Dziewicki a personal copy of The Principles of Mathematics (1903). At this point in 1913 there was clearly an established correspondence between Dziewicki and Russell, although he makes no mention of PM.

   19 March 1913. Dziewicki points out a remark in the Principles of Mathematics, page 25, that “Between any two terms there is a relation not holding between any other two terms.” But, he says, Russell adds: “This principle … is incapable of proof .” Dziewicki constructs an artificial relation between arbitrary classes A and B involving those things that are neither A nor B, which in fact satisfies Russell’s description. The letter concludes with a request for a book with a system of symbolic logic that “would correspond to an ele­mentary algebra”. He notes that he has studied Jevons’ logic,[30] but does not find it sufficient.

   26 April 1913. Dziewicki thanks Russell (again) for his “article on Mathematical Logic”, and complains that he “cannot make out the use of the dots” as he cannot access the work of Peano in which this notation originated.[31]

   24 May 1913. The letter begins with a very low-key way of referring to a gift of two bound volumes of proofs, if that indeed was what Dziewicki received:

 

    I have once more and most heartily, to thank you for your extreme kindness. I have received both your letter and the proofs; and though I am heavily handicapped by my ignorance of mathematics, I hope that “Labor omnia vincit improbis” will prove true in my case.

    What I want to find out is, whether your system of Symbolic Logic can be adequate (or made adequate) for the purposes of Metaphysics. And for that reason, I must first learn to use the Symbols and reason by their means in a continued series of arguments.

    What you note in your letter as to pure mathematics and real actual space, I had already gathered from your Principles of Mathematics, but [End P. 156] was not quite sure whether you would admit the (to me) evident conclusion, that there may be conceptions or series of conceptions, which though absolutely immaterial—i.e. not apprehended by sense—may form “spaces” of n dimensions.…

    You will be (perhaps interested to learn that you are a good deal discussed here in the University, both by pupils and professors, and much appreciated by mathematical specialists in the Academy of Sciences here.

 

He suggests they meet in the south of France in the summer. There is no confirmation that they did so.

   18 June 1913. Dziewicki writes a five-page letter to Russell dis­cussing bound (real) variables and the theory of types, and alludes to a remark on “p. 43 of Principia Mathematica”, which is in the Intro­duction.

   The letters so far suggest that Dziewicki impressed Russell as a serious student of the Principles of Mathematics, then read “Mathe­matical Logic as Based on the Theory of Types” (1908), and, it seems, received proofs of Principia Mathematica from Russell. Wittgenstein’s report that Dziewicki discussed the philosophy of space in their meeting in 1915 also seems to fit.

   The correspondence continued with letters to Russell (dated 5 September 1913, 27 and 28 October 1913, and 24 February 1914), the last when Russell was about leave for Harvard University. In these letters Dziewicki discusses the theory of descriptions from *14 of PM, suggesting that his reading is pro­ceeding.

   [ June 1914]. A puzzling remark appears in the next letter:

 

    It is almost a year since you kindly sent me proofs of Principia Mathematica; and until the present time, I have been constantly working at them, so far as my occupations and capacity for strenuous mental work allowed me. I had great difficulties at first; the proofs,[32] not being a complete set, gave me only an imperfect idea of the system of dots, indispensable for the understanding of your notation. Luckily, I managed in November to get a copy of the book itself; and at present I may say that, so far as mere understanding goes, I have mastered the formal part of the work as far as *38.[33] Perhaps you will not smile when I add that I am rather proud of the feat. [End P. 157]

 

There follows a long, eighteen-page discussion of descriptions and classes, accurately presented in PM notation, and so confirming the claim to have studied up to *38, which comes close to being the whole of Part I on “Mathematical Logic”, with Part II called “Prolegomena to Cardinal Arithmetic”.

   This letter suggests that the “proofs” that Russell sent were “incomplete”, so much so that the system of dots is not made clear by what Dziewicki received. This is confusing. The system of dots is explained in the Introduction, pages 9–11, and so much earlier than passages clearly included in the material he read before November 1913. Possibly he was unable to apply the dot principles. Russell and White­head say in concluding their account of the dot system:

 

    Other uses of dots follow the same principles, and will be explained as they are introduced. In reading a proposition, the dots should be noticed first, as they show its structure. In a proposition containing several signs of implication or equivalence, the one with the greatest number of dots before or after it is the principal one: everything that goes before this one is stated by the proposition to imply or be equivalent to everything that comes after it.(PM, 2nd ed., I: 10–11)

 

This explanation is in the sixteen pages of sheet 1 of PM’s first volume, so possibly it was missing from the proofs Russell sent. (It is an odd sheet to be missing from his gift.) Dziewicki then reports that “in November”, presumably November 1913, he was able to “get a copy of the book itself ” and then proceeded to cor­respond with Russell about issues in Volume I of PM.[34] Calling the three-volume set of PM “the book itself ”, if that’s what he was referring to, is a little odd; and he never explicitly mentions Volumes II and III and yet tells Russell in 1922 that he owns Volume I. The June 1914 letter is thus doubly confusing about the proofs, and perhaps the evidence it provides should be discounted for that. The formulas in his letter show that he became fluent in the dot notation.

   19 December 1922. After the war the correspondence continued, with Dziewicki frequently expressing his debt to Russell. He lists the books [End P. 158] by Russell in his library and makes special mention of the copy of the Principles Russell sent him. There is no mention of the two bound volumes of PM proofs:

 

    I do not know the Tractatus Logico-Philosophicus of Wittgenstein, nor is it possible to get it here: but I should be thankful if you would send it me, as you offered.[35] At present I have the following volumes of your works: Problems of Philosophy ; Philosophical Essays ; Leibnitz ; The External World ; Principles of Mathematics (which you sent me, intimating you might perhaps have to ask for it again); and Vol. I., Principia Mathe­ma­tica. These works, if I were not busy giving lessons, might be a library for me to study till the end of my life.

 

   What, then, is the full provenance of the two volumes of proofs acquired by the Russell Archives? It is clear that Russell sent Dziewicki proofs of part of PM in 1913. The antiquarian bookdealer from whom McMaster University Library purchased the books hypothesized that they had been in the possession of the “Dziewicki family” in Australia, specifically a son, and then found their way via the collection of a Sydney “professor of mathematics” to an antiquarian dealer in Sydney.[36] But Michael Dziewicki was childless.[37] It is our hypothesis that these are not the proofs that Russell undoubtedly sent Dziewicki in May of 1913. The bound proofs have all that Russell and Whitehead have to say in explaining the dot system. They cannot be the “copy of the book itself ” that Dziewicki was able to obtain in November 1913, which was probably the copy of Volume I that he reported owning in 1922. No other corre­spondence in the Russell Archives, as far as anyone is aware, mentions a gift of proofs of the first edition of PM. The bound volumes closely resemble the published first edition, and previous owners may not have realized what they had. Perhaps we should simply say that we refer to these as “the Dziewicki proofs” to honour the relationship between Russell and Dziewicki, without claiming that they are the proofs sent by Russell in May 1913.[38] [End P. 159]

 

Works Cited

 

 

Anon. “Illustrations: Manuscripts Relating to Principia Mathematica”. Russell 31 (2010): 81–4.

Black, M. H. Cambridge University Press 1584–1984. Cambridge: Cambridge U. P., 1984.

Blackwell, Kenneth. “Russell’s Mathematical Proofreading”. Russell 3 (1983): 157–8.

—, and Harry Ruja. B&R.

Bremer, Józef. “Michał Dziewicki—Edy­tor, Logik, Lektor, Tłumacz, Powi­eściopisarz” [Editor, Logician, Teacher, Translator, Novelist]. Przegląd Filozoficzny n.s. 25 (2016): 209–26.

Collins, F. Howard. Authors’ & Printers’ Dictionary. 8th ed. London: Oxford U. P., 1938.

Dziewicki, M. H. “The Standpoint and First Conclusions of Scholastic Philosophy”. Proceedings of the Aristotelian Society 1, no. 2 (1889–90): 28–39.

Grattan-Guinness, I. “The Royal Society’s Financial Support of the Publication of Whitehead and Russell’s Principia Mathematica”. Notes and Records of the Royal Society of London 30 (1975): 89–104.

Jevons, Stanley. The Principles of Science: a Treatise on Logic and Scientific Method. London and New York: Macmillan, 1887.

Linsky, Bernard. The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition. Cambridge: Cambridge U. P., 2011.

—, and Kenneth Blackwell. “New Manuscript Leaves and the Printing of the First Edition of Principia Mathema­­tica”. Russell 25 (2005): 141–54.

Russell, Bertrand. PoM.

—. “Mathematical Logic as Based on the Theory of Types”. American Journal of Mathematics 30 (1908): 222–62. Reprinted in van Heijenoort. 22 in Papers 5.

—. PP. CH.

van Heijenoort, Jean. From Frege to Gödel: a Source Book in Mathematical Logic, 1879–1931. Cambridge, ma: Harvard U. P., 1967.

Westergaard, Christian. “Russell’s Copies of the Corrected Galley Proofs”. sophiararebooks.com/​sep2018.pdf. Pp. 216–21. 2018.

Whitehead, A. N., and Bertrand Russell. PM. 1st ed., 1910–13.

Wiener, Norbert. “A Simplification of the Logic of Relations”. Proceedings of the Cambridge Philosophical Society 17 (1914): 387–90. Reprinted in van Heijenoort.

Wittgenstein, Ludwig. Wittgenstein in Cambridge: Letters and Documents 1911–1951. Brian McGuinness, ed. Oxford: Blackwell Publishing, 2012. [End P. 160]

 

Appendix

Corrections and Markings in the Proof Volumes

 

Images of the corrections and other markings can be viewed in the digitized proof volumes at digitalarchive.mcmaster.ca/islandora/​object/macrepo%​3A90174. Because of the nature of the markings, non-literal descriptions are often resorted to in the second column.

 

PAGE	CORRECTION OR MARKING	EDITORIAL COMMENT	IN ERRATA? CORRECTED IN 1ST EDITION?
Vol. I: p. 1: top left corner of sheet 1 when folded (Illus. 6). This page is discoloured or soiled, presumably from being topmost when the sheet was folded.	pp. 15 . 34 . 103 30	Both strike-throughs refer to pages that were not corrected but appear in the Errata. Corrections to the other 2 pp. were made in the 1st ed. Since p. 103 is in sheet 5, Russell seems to have had a stack of at least sheets 1–5.
I: 15: 2 lines up	Delete “of ” before “ϕx̂ ”.	Not changed.	Yes.   Corrected: no.
I: 17: top left corner of sheet 2 when folded	p. 30	The note is on the 1st p. of sheet 2.
I: 30: 1–2, 4–5 lines up	Four Lambda restorations of “Λ” to “Λ̇”(Illus. 4).	See sec. IV. Note the Errata warning re p. 218: 2 lines up: “[owing to brittle­ness of the type, the same error is liable to occur else­where].”	No.   Corrected: yes. [End P. 161]

 

Illustration 6. Scan of Volume I, p. 1, with the first sheet signed “1” at the lower right.

Noted at the top left are pages with corrections. [End P. 162]

 

PAGE		CORRECTION OR MARKING	EDITORIAL COMMENT	IN ERRATA? CORRECTED IN 1ST EDITION?
I: 33 top left corner of sheet 3 when folded		p. 34	The note is on the 1st p. of sheet 3.
I: 34: line 3 (Illus. 3).		A Lambda restoration of “Λ” to “Λ̇”.	See sec. IV.	No.   Corrected: yes.
I: 34: line 15		“x” is struck through and “R” inserted in ink in margin over pencil scribbling.	The pencil scribbling’s purpose was, perhaps, to mark the passage for consideration later.	Yes.   Corrected: no. In BR’s copy of the 1st ed., “x” is vertically struck through with “R” inserted in the right margin. Yes, in the 2nd ed., p. 33.
I: 97 top right corner of sheet 7 when folded		p. 103 p. 84 p. 487	There is nothing noted on p. 84, and collation with the 1st ed. found nothing.
I: 103: line 7		er	In “assumption” “ump” is struck vertically through; “er” is in margin to make the word “assertion”.	Yes.   Corrected: no. 2nd ed., p. 99, yes.
I: 103: line 25		“r” in left margin to replace final “q”.		Yes.   Corrected: no. 2nd ed., p. 99, yes.
I: 241: top left corner of sheet 16 when folded		pp. 241, 242	See sec. IV. None of the 24 Lambda dots on p. 242 seem drawn in, but some are on p. 243. [End P. 163]
I: 241: 3, 10 lines up		Two Lambda restorations of “Λ” to “Λ̇”.		No.   Corrected: yes.
I: 243: 1, 2, 14 lines up		Three Lambda restorations of “Λ” to “Λ̇”.	See sec. IV and Illus. 4.	No.   Corrected: yes.
I: 304: line 19, right margin of last page of sheet 19 when folded		Long arrow “→” pointing slightly up to right edge.	304 is the last p. of sheet 19. There are no handwritten marks on the “next” page over on this sheet (p. 289) or the “next” p. of the next folded sheet, i.e. p. 305 of sheet 20.
I: 371: 5 lines up		& × 641	In pencil. No caret but the correction must be meant for insertion in “(*83×731)”.	No.   Corrected: no; nor in 2nd ed.
I: 487: line 13		In “*95”, “4” to replace “5”.		Yes.
I: 497: top right corner of sheet 32 when folded		p. 503	In pencil. P. 503 is on the same sheet as p. 497.
I: 503: line 14		In “88×38”, the final “8” is deleted and “6” written in left margin.	In pencil.	Yes.   Corrected: no.
Vol. II: p. 1: top right corner of sheet 1 when folded	p. 101		In pencil. See 101: 12 lines up. Since p. 101 is on sheet 7, Russell seems to have had a stack of at least sheets 1–7 of Vol. II.	[End P. 164]
II: 66: 2 lines up (Illus. 2).	Re two subscripts to the intersection: “Αβ” is to be replaced by “(Λ∩β)” and “Λ∝” by “(Λ∩α)”.		Inserted in 1st ed.: “We note that Λ∩α and Λ∩β indicate respect­ively the Λ’s of the same types as α and β, and accordingly” [here the original wording “We take …” continues but without the concluding asterisk].	No.   Corrected: yes.
II: 66: note	Footnote deleted.		The footnote was: “Here Λ∝ and Λβ have the meaning defined in *65×91, i.e. Λ∝=Λ∩t‘α.”	No.   Corrected: yes.
II: 67: line 3	Re two subscripts to the conjunction.		See 66: 2 lines up for the replacements.	No.   Corrected: yes.
II: 75: line 5	Re two subscripts to the intersection: “β” on left should read: “(Λ∩β)”; “Λ∝” on right should read “(Λ∩α)”.		Only “β” is visible on the scan because the binding is too tight. (See corrections to II: 66.) In the 1st ed. 2 lines are brought back from p. 76, and a new sentence is added at the foot of 76: “These definitions are extended by IIT of the prefatory statement.” (See II: xxv for IIT.)	No.   Corrected: yes. [End P. 165]
II: 76: 3 lines up	Re two subscripts to the conjunction, followed by “[& so throughout]”.		See II: 66. Trimming of the fore-edge removed the upstroke on the handwritten “[”. This may be a note to himself—with the fair copy of the corrected proofs perhaps marking each instance of the subscripts to be changed.	No.   Corrected: yes.
II: 77: 3–			The 1st ed. is revised on several lines in accordance with changes at 75: line 5 and 76: 3 lines up. The lines affected are lengthened, and most are no longer indented or quite as much. P. 86, 3–4 lines up, of the next sheet of the 1st ed. beginning “[*73×1]”, escaped correction. These may not be errors as the subscripts are still defined, and so the results may be provable as asserted.	No.   Corrected: yes.
II: 101: 12 lines up	“:” is to be replaced by “.”		Before “∃!”, BR deleted the top dot of the colon.	Yes.   Corrected: no.
II: 616: 11 lines up	Subscript “P” to “limin” is to be subscript “Q”.			No.   Corrected: no. [End P. 166]