Philosophy is an ambitious, speculative practice, aimed at finding out what wisdom is and how to attain it, in so far as that can be done by explicit discussion and argument. A likely pitfall of any such enterprise is that it loses touch with concerns in human life outside itself and becomes scholastic, in the pejorative sense. Academic institutions which encourage wide and outward-looking intellectual sympathies, and which do not reward narrow point-scoring specialism, are helpful in resisting the tendency to (...) scholasticism. The Moral Sciences Tripos at Cambridge might have provided some of the elements of such a setting, by framing an academic structure in which philosophy was studied in conjunction with other subjects in the humanities and social sciences. As things actually developed, that possibility was not realised. Nevertheless, philosophy at Cambridge maintained vigour and significance, through the intellectual freedom and encouragement it provided to some notable individual philosophers. (shrink)

This volume contains C. D. Broad's Cambridge lectures on Ethics. Broad gave a course of lectures on the subject, intended primarily for Part I of the Moral Sciences Tripos, every academic year from 1933 - 34 up to and in cluding 1952 - 53 (except that he did not lecture on Ethics in 1935 - 36). The course however was frequently revised, and the present version is es sentially that which he gave in 1952 - 53. Broad always wrote (...) out his lectures fully beforehand, and the manuscript on Ethics, although full of revisions, is in a reasonably good state. But his handwriting is small and close and in places difficult to decipher. I therefore fear that some words may have been misread. There was an additional complication. In the summer of 1953 Broad revised and enlarged two sections of the course, namely the section on "Moore's theory" and that on "Naturalistic theories" (both sections occur in Chapter 4). The revised version of the section on Moore is undoubtedly superior to the earlier version, and I have therefore included it. But in my opinion this is not true of the new version of the section on naturalistic theories: although more comprehensive than the earlier version, it is not only repetitive in itself, but also repeats, sometimes almost verbatim, passages which occur elsewhere in the lectures. In brief, the new version is not fully integrated with the rest of the course. (shrink)

We pursue the idea that predicate logic is a “fibred algebra” while propositional logic is a single algebra; in the context of intuitionism, this algebraic understanding of predicate logic goes back to Lawvere, in particular his concept of hyperdoctrine. Here, we aim at demonstrating that the notion of monad-relativised hyperdoctrines, which are what we call fibred algebras, yields algebraisations of a wide variety of predicate logics. More specifically, we discuss a typed, first-order version of the non-commutative Full Lambek calculus, which (...) has extensively been studied in the past few decades, functioning as a unifying language for different sorts of logical systems (classical, intuitionistic, linear, fuzzy, relevant, etc.). Through the concept of Full Lambek hyperdoctrines, we establish both generic and set-theoretical completeness results for any extension of the base system; the latter arises from a dual adjunction, and is relevant to the tripos-to-topos construction and quantale-valued sets. Furthermore, we give a hyperdoctrinal account of Girard’s and Gödel’s translation. (shrink)

In this paper the use of mathematics in economics will be discussed, by comparing two approaches to mathematics, a Cartesian approach, and a Newtonian approach. I will argue that while mainstream economics is underpinned by a Cartesian approach which led to a divorce between mathematics and reality, the contributions of key authors of the Cambridge tradition, like Marshall, Keynes and Sraffa, are characterised by a Newtonian approach to mathematics, where mathematics is aimed at a study of reality. Marshall was influenced (...) by the Newtonian approach that still characterised many aspects of the Cambridge Mathematical Tripos, where the emphasis was on geometrical and mechanical examples rather than on symbolic (Cartesian) mathematics. Keynes, who criticised (Cartesian) symbolic mathematics, was indeed an admirer of Newton and of his method. Sraffa's mathematical constructions are also in line with the Newtonian approach where arithmetic and geometry were strictly separated, since Sraffa's mathematical constructions typically use arithmetic without engaging in the mixture between geometry and arithmetic that occurs in the Cartesian approach. View the Open Peer Discussion of this paper ». (shrink)

The mathematical prowess of pure mathematician J. E. Littlewood (1885-1977), and of his elder cousin the mathematical educator Philippa Fawcett (1868-1948), is illustrated in the context of the Mathematical Tripos examination at Cambridge. Littlewood’s brilliant though highly condensed treatment in his splendid Miscellany (1953) of a perplexing problem from an old Tripos paper – familiar to some as “The Paradox of the Second Ace” – is then expanded with reference to Coxeter’s treatment of it in his revision of (...) Rouse Ball’s Mathematical Recreations (1939) and ultimately explained in the light of Wittgenstein’s later philosophy. The discussion touches on the nature of mathematical supposition. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:RUSSELL AND G. H. HARDY: A STUDY OF THEIR RELATIONSHIP I. GRATTAN-GUINNESS Faculty of Science, Engineering and Mathematics Middlesex Polytechnic Enfield, Middlesex EN3 45F, England I. INTRODUCTION Prom time to time the name of Hardy turns up in Russell's career: a common interest in set theory and the philosophy of mathematics, similar political and religious sentiments, and certain matters of mutual concern arising at Trinity College Cambridge and in (...) the university in general. However, there is no connected account of their contacts. The purpose of this article is to fill a gap in the literature on both men. After enduring private instruction at home, Bertrand Russell gained a minor scholarship in mathematics at Trinity College in 1890; he took Part I of the Mathematical Tripos until 1893 and then Part II of the Moral Sciences Tripos in the following year. In 1895 he gained a Prize Fellowship, which he held until 1901; in 19IO.he was awarded a college lectureship which he lost six years later under circumstances noted in section IV below. Much of the intervening time was spent in Oxford or London; however, he spent part of each year in Cambridge.1 The later years are brieHy recorded in section IV. Born into an intellectual family ofmodest means in 1877 (five years younger than Russell, therefore), Godfrey Harold Hardy won a scholarship to Winchester College and then went to Trinity College in I Standard biographical information on Russell is easily available; see, for example, R. W. Clark, The Life ofBertrand Russel~ specific phases and events are dealt with in succeeding footnotes. The Autobiography ofBertrand Russell is of lower quality than one might imagine; for example, Hardy is not mentioned at all! rus.ell: the Journal of the Bertrand Russell Archives McMasrer Unive~ity Library Press noS. 11 (wimer 1991-92): 165-79 ISSN 0036-01631 166 I. GRATTAN-GUINNESS 1896, just after Russell had gained his fellowship. He was elected to the Apostles (the "Society") in 1898, the year after Russell "took wings" after five years' active membership; he seems to have been less active than Russell as a speaker during his own three years there.2 At some stage he also joined the Cambridge University Moral Sciences Club, which Russell had joined in. 1891; a surprising contribution will be described in section IV.3 Graduating as fourth wrangler in Part I of the Mathematical Tripos in 1898 and gaining a high place in Part II in 1900, Hardy received at once a Prize Fellowship (like Russell). Upon its termination six years later, he obtained a colleg~ lectureship, which he held until 1919. He was elected a Fellow of the Royal Society of London in 1910 (two years after Russell),4 and in the following year he began his life-long collaboration with his younger colleague ]. E. Littlewood (1885-1977), also a Trinity College graduate and then Fellow, and also a friend of Russell.5 The next stages of Hardy's career will be described in section IV: his personality is assessed in a concluding section v. 1 On Russell'~ and Hardy's roles in the Apostles, see passim in P. Levy, Moore: G. E Moore and the Cambridge Apostles (London: Weidenfeld and Nicolson, 1979). 3 The chief obituary of Hardy is by E. C. Titchmarsh, published in slightly different forms in Obituary Notices ofthe Royal Society ofLondon, 6 (1949); 447-61, and Journal ofthe London Mathematical Society, 25 (1950): 81-101 (followed by more technical surveys of his mathematics by Titchmarsh and eight other authors on pp. 102-38). The first version is reprinted with a few changes in Hardy's Collected Papers, 7 vols. (Oxford: Clarendon P., 1966-79), I: 1-12. No major study has been written on him since. 4 Hardy was n~minated for a Royal Sociery fellowship in 1907 by A. R. Forsyth, seconded by J. W L. Glaisher, and supported "on personal knowledge" by W Burnside, E. W Hobson, P. A. MacMahon, A. N. Whitehead, A. E. H. Love, E. B. Elliott and T.]. d'A. Bromwich; the proposal was "suspended" (put up for voring) in 1908, 1909 and 1910 (Royal Sociery Cettificates, 12: foJ. 311). Although Russell was... (shrink)

In the 1860s and 1870s the logic of Boole and the calculating machines of Babbage were key resources in W. S. Jevons’s attempt to construct a mechanical model of the mind, and both therefore played an important role in Jevons’s attempted revolution in economic theory. In this same period both Boole and Babbage were studied within the Cambridge Moral Sciences Tripos, but the Cambridge reading of Boole and Babbage was much more circumspect. Implicitly following the division of the moral (...) sciences into material and ‘real’ as established by the Rev. Grote, John Venn treated Boole’s logic as a purely formal science, while Alfred Marshall based his psychological model of the mechanical part of the human mind upon Babbage’s two-level machine. From the different perspectives of logic and psychology, Venn and Marshall did not simply incorporate their readings of Boole and Babbage, but also attempted to establish the limits to any mechanical explanation of the mind. This comparison of the attitudes to mental science of Jevons and Marshall provides a foundation from which the differing conceptions of economic theory of the two men can be established.Keywords: Alfred Marshall; Charles Babbage; George Boole; John Venn; Logic; Psychology. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:russell: the Journal of Bertrand Russell Studies n.s. 33 (winter 2013–14): 173–90 The Bertrand Russell Research Centre, McMaster U. issn 0036–01631; online 1913–8032 c:\users\kenneth\documents\type3302\rj 33,2 114 red.docx 2014-01-31 8:29 PM oeviews MODES AND LEVELS OF PERPLEXITY I. Grattan-Guinness Middlesex U. Business School Hendon, London nw4 4bt, uk [email protected] John Ongley and Rosalind Carey. Russell: a Guide for the Perplexed. London: Bloomsbury, 2013. Pp. ix, 212. isbn: 978-0-8264-9753-6. £45 (hb), (...) £14.99 (pb); us$80 (hb), us$24.95 (pb). i his book is the 41st in a series of guides to the work of various philosophers and philosopher groups, written at a level of readability for students. The authors survey the course of Bertrand Russell’s philosophical career, starting out with his work on logic and mathematics. The main philosophical tools are presented: in logic, they are term, proposition, proposition function, relation, paradox, and first- vis-à-vis higher-order logic. Then, moving on to epistemology, the principal philosophical notions are presented, such as sense-data, facts related to language, Russell’s overriding preference for positivistic philosophies and suspicions of metaphysics, knowledge by acquaintance and by description, theories of truth, logical atomism, percept, events, meaning, and inference in the context of scientific theories. It is nice to have many of the principal components of Russell’s philosophy exhibited together, including the later works An Inquiry into Meaning and Truth and Human Knowledge. The perplexed reader would like to be given precise references for Russell’s assertions on various points, especially when he was so prolific. A cited short item does not need more precision; but the two main chapters that cover the logic and epistemology story often seem to invoke The Principles of Mathematics or Principia Mathematica and yet contain only one precise citation of a longer text in their 64 pages (p. 85). The other chapters of the book are somewhat better in this respect. The index is excellent, though W. V. Quine was missed at pp. 29–30. The table of contents would have benefited from including the titles of the sections. q= 174 Reviews c:\users\kenneth\documents\type3302\rj 33,2 113 red.docx 2014-01-15 10:04 ii Much ground is covered; however, the account is mitigated by the failure to provide a biographical factual survey that should have constituted the opening chapter. Little or no description or explanation is given of, among others, Cambridge University, its mathematical tripos, Russell’s research fellowship in 1895, the philosophical journals Mind and The Monist, Russell’s conversion from neo-Hegelian to positivistic philosophy following G. E. Moore around 1899, the start of personal contacts with Giuseppe Peano in 1900, the gradual involvement of A. N. Whitehead from around 1902, the financial rescue of Principia Mathematica by the grant from the Royal Society in 1909, the serious mistake in Volume 2 detected by Whitehead in 1911 while it was in press, the initial contact with Ludwig Wittgenstein from 1911, Russell’s switch from logic to epistemology in the early 1910s, Whitehead’s intentions for the fourth volume of Principia that was abandoned in 1918, the circumstances of the second edition published in the mid-1920s, Russell’s partial return to serious philosophical writings from the mid-1930s onwards, or the Trinity fellowship from 1944. Presumably the authors have made most of these omissions intentionally ; but the target audience is the loser. The opening “introduction” does mention some of these events and publications ; but its purpose is to provide a preliminary look at some of the main features of Russell’s logic, including the comprehension axiom “that every predicate defines a class” (p. 3), type theory, definite descriptions, “the noclass theory of classes” (p. 10), and the status and role of “analysis”. Why do these features need prologues when the others do not? When they are re-discussed in the later chapters on logic and epistemology, several near-repetitions occur. Furthermore, quantification does not receive sufficient consideration in the book; and the logical connectives and rules of inference none at... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:178 Reviews c:\users\kenneth\documents\type3302\rj 33,2 113 red.docx 2014-01-15 10:04 THE EARLY MOORE AND RUSSELL Ray Perkins, Jr. Philosophy / Plymouth State U. Plymouth, nh 03264 1600, usa [email protected] G. E. Moore. Early Philosophical Writings. Edited and with an Introduction by Thomas Baldwin and Consuelo Preti. Cambridge and New York: Cambridge U. P., 2011. Pp. lxxxv, 251. isbn: 978-0521190145. £68.00; us$114.00. aldwin and Preti have put together a very nice book (...) which gives us G. E. Moore’s 1897 and 1898 Trinity College dissertations and an informative look at the historical context in which they were written. This story—including information about Moore’s early life, the philosophical influences at Cambridge and a critical commentary on his dissertations and readers’ reports— is clearly and carefully presented in their 78-page introduction.1 The book is a valuable addition to the history of analytic philosophy and will be of special interest to Moore (and Russell) scholars and to historians generally who wish to know more about the genesis of the ideas shaping the new analytic philosophy at the end of the century. Moore entered Trinity in 1892 to study classics. There he met Russell (who was in his third year) and took his advice to study philosophy in his last two years and take his final exams (Tripos, Part ii) in both disciplines, which he did successfully in 1896. And like Russell—who had won a Trinity prize fellowship in 1895 (with a dissertation on the foundations of geometry2 ) only one year after his graduation—he submitted a dissertation (1897) in hopes of winning a prize fellowship. Moore’s first attempt failed, but his 1898 version was successful. And not only did the success of the 1898 dissertation launch Moore’s career as a professional philosopher, it also paved the way for the new analytic philosophy of the next century. Moore’s dissertations and his Trinity examiners’ reports (by Caird, Sidgwick, Ward and Bosanquet3 ) are fascinating reading, and it’s a great convenience to have them handy in a single volume. But the editors deserve special 1 Hereafter I shall use the editors’ convention of referring to the pagination of their introduction with roman numerals and to Moore’s dissertations (plus examiners’ reports) with arabic numerals. 2 Russell’s dissertation was published in 1897 as An Essay on the Foundations of Geometry. 3 Edward Caird was an idealist and highly respected Kant scholar at Oxford. Henry Sidgwick was one of Moore’s teachers at Cambridge and author of the influential _= Reviews 179 c:\users\kenneth\documents\type3302\rj 33,2 113 red.docx 2014-01-15 10:04 praise for not only giving the reader an astute critical summary of the dissertations, but also for their skillful reconstruction of Moore’s surviving, but incomplete, 1898 manuscript from which parts of the early chapters had been removed. The editors make a good case (pp. lxxv–lxxix) that those pages became the basis of Moore’s 1899 Mind article, “The Nature of Judgment”. (Those familiar with Russell’s early work may recall it as an article that Russell claimed as of paramount importance for his own early work.4 I’ll return to the question of Russell and Moore and this article’s significance.) the dissertations, 1897 and 1898 Moore’s dissertations reveal a young Moore with remarkable powers of analysis and more than a hint of the careful, courageous scepticism and intellectual honesty for which he later became known. But as the editors make clear, their main importance is the record they reveal of the transition away from Kant and Hegel to the new philosophy, which put a premium on conceptual analysis and metaphysics without Kantian or neo-Hegelian idealism. The 1897 dissertation (“The Metaphysical Basis of Ethics”) is an analysis of the basic concepts of ethics with considerable critical discussion of Kant, especially concerning freedom and reason, and Moore’s attempt to fashion his own good-based ethics utilizing a little from Kant and much from Bradley (p. l). At this time both Moore and Russell were still under the influence of Kant... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:March 13, 2008 (7:35 pm) G:\WPData\TYPE2702\russell 27,2 054.wpd 272 Reviews 1 See Brian J.yL. Berry and Donald C. Dahmen, “Paul Wheatley, 1921–1999”, Annals of the Association of American Geographers 91 (2001): 734–47. THE LIVES OF THOSE WHO WOULD BE IMMORTAL Richard Henry Schmitt U. of Chicago Chicago, il 60637, usa [email protected] David Leavitt. The Indian Clerk: a Novel. London: Bloomsbury, 2008; New York: Bloomsbury, 2007. Pp. 485. isbn 1-59691-040-2. (...) £16.99; us$24.95 (hb). From the start, this novel interested me for two reasons. First, it attempts to tell us the personal stories of two individuals who were working at the highest level in a very abstract Weld, namely G.yH. Hardy (1877–1947) and Srinivasa Ramanujan (1887–1920) during their collaboration on pure mathematics between spring 1914 and spring 1919. Obviously the same problems would arise in trying to tell the personal story of Bertrand Russell’s supervision of Ludwig Wittgenstein in mathematical logic, which occurred at Cambridge University in the years just before the start of the Great War. It is a great challenge to try to tie personal dynamics and abstract thought into a single coherent narrative. There are implications for the philosophy of mathematics and the history and sociology of science. So, of course, we have to ask: how does author David Leavitt rise to this challenge? Second, a more personal reason: Paul Wheatley1 told me shortly before his death that he thought this period at Cambridge represented the highest accom- March 13, 2008 (7:35 pm) G:\WPData\TYPE2702\russell 27,2 054.wpd Reviews 273 2 G.yH. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (Cambridge: Cambridge U. P., 1940). Two lectures were presented at Harvard in 1936; the Wrst, a more personal recollection, was printed unchanged. The quote is from p. 2. The second lecture was expanded into the remaining published lectures, all considering speciWc mathematical topics. plishment possible for an academic institution: its fellows and masters had managed to attract and then recognize the genius of Ramanujan and Wittgenstein and to admit them to advanced studies without any real academic credentials. Wheatley had been the chair of the Committee on Social Thought at the University of Chicago; so, he knew something about such matters, as he did about many things involving humans, human settlements, and their arrangement in the world. Incidentally, Wheatley himself appeared as a character, Battle, in Ravenstein, Saul Bellow’s roman à clef about Allan Bloom. So, to the extent that Cambridge University just before and during the Great War plays a role here, we want to learn as much as we can about the atmosphere of the place. The Indian Clerk is a historical novelz—zin this case naming actual names, elaborating what we know about real people and occasionally adding Wctional charactersz—zall centered on the extraordinary mathematical genius Ramanujan and his equally extraordinary importation from India to Cambridge. The story is told largely in the third person, by an omniscient narrator, but repeatedly we also have the inner voice of G.yH. Hardy: there are a number of chapters with the indication “New Lecture Hall, Harvard University”, dated 1936, in which Hardy speaks in the Wrst person. In these passages David Leavitt uses parts of the published lectures, along with G.yH. Hardy’s private thoughtsz—zas imagined by Leavittz—zabout this “one romantic incident in my life” and about other matters that still haunt him.2 The novel is thus in some sense more about G.yH. Hardy and his inner life than it is about Srinivasa Ramanujan. The triumph of the novel is its ability to reconstruct and convey in a lively manner the circumstances of the time, the look and smell of the place, the crosscurrents, dynamics, and dislocations of people during these years. Leavitt has woven together a great deal, from many diTerent realms: pre-war meetings of the Apostles, the high table, the pre-war mathematics tripos, the method of collaboration between Hardy and J.yE. Littlewood, Cambridge as military training grounds and as hospital for the wounded, vegetarian cookery, feminism, Hindu... (shrink)

In each of Parts 1A, IB and II of the Philosophy Tripos, there is an Essay paper in which you are asked to write for three hours on a single topic. In these notes I offer some suggestions about how to tackle this paper, and try to answer some Frequently Asked Questions. The notes are based (in the second half, very closely indeed) on notes written by Jane Heal -- I'm very grateful to her for allowing me to snaffle (...) some of her best suggestions, though she is not responsible for the final result. Do note, though, that the result is still just one view ... Consult other supervisors/directors of studies for additional advice. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:53. AN INDEX OF HUME'S REFERENCES IN A TREATISE OF HUMAN NATURE The index below of Hume's references in the Treatise te the works of other authors excludes those which are accurate and full in his text (of which there are few) and those which are so general, e.g., to Spinoza's atheism, that no passage is specifiable. Hume mentions other writings, for which this index is compiled, in several (...) different ways. Occasionally he mentions the author's name, the title of his book and gives a reference which is less specific than it could be. These have been identified. Often he mentions an author's name only, e.g., de Retz, and in such cases the fullest possible reference has been given. One of Hume's notable intellectual gifts was his ability to distil several pages of a book into one or two sentences of crisp and accurate synthesis. (This skill is most apparent in his summaries of articles in Bayle' s Dictionary in his "Notes on Philosophy", of which the manuscript is in the Royal Society of Edinburgh Library.) In these instances, page references are impossible and the closest indication one can give is a section or chapter. Some of his references are anonymous, e.g., as an 'elegant writer' says, and so are some quotations. These have been identified with one exception. One anonymous reference (number 24 below) requires explanation because it is both anachronistic and interesting. Hume refers to an observation by "a late eminent philosopher". It is anachronistic because the book to which he refers was published after the Treatise; it is interesting because it provides further evidence of Hutcheson's influence on Hume and the latter' s regard for him. The explanation, for Hutcheson was still alive when Vol.11 of the Treatise appeared in 1739, is that 'late' is here being used in the sense of 'recent' - Hutcheson himself uses the word in the same way in referring to Mandeville when the latter was 54. alive. (An enquiry concerning moral good and evil. Section 1, VI.) Further, the System circulated widely among Hutcheson's friends in Scotland and over so many years that it finally appeared posthumously. That Hume could not cite a published work also accounts for the anonymity of the reference to someone he admired. It is often impossible to determine in which language or in which edition Hume read a particular author. Where there is evidence as to which language he used, the title has been given in that language. There are now so many extant editions of the Treatise that Volume, Part, Chapter and Section references are given, as well as the pagination of Selby-Bigge' s edition, so that readers of other editions may be able to use the index. 1.Vol. 1. Title-page. Tacitus, The Histories, Bk. I. 1. 2.Part 1, Sect. 1, p. 2, n. John Locke, An Essay concerning Human Understanding, Bk. I, Chap. I, 8. 3.Sect. VII, p. 17, n. George Berkeley, A Treatise concerning the Principles of Human Knowledge, Introductixi, Sect. 7, e_t seq. 4.Part II, Sect. II, p. 30, n. Nicolas de Malezieu, Elementa Geometrica. 5.Sect. Ill, p. 35, n. John Locke, Essay, Bk. II, Chap. XIV. 6.Sect. IV, p. 43, n. Antoine Arnauld, La logique ou l'art de penser. Part I, Chap. 5. (In some editions Pierre Nicole is named as co-author. The book is also known as the Port Royal Logic). 7.Sect. IV, p. 46, n. Isaac Barrow, Mathematical Lectures. 8.Part III, Sect. Ill, p. 80, n. Thomas Hobbes, Elements of Philosophy, Part Second, Chap. 9. And Tripos : in Three Discourse. Ill, of Liberty and Necessity. 55. Sect. Ill, p. 80, n. e.g., Samuel Clarke, A Demonstration of the Being and Attributes of God, Props. I-III, et. seq. 10.Sect. Ill, p. 81, n. John Locke, Essay, Bk. IV, Chap. X. 11.Sect. VIII, p. 100 and appendix Vol. Ill, p. 630. Cicero, De Finibus Bonorum et Malorum, Bk. V. 1.2. 12.Sect. XIII, p. 153. Jean Francois Paul de Gondi, Cardinal de Retz, Mémoires, Bk. III. The second 'observation' is from Book... (shrink)

Sir Arthur Norrington deserved better of the world than to be known for his table. The Norrington Room, his presidency of Trinity, his long service to the University Press, deserve repeated coverage in the papers. But the only thing they say about him year after year is that he devised the table for comparing the academic prowess of the colleges in the Schools. It is not even true. Long before the Norrington table was first published, when I was an Assistant (...) Tutor in a Cambridge college, I used to see the table which the Tutor drew up each year to show how our college was faring in tripos in comparison with other colleges. And, as a private tutorial check on Schools results, it is a legitimate and useful tool. But, published in the newspapers and made the subject of tea-time conversation in the country, it is a menace and counterproductive to the good things that Oxford should be chiefly concerned to foster. (shrink)

F. Richman raised the question of whether the following principle of second order arithmetic is valid in intuitionistic higher order arithmetic $\mathbf{HAH}$: $\forall X\lbrack\forall x(x \in X \vee \neg x \in X) \wedge \forall Y(\forall x(x \in Y \vee \neg x \in Y) \rightarrow \forall x(x \in X \rightarrow x \in Y) \vee \forall x \neg(x \in X \wedge x \in Y)) \rightarrow \exists n\forall x(x \in X \rightarrow x = n)\rbrack$, and if not, whether assuming Church's Thesis CT and (...) Markov's Principle MP would help. Blass and Scedrov gave models of $\mathbf{HAH}$ in which this principle, which we call RP, is not valid, but their models do not satisfy either CT or MP. In this paper a realizability topos Lif is constructed in which CT and MP hold, but RP is false. (It is shown, however, that $RP$ is derivable in $\mathbf{HAH} + \mathrm{CT} + \mathrm{MP} + \mathrm{ECT}_0$, so RP holds in the effective topos.) Lif is a generalization of a realizability notion invented by V. Lifschitz. Furthermore, Lif is a subtopos of the effective topos. (shrink)