BSHM Bulletin: Journal of the British Society for the History of Mathematics ISSN: 1749-8430 (Print) 1749-8341 (Online) Journal homepage: http://www.tandfonline.com/loi/tbsh20 Did Lewis Carroll own a copy of George Boole's Laws of thought? An argument from the sale catalogues Amirouche Moktefi To cite this article: Amirouche Moktefi (2017): Did Lewis Carroll own a copy of George Boole's Laws of thought? An argument from the sale catalogues, BSHM Bulletin: Journal of the British Society for the History of Mathematics, DOI: 10.1080/17498430.2017.1384200 To link to this article: http://dx.doi.org/10.1080/17498430.2017.1384200 Published online: 16 Oct 2017. Submit your article to this journal Article views: 7 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=tbsh20 Download by: [UAE University] Date: 25 October 2017, At: 09:26 BSHM Bulletin, 2017 http://dx.doi.org/10.1080/17498430.2017.1384200 Did Lewis Carroll own a copy of George Boole’s Laws of thought? An argument from the sale catalogues AMIROUCHE MOKTEFI Downloaded by [UAE University] at 09:26 25 October 2017 Tallinn University of Technology, Estonia Private libraries of scientists offer valuable information on their character, work, and acquaintances. Charles L Dodgson (alias Lewis Carroll) constructed an impressive library of several thousand volumes. The sale catalogue of Carroll’s library reveals that it contained at his death most of the major logic works that would be expected for a British mathematical logician of the time. However, there is dispute as to the presence of the most important logic book of all: George Boole’s Laws of thought (1854). The absence of this work would make both an unfortunate and an intriguing gap. This paper explains the source of this dispute and introduces a new argument from the sale catalogues centred on the dissemination of the books after the sale of the library. Introduction t is well known that Charles L Dodgson, better known as Lewis Carroll, the author of the Alice tales, was a mathematical lecturer at the University of Oxford (Wilson 2008). In his rooms at Christ Church, he constructed an impressive private library of several thousand volumes. Its content is partly known to us thanks to the sale catalogues issued at Carroll’s death in 1898. There currently exist two indexes of Carroll’s library. The first was published by Jeffrey Stern in 1997, together with a reprint of several sale catalogues of the library (Stern 1997). The second index has been published by Charlie Lovett in 2005 and includes the books Carroll owned or ‘read, even if there is no evidence he owned a copy and even if we can only prove that he read part of it’ (Lovett 2005, 2). Carroll’s library is often mentioned in scholarship about his character, his work, and his acquaintance with his contemporaries. For instance, it has been stated that Carroll ‘read comparatively little of the works of other mathematicians or logicians, preferring to develop his theories out of his own mind’ (Hudson 1976, 132). For such ‘library arguments’, it is crucial to identify the volumes owned by Carroll. As an example, we discuss here the disputed presence of George Boole’s seminal book The Laws of thought (1854) in Carroll’s library. This case is of importance as it relates to Carroll’s standing as a logician and his awareness of the achievements of his time (Moktefi 2008; Abeles 2010). Boole’s Laws of thought opened the way to mathematical logic and framed to a great extent British research in the field for the next fifty years (Grattan-Guinness 2011). Carroll worked in his late years on a logical treatise that would make logic accessible for a wide audience (Moktefi 2015). Carrollian scholars disagree as to the presence of Boole’s book in Carroll’s private library. Stern included it in his index while Lovett did not. In the following, we will explain this difference and introduce a new argument from the sale catalogues centred on the I Ó 2017 British Society for the History of Mathematics Downloaded by [UAE University] at 09:26 25 October 2017 2 BSHM Bulletin dissemination of the books. However, it is important to make two preliminary remarks that are necessary to understand the scope of the present paper and the force of the argument that it introduces. First, it should be kept in mind that the possession of a book is not a definitive argument for familiarity with its content and its author. Of course, if it is shown that Carroll owned a copy of Boole’s Laws of thought, then our body of evidence for Carroll’s familiarity with Boole’s logic will be enhanced. Still, it is necessary to maintain caution and to corroborate this evidence with other historical sources. Second, it is important to keep in mind that the list of books in the sale catalogue of the library should not be strictly equated to the set of books that was owned by Carroll. There certainly were books that Carroll owned but that were not offered for sale because they were kept by family members. Also, Carroll might have owned in his lifetime books that were not in his library at his death. Finally, the sale concerned only the library he assembled in his Christ Church rooms. He might very well have owned books that were kept in other locations such as the family house in Guildford. Hence, the absence of Boole’s Laws of thought from the sale catalogue is not a definitive argument that Carroll did not own a copy of it. With these two remarks in mind, it becomes clear that our paper does not assess Carroll’s overall familiarity with Boole’s logic and restricts itself to what the sale catalogue teaches us on Carroll’s ownership of a copy of Boole’s Laws of thought. Lot 505 Carroll died at Guildford, England, on 14 January 1898. An auction sale of his library took place in Oxford on 10 May 1898. For the purpose, the auctioneer M J Brooks organized the books in about a thousand small lots and prepared a primary catalogue describing each lot. Lot 505 was described as follows (Stern 1997, 25): Jevon’s Principles of Science (2 vols.), Keyne’s Formal Logic, Laws of Thought, and 4 others. The description is poor as only minimal information is given on the described books and many others are left undescribed. The misspelling of the authors’ names (it should have been Jevons and Keynes) suggests that the catalogue was dictated while being organized in lots. It is also notable that books that are part of the same lot usually belong to the same area. This organization is confirmed by the juxtaposition of lots containing logic books (lots 505, 506, 508, 509, 510, then lots 515, 516, 517). Hence, it is reasonable to assume that the undescribed books in the lots belonged to the same area (here logic) as the described books, or to an area close to it. The described books were probably those that would secure better sales for each lot. The identification of the books described in lot 505 appears easy. The first title is evidently William Stanley Jevons’s The principles of science: a treatise on logic and scientific method first published in 1874. The second title refers to John Neville Keynes’ Studies and exercises in formal logic first published in 1884. The third title is more problematic as it gives the title alone without the name of the author. A natural candidate is George Boole’s An investigation of the laws of thought published in 1854 but other works are possible. The British Library Catalogue lists three other books that might compete (published before Carroll’s death): William Thomson’s An Volume 0 (2017) 3 Downloaded by [UAE University] at 09:26 25 October 2017 outline of the necessary laws of thought first published in 1842, Alexander Robertson’s The laws of thought, objective and subjective first published in 1864, and finally John Powell Hughlings’ The logic of names, an introduction to Boole’s laws of thought published in 1869. Boole’s Laws of thought There are many good a priori reasons to bet on Boole’s An investigation of the laws of thought. First, it was commonly referred to as Laws of thought among his contemporaries and followers, as can be noticed in the above title of Hughlings which refers to it. Then, the very fact that it was described in the catalogue suggests that it stands as an important title in the lot. Boole’s work is regarded today as one of the most important books in the history of logic and had already acquired notoriety in Carroll’s time (Grattan-Guinness 2005; Durand-Richard and Moktefi 2014). It certainly was a much discussed work in the symbolic tradition of logic to which Carroll belonged and it is easy to speculate that it was a book he would have wanted to own and read. There is no doubt that Carroll knew Boole’s work. His mathematical manuscripts in Princeton Library include sheets dated from May 1867 ‘containing solutions of differential equations, the problems all being taken from Boole’ (Weaver 1980, 221). Later, Carroll referred to Boole in his journal when he recorded his early logic investigations. On 25 May 1876, he reported using a logic notation following ‘Boole’s plan but with an addition which occurred to [him] the other day’ (Wakeling 2001, 463–464). On 20 November 1884, Carroll noted that he was ‘getting to a simpler notation than Boole’s’ (Wakeling 2004, 153). The library provides additional evidence of Carroll’s acquaintance with Boole. Indeed, Carroll indisputably owned a copy of Boole’s Treatise on the calculus of finite differences (Stern 1997, 115; Lovett 2005, 49). Finally, and most importantly for our purpose, Carroll cited Boole’s Laws of thought in his uncompleted Symbolic logic treatise. It is well known that Carroll projected to write his book in three volumes, by level of difficulty. The first part appeared in 1896. Subsequent parts never appeared but surviving fragments have been collected and edited by Warren W Bartley III in 1977. It included a chapter of problems set by other logicians, including problems from Boole’s Laws of thought (Bartley 1986, 477). Many Carrollian scholars unhesitatingly reported that Carroll owned a copy of Boole’s Laws of thought. For instance, Edward Wakeling stated in his early study of Carroll’s logic that Boole’s Laws of thought was ‘listed in the Dodgson Sale Catalogue, amongst a list of other well-known mathematical and logical texts of the day’ (Wakeling 1978, 4). Wakeling repeated this claim in his recent book Lewis Carroll: the man and his circle (Wakeling 2015, 136). Similarly, Bartley referred to the sale catalogue to affirm that it included ‘works in logic’ by Boole and other logicians (Bartley 1986, 31). In the first index of Carroll’s library, Stern also listed Boole’s Laws of thought as item 532, with specific reference to lot 505 of the primary sale catalogue (Stern 1997, 115). Other scholars were more cautious. For instance, Lovett did not include Boole’s Laws of thought in his index, even though he recognized that Carroll may have owned a copy of it (Lovett 2005, 314). It is paradoxical that Lovett was more cautious than Stern when we remember that he included in his index works that Carroll was known to have read regardless of whether he owned them or not. Historians of logic 4 BSHM Bulletin Francine Abeles and Amirouche Moktefi apparently shared Lovett’s reserve. Abeles (2007, 16) did not include Boole among the logicians present in Carroll’s library. Moktefi affirmed that Carroll ‘owned copies of the works’ of Boole and other logicians but did not specify if those were works of logic (Moktefi 2008, 498). The major obstacle to the identification of Boole’s Laws of thought in Carroll’s library is that it does not appear in the catalogues issued by booksellers who heavily bought at the original auction. Downloaded by [UAE University] at 09:26 25 October 2017 Thomson’s Laws of thought Several secondary sale catalogues were issued and offer more details on the items at sale. They notably reveal new titles that were hidden in the primary catalogue prepared by Brooks. Boole’s Laws of thought is not found in any of the known catalogues while two of his rivals are listed. First, in June 1898, just one month after the Brooks auction, H H Blackwell issued a catalogue of about 360 books that were in Carroll’s library. Item 1257 is described as follows (Stern 1997, 57): Thomson (W.). An outline of the laws of thought: A treatise on pure and applied logic, 12mo, cloth, 3/ Pickering, 1849. Then, another secondary catalogue issued by the Art and Antique Agency in 1898 listed more than 400 items, among which number 235 is described as follows (Stern 1997, 83): The Logic of Names, and Introduction to Boole’s laws of thought, by J. P. Hughlings, post 8vo, cloth labelled, faded, 2s. 6d, 1869. Boole’s theory put into nonmathematical language. These descriptions confirm that Carroll owned copies of Thomson and Hughlings’ less-known works. Hence, each of them could have been the item referred to as ‘Laws of thought’ in lot 505 of the primary sale catalogue. Thomson’s Laws of thought is a particularly good challenger of Boole. There is no surprise to find it in Carroll’s library as it enjoyed some success in his time. It went through several editions and was viewed as a ‘recognised text-book for Oxford classes’ (Thomson 1919, 6). The fact that Carroll owned an early edition of the book suggests that he might have got it in his early Oxford years. Thomson was an Oxford man who shared Carroll’s passion for photography (Thomson 1919, 318). Carroll knew him and mentioned him twice in his journal on photography matters. First, on 15 February 1858, Carroll met ‘Thomson, the Provost of Queens’ and planned to go see his photographs (Wakeling 1995, 155–156). Then, on 24 June 1864, Carroll ‘called on the Archbishop of York, to ask him to sit for a photograph, but he was out’ (Wakeling 1997, 316). Hughlings’ book is a less forceful candidate. First, it was less successful than Boole or Thomson, and thus had less chance to stand as a described book in a lot of logic items. Then, if it ever were to be described in the primary catalogue, one would expect it to be listed as the ‘Logic of names’ rather than the ‘Laws of thought’ which merely appears in its subtitle. We alluded earlier to Robertson’s Laws of thought as another candidate, but its chances are ever shorter. It shares with Boole the handicap of not being described in any of the known sale catalogues. Unlike Boole however, it Downloaded by [UAE University] at 09:26 25 October 2017 Volume 0 (2017) 5 is a minor work and there is no evidence that Carroll ever knew it. So Boole and Thomson are evidently the most likely authors of the disputed Laws of thought copy. Naturally, Carroll could have owned both Boole’s and Thomson’s books. Stern actually listed both in his index with the understanding that Boole’s copy was listed in the primary catalogue (lot 505) while Thomson is identified thanks to the secondary catalogue cited above (Stern 1997, 115, 155). Lovett rather considered it to be ‘most likely’ that both catalogues referred to the ‘same book’, that is Thomson’s (Lovett 2005, 314). Lovett is certainly right that single authorship offers a simpler hypothesis rather than the double assumption that it was Boole’s title that was described in lot 505 of the primary catalogue and that Thomson’s was undescribed in an unknown lot of that catalogue. Naturally, several other scenarios exist, especially if we consider the possibility that Carroll owned several copies (same or different editions) of the same title. But such hypotheses are more demanding than Stern’s. It must be kept in mind that what is searched for here is the most plausible solution, even though we might never know for sure what that book in lot 505 actually was. Boole and Thomson are our best options, the latter having the advantage of being supported by secondary sale catalogues. An argument from the sale catalogues In the following we introduce a new argument based on the reconstruction of the books’ routes of dispersal thanks to the secondary catalogues of booksellers who bought books at the original sale. Recall that Brooks offered a primary list of the books in Carroll’s library for the 10 May 1898 auction. Three booksellers who heavily purchased books at the sale are of interest to us: H H Blackwell, J Parker, and the Art and Antique Agency. These were the only booksellers that listed logic books in their catalogues. Hence, we assume that Carroll’s logic books were disseminated through them or were not reoffered for sale by their purchasers as shown in this figure: Since the library was originally sold by lots, volumes that were part of a lot are expected to be found in the same secondary catalogue. Accordingly, volumes listed in different secondary catalogues likely were not in the same original lot. It is therefore expected that the volumes forming lot 505, including Laws of thought, were sold together and are to be found in the same secondary sale catalogue. Remember that lot 505 contained Jevons’ Principles of science (in two volumes), Keynes’ Formal logic, the disputed Laws of thought, and four others undescribed volumes. Jevons’ book is not found in any secondary catalogue. Carroll cited Jevons’ book (1874 edition) in his Symbolic logic (Bartley 1986, 478). This might be the volume to which the 6 BSHM Bulletin primary catalogue refers. Keynes’ book (third edition) is listed in the secondary catalogue issued by J Parker as follows (Stern 1997, 67): Keynes (J. N.), Studies and Exercises in Formal Logic, including a generalization of logical processes in their application to complex inferences. London, 1894. 8 vo., cloth. 7S. 6 d. Rev. C. L. Dodgson, with the Author’s kind regards. Downloaded by [UAE University] at 09:26 25 October 2017 It might at first look perplexing that Keynes’s book was listed in the Parker catalogue but not Jevons’. However, a close look shows that Carroll actually owned another copy of Keynes’ book. This copy is listed in lot 508 of the primary catalogue with Keynes’s name misspelled again (Stern 1997, 25): Bosanquet’s Logic (2 vols.), De Morgan’s Formal Logic, Kynes’ Formal Logic and 3 others. The works of Bosanquet and De Morgan from this lot 508 are also found in the Parker catalogue. It is reasonable to infer that the Keynes copy described (above) in the Parker catalogue was part of the same lot. Therefore, the copy of Keynes that was in lot 505 does not appear in any secondary catalogue. This is consistent with the above observation that Jevons’ Principles of science also was not found. Carroll mentioned Keynes’ Formal logic twice in his private journal: on 22 June 1894 (no edition indicated) and 30 October 1894 (“new edition”, evidently the third edition) (Wakeling 2005, 152, 180). Carroll also cites in his Symbolic logic both second (1887) and third (1894) editions of Keynes’ book. These might be the two volumes listed in the catalogue sales. The absence of Jevons and Keynes’ volumes from secondary catalogues suggests that lot 505 was not bought by one of the major booksellers who issued those subsequent catalogues or if it was, then it had not been re-offered for sale. Several other lots of logic books are in the same situation, listed in the primary catalogue but not found in the secondary ones. Such is the case of lot 515, for instance, containing Francis H Bradley’s Principles of logic (Stern 1997, 116; Lovett 2005, 54). If the other books of lot 505 are not found in the secondary sale catalogues, then it is unlikely that the ‘Laws of thought’ volume would refer to Thomson’s book (found in the Blackwell catalogue) or to Hughlings’ book (found in the Art and Antique Agency catalogue). These two volumes rather seem to come from other lots where they were undescribed. Interestingly, the logic books described in the primary catalogue and listed in the Blackwell catalogue all come from either lot 509, 510 or 517. Among them, only lot 517 includes undescribed items. Hence, it is likely that Thomson’s volume was part of it. None of the logic books found in the Art and Antique Agency catalogue is described in any of the lots of the primary catalogue. It is therefore not possible to ascribe them to any specific lot. Conclusion The books in lot 505 of the sale catalogue of Carroll’s private library apparently were not re-offered for sale. Unless a copy of the Laws of thought reappears, it is not possible to reconstruct its path. We might never know which Laws of thought was in lot 505. Boole’s and Thomson’s are commonly viewed as the most likely candidates. The Downloaded by [UAE University] at 09:26 25 October 2017 Volume 0 (2017) 7 paradoxical force of the argument developed in this paper, based on the dissemination of the books through secondary sales, is that it reverses the usual argument. Indeed, it was hitherto assumed that Thomson’s Laws of thought is a better candidate because it was found in the secondary sale catalogues. The argument developed in this paper rather shows that Thomson’s actually is a weaker candidate precisely because it was found in the secondary catalogues. Our argument rather supports Boole’s work since Thomson’s most likely was in another lot, possibly lot 517. The method described here, based on the books’ routes of dispersal, follows from a simple observation: since the library was sold by lots, the books within the same lot likely were sold to the same purchaser. This principle can be used with benefit to identify items that were left undescribed in the original sale catalogue. In this paper, we applied this method to identify a specific item found in a given lot. This narrow application was imposed by the research question we were addressing. It is evident that this method could be extended and used with benefit to study larger sets of books or the whole content of the sale catalogue. Hence, it is hoped that this method will provide help to future studies and surveys of Carroll’s library. Carroll’s library certainly contained at his death most of the major logic works that would be expected for a British logician of his time (Moktefi 2017). One finds works by Augustus De Morgan, Sir William Hamilton, John Stuart Mill, Jevons, John Venn, Keynes, Bradley, and many others. Boole was most likely present as well. As valuable as this information might be, the presence of these books in his library does not suffice to make high claims about Carroll’s acquaintance with the logic achievements of his time. One still needs to explore further the history of the acquisition of these works and the extent to which Carroll was familiar with them. The absence of a book from the library should also be carefully interpreted since it does not entail unacquaintance with its author. For instance, John Cook Wilson, the Professor of Logic at Oxford, is absent from Carroll’s library despite heavily exchanging with him on logic matters all along the 1890s (Marion and Moktefi 2014). Library arguments are to be used with caution. Acknowledgements I would like to express my gratitude to the anonymous reviewers for their careful reading and valuable comments that helped to improve a previous version of this paper. This work draws upon research support from the ERC project ‘Abduction in the age of uncertainty’ (PUT 1305, Principal Investigator: Professor Ahti-Veikko Pietarinen). Disclosure statement No potential conflict of interest was reported by the author. Funding This work was supported by the Estonian Research Council [PUT 1305]. Bibliography Abeles, Francine F, ‘Lewis Carroll’s visual logic’, History and Philosophy of Logic, 28 (2007), 1–17. Downloaded by [UAE University] at 09:26 25 October 2017 8 BSHM Bulletin Abeles, Francine F, The logic pamphlets of Charles Lutwidge Dodgson and related pieces, New York: The Lewis Carroll Society of North America, 2010. Bartley III, William W (ed), Lewis Carroll’s symbolic logic, New York: Clarkson N Potter, 2nd edition, 1986. Boole, George, An investigation of the laws of thought, London: Walton & Maberly and Cambridge: Macmillan, 1854. Durand-Richard, Marie-Jose, and Moktefi, Amirouche, ‘Algebre et logique symboliques: arbitraire du signe et langage formel’, in Jean-Yves Beziau (ed), La pointure du symbole, Paris: Petra, 2014, 295–328. Grattan-Guinness, Ivor, ‘George Boole, An investigation of the laws of thought on which are founded the mathematical theory of logic and probabilities (1854)’, in Ivor Grattan-Guinness (ed), Landmark writings in western mathematics 1640–1940, Amsterdam: Elsevier, 2005, 470–479. Grattan-Guinness, Ivor, ‘Victorian logic: From Whately to Russell’, in Raymond Flood, Adrian Rice, and Robin Wilson (eds), Mathematics in Victorian Britain, Oxford: Oxford University Press, 2011, 359–374. Hudson, Derek, Lewis Carroll: an illustrated biography, London: Constable, 2nd edition, 1976. Lovett, Charlie, Lewis Carroll among his books: a descriptive catalogue of the private library of Charles L. Dodgson, Jefferson, North Carolina and London: McFarland, 2005. Marion, Mathieu, and Moktefi, Amirouche, ‘La logique symbolique en debat a Oxford a la fin du XIXe siecle: les disputes logiques de Lewis Carroll et John Cook Wilson’, Revue d’Histoire des Sciences, 67 (2014), 185–205. Moktefi, Amirouche, ‘Lewis Carroll’s logic’, in Dov M Gabbay and John Woods (eds), British logic in the nineteenth century (Series Handbook of the History of Logic, 4), Amsterdam: North-Holland, 2008, 457–505. Moktefi, Amirouche, ‘On the social utility of symbolic logic: Lewis Carroll against “The Logicians”, Studia Metodologiczne, 35 (2015), 133–150. Moktefi, Amirouche, ‘Are other people’s books difficult to read? The logic books in Lewis Carroll’s private library’, Acta Baltica Historiae et Philosophiae Scientiarum, 5/1 (2017), 28–49. Stern, Jeffrey, Lewis Carroll bibliophile, Luton, Bedfordshire: White Stone publishing, 1997. Thomson, Ethel H, The life and letters of William Thomson Archbishop of York, London: John Lane, 1919. Wakeling, Edward, The logic of Lewis Carroll, privately printed, 1978. Wakeling, Edward (ed), Lewis Carroll’s diaries: the private journals of Charles Lutwidge Dodgson (Lewis Carroll), Luton, Beds and Clifford, Herefordshire: The Lewis Carroll society, 10 vols, 1993–2007 (vol 3, 1995, vol 4, 1997, vol 6, 2001, vol 8, 2004, vol 9, 2005). Wakeling, Edward, Lewis Carroll: the man and his circle, London and New York: I B Tauris, 2015. Weaver, Warren, The mathematical manuscripts of Charles Lutwidge Dodgson (Lewis Carroll) in the Morris L Parrish collection, Princeton: Princeton University Library, microfilm, 1980. Wilson, Robin, Lewis Carroll in Numberland: his fantastical mathematical logical life, London: Allen Lane, 2008.