This is the home page of J.R. Lucas, Fellow of Merton College, Oxford

Fellow of the British Academy

Contact details:

address I have now left Oxford. My new letterhead is:

Mr J.R. Lucas, F.B.A.
Lambrook House,
East Lambrook,
Somerset, TA13 5HW England

Telephone 01 460 240413
Fax (use voice first, and ask for fax)
Station Crewkerne
OS grid reference ST 433188
E-Mail john.lucas `at' (I have deleted the simple mailto command, because spamsters are now searching the internet for the `at' sign, and thus obtaining further addresses for their objectionable messages.)

wprowadzenie w.j. polskim-kliknij TUTAJ

Questa pagina in lingua italiana contiene una breve presentazione degli altri contenuti del sito wuesto


  • ``Reality and Time: Reply to Contributors'' in International Studies in the Philosophy of Science, Volume 11, Number 1, March 1997


    September 22nd, 2008. I have just spotted some bad typos (omitted negation symbols) in ch.2 of Reason and Reality p.32. If you have downloaded this chapter, please do so again from the corrected version.

    October 2nd, 2008. I was dismayed to find yesterday that although I had entered many corrections to ch.2, my computer had managed to replace the corrected files with uncorrected ones. I think the current text is correct. But if you spot any errors, please E-mail me.

    Old News

    September 16th, 2006

    I have put chapters of my book, Reason and Reality, on the web, as a series of pdf files. My reasons are partly prudential, partly ideological. Publishing hardback in the traditional manner is slow and tedious, and offers no opportunity of rectifying errors (and I make many typos, as well as more serious mistakes) until the print run is sold out. Plato said that books were a poor substitute for dialogue, f and the internet allows for intellectual interchange in a way that was impossible with the old technology. And finally, hardback books are too expensive for most people to buy. I have always warmed to Hillaire Belloc's lines

    When I am gone, let only this be said:
    His sins were scarlet, but his books were read

    I, too, would rather be read than be rich. You are welcome to download and print for your own use what I have put on the web, as outlined in my copyright notice below. It seems that enough people would want hardcopies to interest a publisher, namely Ria University Press. The hardback edition (ISBN 13: 978-1-934297-04-9) and the paperback edition (ISBN-10: 1934297046) have now been published in the USA at $44.44, and can be ordered through and and should be available from all Expresso Book Machines world wide. Blackwell's have an Expresso Book Machine in their Charing Cross Road branch, 100 Charing Cross Road, WC2H 0JG.

    Corrigendum p.270, l.21 should read ``The dual parentage of space endows it with different ambitions.''

    If you cannot get a printed copy, then it is still available on the web: to read particular chapters, use this link to take you to the table of contents; and then to view a particular chapter, click on the chapter number. Or go to section VI below. I recommend 100% or 125% magnification. I haven't yet learnt how to do an index in TEX or pdf. In some chapters my computer complains she cannot find the right font, and suggests using Helvetica instead. If I click OK, she seems to be happy to go on.

    Less New News

    Each week on Sunday morning I receive an E-mail telling me what hits I have had during the previous week; which may make me suffer from the sin of pride, or, more usually, from depression, before I go to our village church. Recently there has been a sudden jump in the hits for my ``Tables''---79 last week. When I looked at it myself, I found that it was not one I had written against the Norrington Tables for Oxford in 1980, but a subsequent follow up article in the Oxford Magazine. I think the earlier one was better, and have now included Norrington Blues
    I have now managed to convert TEX files including diagrams into PDF ones that can be read by Adobe Acrobat. I am producing replacement chapters for those in my The Conceptual Roots of Mathematics containing typographical errors. For details see

    Corrigenda to The Conceptual Roots of Mathematics,

    On November 6th, 2003, I stood in for Bishop Wilberforce at the British Academy, at 5.15pm, saying what he might have said now, with the benefit of 143 years hindsight, to a neo-Huxley (represented by Professor Janet Browne).

    I have put a summary of the case for Bishop Wilberforce on the web, together with a semi-transcript of Professor Browne's and my contributions

    An Engagement with Plato's Republic, by Basil Mitchell and me, has been published by Ashgate.

    It is not a standard commentary. Rather, it is a deliberately anachronistic attempt to make Plato accessible to the modern reader, and to engage him in dialogue with modern problems. Publisher's Blurb It was published on September 5th. It should have come out much earlier, but most unfortunately there was a muddle over the book-jacket, which was to be an adaptation of Raphael's School of Athens showing Plato talking with his pupils, some of them altered to be in modern dress and using a word-processor. Owing to a breakdown in communication an uncorrected proof was used, with Plato more or less eclipsed by `Basil Mitchell' and `J.R. Lucas'. This was not the message we wish to convey. A new book-jacket has been printed, both for the hard-back and for the paper-back editions. If you buy the paper-back, make sure you have the correct outside, with us deferentially down in the right hand corner, taking our place among Plato's pupils, not lording it over them. To encourage you to read further, I have made available on this site as pdf files: the contents, introduction, envoi and an analysis of the text , together with chapters 1, 3 and our most provocative chapter, 10, Sex, Self and Power

    (They can be read by Adobe Acrobat---I recommend 150% magnification).

    The book can be ordered from Ashgate:

    Bookpoint Ltd, 130 Milton Park, Abingdon, Berks, OX 14 4SB, UK
    Tel. +44 (0) 1 235 827730
    Fax +44 (0) 1 235 400454
    Ashgate Publishing, 2252 Ridge Road, Brookfield, VT, 05036-9404, USA,
    Tel. (+1) 802 276-3162
    Fax (+1) 802 276-3837
    Ashgate Publishing, 240 MacPherson Road, #08-01 Pines Industrial Building, Singapore 348574
    Tel. (+65) 7415166
    Fax (+65) 7429356
    Ashgate Publishing, 3/303 Barrenjoey Road, Newport NSW 2107, Australia
    Tel. +61 (0)2 9999 2777
    Fax +61 (0)2 9999 3688
    Hardback (ISBN 0 7546 3365 9) 40.00 Paperback (ISBN 0 7546 3366 7) 15.99 (Postage 3.50)
    When ordering make sure to ask for the revised book-jacket.

    \pdfdest name {Copyright} fit %Copyright


    Except for the Darwin lecture on Time and Religion, you are welcome to download a single copy of anything on this site for your own personal use, and to make further copies for teaching purposes that are not profit-making. If you want to include an article of mine in an anthology, you should ask my permission, which will be granted on the following terms:
    1. . TWO copies to be given me (one for me, one for Merton Library).
    2. . A royalty on each copy sold, calculated thus:

      (recommended retail price divided by 10) times (number of pages of my contribution divided by total number of pages).

      [For short runs---under 1,000---I am prepared to waive the payment as being negligible. But a few of my articles have been much reprinted, and I think it is only fair that I should have some share in the proceeds.]

    One hundred and thirty five entries at present:

    I Gödelian Papers

    1. . ``Minds, Machines and Gödel''
    2. . ``Satan Stultified: A Rejoinder To Paul Benacerraf''
    3. ``Human and Machine Logic: a Rejoinder'', British Journal for the Philosophy of Science, 19, 1968, pp.155-156.
    4. ``Lucas Against Mechanism: A Rejoinder'', Philosophy, pp.149-151.
    5. ``This Gödel is Killing Me: a Rejoinder'', Philosophia, 6, no.1, March 1976, pp.145-148.
    6. Review of Judson Webb, Mechanism, Mentalism and Metamathematics, in The British Journal for the Philosophy of Science, 33, 1982, pp.441-444.
    7. . Criticisms and discussions of the Gödelian argument, based on a list which I distributed at the Turing Conference in Brighton some years ago, with some further additions. In the Proceedings, Machines and Thought, ed. Peter Millican and Andy Clark, Oxford, 1996, Robin Gandy gives a much earlier reference: Emil L. Post, `Absolutely Unsolvable Problems and Relatively Undecidable Propositions---Account of an Anticipation', in Martin Davis, (ed.), The Undecidable (New York: Raven Press, 1965), pp.340-435, esp. pp.417-24. Chalmers gives a more up-to-date list in his bibliography---which used to be but has now moved to Arizona: click here for pursuing his references I am grateful to various correspondents who have helped me to up-date the list given here, and welcome further items.
    8. ````Minds, Machines and Gödel: A Retrospect'', in P.J.R.Millican and A.Clark, eds., Machines and Thought: The Legacy of Alan Turing, Oxford, 1996, pp.103-124.
    9. . the text of Turn Over the Page a talk I gave on 25/5/96 at a BSPS conference in Oxford
    10. . the text of A (n Over) Simplified Exposition of Gödel's Theorem a talk I gave on 14/10/97 in King's College, London
    11. . The Implications of Gödel's Theorem the text of a talk I gave in Manchester in November 1996
    12. . The Implications of Gödel's Theorem the text of a talk I gave to the Sigma Club in London on February 26, 1998
    13. . A handout for the talk on Implications of Gödel's Theorem that I gave to the Sigma Club in London on February 26, 1998
    14. ``Commentary on Turing's ``Computing Machinery and Intelligence'', Forthcoming in The Turing Test Sourcebook to be published by Kluwer in 2005.
    15. ``A response to a paper by Professor Feferman, forthcoming in a volume edited by Richard Swinburne.
    16. An E-mail from Dr Jeffrey Ketland
    17. An E-mail from Mr Michael Harris

    Note: Most critics concentrate their fire on ``Minds, Machines and Gödel'', without looking at the fuller statement in The Freedom of the Will, which includes the rebuttals first published in ``Satan Stultified''. In recent years it has been out of print. But under a new intitative by OUP, it is now available again. Single copies are printed on a one-off basis. I commend it to those who think there are holes in my original ``Minds, Machines and Gödel''

    A full discussion of the issues raised is now available Etica e Politica, 2003.

    A helpful discussion by P.Madden, aimed at an undergraduate readership at Warwick University, with recommendations for further reading, is now available The Lucas Debate and Related Issues

    Etica e Politica .

    II Academic

    1. . a bibliography of my published academic work
    2. . ``Reality and Time: Reply to Contributors'', in International Studies in the Philosophy of Science, Volume 11, Number 1, March 1997
    3. . ``The Lesbian Rule'', first published in, Philosophy, 1955, XXX, no. 114, July, 1955, pp.195-213
    4. ``Not `therefore' but `but',
      Philosophical Quarterly, 16, no. 65, October, 1966.
    5. ``True'', Philosophy, XLIV, no.169, July 1969, pp.175-186.
    6. . ``Ethical Intuitionism II'', Philosophy, XLVI, No.175, January 1971, pp.1-11.
    7. . Butler's Philosophy of Religion Vindicated, Durham, 1978.
    8. . ``Wilberforce and Huxley: A Legendary Encounter'', The Historical Journal, 22, 2 (1979), pp. 313-330
    9. ``The Nature of Law'', Philosophica, 23, 1979 (i), pp.37-50.
    10. The Restoration of Man: A Lecture given in Durham on Thursday October 22nd, 1992, to mark the Fiftieth Anniversary of C.S. Lewis's The Abolition of Man
    11. ``A View of One's Own'', Philosophical Transactions of the Royal Society, 349, 1994.
    12. ``Reflections on the Atonement'': ch.12 in A.G.Padgett, ed., Reason and the Christian Religion, Oxford, 1994, pp. 265-276.
    13. ``A Mind of One's Own'', Philosophy, 68, 1993, pp.457-471.
    14. ``The Lay-out of Arguments'', in W.Krawietz, N.MacCormick, G.H.von Wright, eds., Prescriptive Formality and Normative Rationality in Modern Legal Systems, Berlin, 1994, 285-295
    15. ``On the Nature of Things'', Presidential Address to British Society for the Philosophy of Science, 1993
    16. ``The Unity of Science without Reductionism'', Acta Analytica, 15, 1996, pp.89-95.
    17. . Intimations of Reality the text of a talk I gave in Cambridge in June 1997
    18. . Transcendental Tense II A draft of my reply to Professor Mellor's Transcendental Tense I at the joint meeting of the Aristotelian Society in July 1998.
    19. . Polychromatic Derivation of the Lorentz Transformations A revision of old lecture notes, which I think might be useful for others giving lectures on the philosophy of physics.
    20. . An extract of the letters from Polychromatic Derivation of the Lorentz Transformations, which might be suitable for making transparencies
    21. . An extract of Derivation of the Lorentz Transformations, which might be suitable for making transparencies
    22. . A version the Lorentz Transformations, which might be suitable for making transparencies
    23. . The Ontological Argument a talk given at Centre for Philosophical Studies at King's College, London, on March 4th, 1998
    24. . Handout for a talk given at Centre for Philosophical Studies at King's College, London, on March 4th, 1998
    25. . Charles Dodgson a talk given at St Mary's, Guildford, on May 17th, 1998
    26. . A Century of Time A contribution to the British Academy's Centennial volume, The Arguments of Time, ed. Jeremy Butterfield, Oxford, 1999.
    27. . The Philosophical Background to Eucharistic Theology ch.1 of Thinking about the Eucharist, London, 1972
    28. . `` The Soul'' ch.5 of Faith and Logic, ed. B. G. Mitchell , Allen and Unwin, London, 1957, pp.132-148., London, 1972
    29. . `` ``Historian Malgré Moi'''' ch.10 in L.Pompa and W.H.Dray, Substance and Form in History, Edinburgh, 1981, pp.133-144.
    30. . `` Against Equality''
    31. . `` Equality in Education''
    32. . `` Against Equality Again''
    33. . `` Because You are a Woman''
    34. . `` Vive la Différence''
    35. . `` The Alternative Sex''
    36. ``Plato's Philosophy of Sex'', in E.M.Craik, ed., Owls to Athens, Oxford, 1990, pp. 223-231.
    37. . `` The Philosophy of the Reasonable Man''
    38. ``Philosophy and Philosophy Of'', Proceedings of the British Academy, 1986, pp.248-267.
    39. ``The Responsibilities of a Businessman'', , in Business Ethics, ed. C.Cowton and R. Crisp, Oxford, 1998, pp.59-77.
    40. . `` Time and Religion'', a lecture deliverd in Darwin College, Cambridge, in March, 2000, and published by Cambridge University Press, in Time, ed. K.Ridderbos, 2002
    41. . `` ACE: Assess Cost of Error'' published in The Risk of Freedom Briefing, Issue no.5 October 2000
    42. . `` Towards a Theory of Taxation '' published in Social Philosophy and Policy, Volume 2 Issue 1, Autumn 1984, pp.161-173.
    43. ``The Language of Liberty'' , in Maurice Cranston and Peter Mair, eds., Language and Politics, Brussels, 1982, ISBN 2-8027/0294/7 Bruylant, D/1982/0023/7, pp.199-212.
    44. `` ``The Worm and the Juggernaut: Justice and the Public Interest'', '' Business and Professional Ethics Journal, 6, no.2, pp.51-59.
    45. . ``Moralists and Gamesmen'', Philosophy, XXXIV, No.128, January, 1959, pp.1-11.
    46. . ``On Not Worshipping Facts published in The Philosophical Quarterly, 8, 1958, pp.144-156.
    47. ``Euclides Omni Naevo Vindicatus'', British Journal for the Philosophy of Science, XX, 1969, pp.1-11.
    48. ``From Euler to Euclid'', The Way the Academy's Research Programme should have gone.
    49. ``The Phenomenon of Law'', ch.4, in P.M.S.Hacker and J.Raz, eds., Law, Morality and Society, Oxford, 1977, pp.85-98.
    50. . `` The Concept of Justice'' A paper was read to the Societas Ethica at Noordwijk aan Zee, Holland, in 1977, and subsequently published in their Proceedings. It was my first exposition of the ideas I subseqently developed in my book On Justice
    51. ``Reason Restored'', ch.5 in W.J.Abraham and S.W.Holtzer, The Rationality of Religious Belief: Essays in Honour of Basil Mitchell , Oxford, 1987, pp.71-84.
    52. ``Methodological Individualism'', A section I had written for my Principles of Politics, but decided not to use. I recently dug it out for an American friend. I publish it here, in case it is of use to anyone else.
    53. The University Sermon on the Sin of Pride, Preached in the University Church of St. Mary the Virgin, Oxford, at 10.15am on Sunday 26 November 1978.,
    54. Jesus Barabbas: The Question Pilate Actually Asked
    55. ``A Plea for the Moral Sciences'' A piece which I found myself writing recently (when I should have been doing something else), and which I might work up for publication at a later date, but meanwhile expose to your comments and criticism.
    56. ``Time and Reality'' A Talk given to the PPE Society in Oxford on February 11th, 2009
    57. ``Questions Asked'', (Chapter 1 of An Engagement with Plato's Republic, Ashgate, 2003, is a pdf file, and can be read by Adobe Acrobat (I recommend 150% magnification).
    58. ``The Return of the Self'', (Chapter 3 of An Engagement with Plato's Republic, Ashgate, 2003, is a pdf file, and can be read by Adobe Acrobat (I recommend 150% magnification).
    59. ``Sex, Self and Power'', (Chapter 10 of An Engagement with Plato's Republic, Ashgate, 2003, is a pdf file, and can be read by Adobe Acrobat (I recommend 150% magnification).
    60. ``Schematic Analysis of the Republic'', (An Appendix to An Engagement with Plato's Republic, Ashgate, 2003, may be of use to those set to read the Republic during the summer. It is a pdf file, and can be read by Adobe Acrobat.
    61. How a tutorial with a pupil, F.P.E. Marsland, led to my writing the following:
    62. ISONOMIA.pdf (It is a pdf file, which can be read by an Acrobat Reader. I recommend 150% magnification).
    63. Corrigenda to The Conceptual Roots of Mathematics,
    64. A Polychromatic Proof of Desargues' Theorem---An Appendix to Chapter 2 of The Conceptual Roots of Mathematics, This is not in the least original, but it might be of use to someone needing to teach it: the use of different colours makes it easier to visualise the different planes involved.
    65. A Polychromatic Discussion of Desargues' Theorem in 2-dimensional Projective Geometry---A Second Appendix to Chapter 2 of The Conceptual Roots of Mathematics,
    66. Waismann at Oxford''. A talk delivered at the Waissman Conference in Vienna, on October 2nd, 2010; printed in the Oxford Magazine, No.395, Fifth Week, Michaelmas Term, 2010, pp.20-21.
    67. A draft paper I wrote in the 1970s as possible contribution to the Festscrift for H.L.A.Hart, now published at the request of a correspondent.
    68. A synopsis of the arguments against there being any place for moral arguments in economics, and the counters to them.
    69. A brief response to a discussion on Free Will on the radio.
    70. An Unreverential Read of the Gospels. Comments and Criticisms welcome. Tribute
    71. ISONOMIA.pdf .
    72. Hell
    73. Lazarus3

    III Less Academic

    Nos. 1, 2, 3 are to do with the Franks Commission; they have become relevant again, as Oxford is now having another commission, the North Commission.

    1. . The evidence I submitted to the Franks Commission in 1964.
    2. . My viva on the evidence I submitted to the Franks Commission in 1964.
    3. . An article I wrote for Oxford on the Franks Commission.
    4. . The evidence I submitted to the Royal Commission on Reform of the House of Lords in March 1999.
    5. . An exchange of E-mails with Professor Vicki Bruce about the web-site of the British Academy.

    IV Mostly articles I have contributed to the Oxford Magazine, which people have asked to have available.

    1. . An Academy for Non-academics
    2. . Exploiting the Young
    3. . Norrington Blues
    4. . A Plea for Incompetence
    5. . The M.A.
    6. . "The Polity of Academe"---A Reply to Dean Roscow
    7. . ``Statement V'', in The Oxford Magazine,
      Eighth Week, Trinity Term, 1992, pp.5-6.
    8. . Size and Shapelessness
    9. . SXOLH
    10. . Tables
    11. . Too Much Teaching
    12. . Recovering the Vacs
    13. . Access
    14. . Strategy for Survival
    15. . Jowett v. Pattison
    16. . Judge Not . . . .
    17. . Endowment and Morality
    18. . Olympian Alliances
    19. . ``A Don's Defence'', in Oxford, November 1999.
    20. . ``An Earlier Year'', in The Oxford Magazine, Noughth Week, Michaelmas Term, 1996, p.4.
    21. . ``Dead Wood'', in The Oxford Magazine, Fourth Week, Michaelmas Term, 1995, p.5.
    22. . ``In Defence of Teaching'', in The Oxford Magazine, Trinity Term, 1996, p.5.
    23. . ``Publish and Perish'', in The Oxford Magazine, Eighth Week, Hilary Term, 1996, p.11.
    24. . ``Relocation'', in The Oxford Magazine, Eighth Week, Trinity Term, 1996, pp.5-6.
    25. . ``Gownlessness'', in Oxford , 1986.
    26. . ``Theses'', in The Oxford Magazine, 1990.
    27. . ``. . . et dona ferentes'', A Critical Review of The Lambert Review of Business-University Collaboration, in The Oxford Magazine, 1994.
    28. . ``Not a Green Light'', in The Oxford Magazine, Hilary Term, 2005.
    29. . ``My Harem'', in The Oxford Magazine, Trinity Term, 2007.
    30. . ``Flagships'', in The Oxford Magazine, Michaelmas Term, 2007.
    31. . ``Confessions of a Hexist'', in The Oxford Magazine, Michaelmas Term, 2007.
    32. . ``Haecceity in my Harem'', in The Oxford Magazine, Trinity Term, 2008.
    33. . ``The Open Society and '', in The Oxford Magazine, Trinity Term, 2008.
    34. . ``If I were very Rich'', in The Oxford Magazine, Trinity Term, 2008.
    35. . A Letter to Mr Hayes about the Proposal to move the South Petherton Surgery .
    36. . ``Metricated Charity'', in The Oxford Magazine, Eighth Week, Hilary Term, 2009.
    37. . Confessions of an Inadequate Examiner, in The Oxford Magazine, Eighth Week, Hilary Term, 2011.
    38. . Metricated Inefficiency, in The Oxford Magazine, Second Week, Michaelmas Term, 2012.
    39. . Donor Fatigue, in The Oxford Magazine, Eighth Week, Michaelmas Term, 2012.
    40. . Ryle (some typos uncorrected, in The Oxford Magazine, Fifth Week, Hilary Term, 2013 .
    41. . The Ebdon Fallacy, in The Oxford Magazine, Eighth Week, Hilary Term, 2013.
    42. . Whar Should we be Paid?, in The Oxford Magazine, Noughth Week, Trinity Term, 2013.
    43. . Admission, in The Oxford Magazine, Eighth Week, Trinity Term, 2013.
    If there is some other article of mine you would like to have available on this site, send me an E-mail at the address given above.

    V Memoirs

    A Memoir of Professor R.M. Hare, FBA, published in The Balliol College Annual Record 2002, pp.30-32.
    A Memoir of T.F.G.R. Braun, Fellow of Merton
    An Address Delivered in Merton Chapel on January 31st, 2009 at the Memorial Service for T.F.G.R. Braun

    VI Reason and Reality

  • . Title Page
  • . Contents
  • . Chapter 1 Falliblity and Reality
  • . Chapter 2 The Development of Normative Reason
  • . Chapter 3 A Critique of Critical Reasoning
  • . Chapter 4 Cause and Explanation
  • . Chapter 5 Projection and Probability
  • . Chapter 6 The Tree in the Lonely Quad
  • . Chapter 7 Existence and Universals
  • . Chapter 8 Appearance and Unreality
  • . Chapter 9 The Search for the Ultimate
  • . Chapter 10 Points of View
  • . Chapter 11 Quantum Mechanics
  • . Chapter 12 Time
  • . Chapter 13 Reductionism
  • . Chapter 14 Persons
  • . Chapter 15 Inconclusions

    At the end of each chapter there are places to click on which will take you to the next chapter, to the contents, or to this (the Home) page. In the Contents clicking on a chapter number will take you to that chapter.

    VII The Conceptual Foundations of Mathematics, Revised

    There were an embarrassing number of typos in the published edition. These are listed in Corrigenda to The Conceptual Roots of Mathematics, together with pdf files of the corrected chapters. But I have been worrying away at some of the loose ends I had not tied up properly, and have now written three chapters that are markedly different from the published version.

  • . Chapter 9A, ``What is Logic'' partly replaces the old Chapter 13, ``Chastened Logicism?'', but needs to come before the new
  • . Chapter 9B, ``Transitive Relations'', which, on the urging of a correspondent, has been substantially re-written.
  • . Chapter 10A , ``Protopology'', which attempts to replace Whithead's unsuccessful programme of ``extensive abstraction'', basing topology on mereology together with infinite sequences, by one ``Boolean Plus'' that bases it on the most minimal extension of mereology.

    This I need to supplement with a further account of Nextness and Nearness. In ordinary life nextness is a feature of the space we live in. Neighbours live near us; some next door. When visitors call in on us, they expect us to stop what we are doing and attend to them, because they are now in our immediate vicinity. But in the electronic world there is no natural criterion of nearness or nextitude. At first it was acceptable to answer a telephone call, and say to the person one had been talking to ````Mind if I take this call?'', but now it would be rude to disattend to someone merely to talk to someone else on the telephone. (When a guest let her telephone ring during a royal luncheon party, the Queen said ``You had better take the call---it might be someone important'') In the absence of space, we can use the Cantorian and Dedekindian approaches. The former runs into difficulties again, but Least Upper Bounds look hopeful.

    I also need to bolster my chapter 48 Athanasius intra Mundum in my A Treatise on Time and Space, (Methuen, 1973) with another more fundamental argument (which I found in a lecture by Sir Arthur Eddington, originally in New Pathways in Science, Cambridge University Press) ``The Theory of Groups and Orthogonality'' for the three-plus-one dimensionality of space and time. Eddington considers four operators: A,B,C,D, which can be interchanged, and also turned upside down. He constructs from these four a further five: E1, E2, E3, E4, E5, which all anticommute with one another; E1E2=-E2E1, etc. for all ten pairs. He then shows that E1 squared = E2 squared = E3 squared - 1 and E4 squared = E5 squared = -1 E12=E22=E32=1 and E42=E52=-1 A pentad always consists of three operators whose square is 1, and two whose square is -1. The anticommutative ones give an abstract explication of orthogonality. This yields a different explanation of orthogonality from mine in Athanasius intra Mundum in A Treatise on Time and Space---and more fundamental.

    I need to give a better account of infinity, and re-do the final chapters, but I have other pressing concerns, so publish these three chapters on their own.

    VIII Bibliographies

    I have been trying to persuade the British Academy, Corpus and Oriel to put these bibliographies on their web sites, but I have not succeeded thus far.

  • . Complete Bibliography of the Philosophical Writings of R.M. Hare
  • . Complete Bibliography of the Philosophical Writings of B.G. Mitchell
  • . Complete Bibliography of the Philosophical Writings of Helen Oppenheimer
  • . Bibliography of Michael Oppenheimer
    "Wojtek links

    IX For Browsers

  • . a note of links to other web sites
  • . My son, Edward's web page
  • . Next Sunday's Service at St James' Church, East Lambrook.
  • . Wishing for a Well A local charity that raises money in Somerset, and uses it to build wells and dams in an impoverished region of East Africa.

    Can a businessman be moral? What are the values implicit in a business deal? Is there such a thing as economic justice?

    Ethical Economics, by M.R. Griffiths and J.R. Lucas was published (at last) on January 8th, 1997, by Macmillans.
    It examines the fundamental principles of economic activity in order to enable people to answer these questions, and think through the problems they face, and to reach their own decisions. It argues that business relations are sustainable only against a background of the parties having some values in common, and in consequence there is a point of entry for ethical considerations in economics: but there are significant divergences of interest between the parties to a business transaction, and therefore the morality of business life is less personal and more external than it is in families and close-knit communities.

    It was reviewed by Samuel Brittain in The Financial Times, June 5th, 1997.

    By February, 2007, it was almost unavailable, though Amazon can sell copies at $95 plus $9.95 packing and posting. By the end of 2008 it had earned a place in my ``I Told You So'' column. I hope to have made most of it available by clicking on on the link: Ethical Economics,

    During the course of 2010 I have been rethinking the whole subject, with a view to a second edition being produced by Michael and me. It seemed to me that though much of what we had said was true and timely---especially the dangers of short-termism, we were not getting a hearing. because economists were trrapped by assumptions they took for granted as defining their subject. Economics was studid in isolqation, not as one of the humanities along with history, law and the like. The result was that general arguments of humanity had no point of entry into economic discourse. The only arguments that counted were ones that could be derived from the assumption that every agent was an ``economic man'' who souight to maximise the realisqtion of his own preferences. I needed, therefore, to write a prolegomenon, ``Economics as a Moral Science'', to liberate readers from assumptions that prevented them from seeing economic activity in its full human and social context, and in particualr from the false understanding of rationality as maximising one's own ``pay-offs''. The title I took from Keynes, who realised that economics could be properly understood only if it was viewed in the context of human behaviour generally. The same, I claim, holds good of law ande history and other humane disciplines, which suffer if studied only in isolation by specialists. Economics is the study of decentralized choice, but though the choosers are separate3, the dconsideartions theyb take into account need not be. The Theory of Games shows that the polidcy of each chooser always seeking to maximising his own pay-off, far from being the paradigm of rationality, can lead to sub-optimal results. We do better if we are not separate individual atoms, but can take a collective view, having regard not only to one's own preferences, but also to those of others. Furthermore, not only do I fare better if I can take a first-person plural view as well as a first-person singular one, but I am impelled to conjugate also over person, tense and mood. Thus although in economics decisions ee taken by different agents, each agent is under rational pressure to consoder things not just from where he sits, but to take a wider, longer and deeper view. We find it difficult to adopt this conclusion whole-hearte3dly, because we rightly regard money as something we could do nwith more of, and extrapolate to a simple maximising policy, forgetting that the inference from the comparative to the superlative only holds if other things are equal, which they often are not. Once it is accepted that economic activity is a form of social activity, and that rationality does not require one always to maximise, the way is open for an aent to bring wider, including ethical, considerations to bear on his decidion-making in economic affairs. But economics is very largely concerned with money, which is much misunerstood. The Thelory of Games provides an understanding of money not as a substance, surrogate gold, but acilitator of cooperation in cases when the natural benefits of cooperation accrue unevenly to the parties involved. It is fundamentally a lubricant, but in our moneyed society often taken to be a fuel. But also, thanks to banks, it ceases to be limited in the way real fuels are, and becomes indefinitely though not infinitely extensible through credit. Economic activity is greatly enhanced thereby, but becomes vulnerable to an inherent risk of lemming-like3 behaviour. This opens up a number of macro-economic issues we did not explore in *Ethical Economics*. A lack of moral integrity was a root cause of the present financial crisis. But the remedies being currently pursued, particulalry the continual inflation of teh currency, are also open to severe criticism. I havce tried to understand Keyneseian economics, but though I find his criticisms of other economists cogent, I cannot follow the aegumentation of the General Theory. I am not putting my detailed difficulties on the web: others are much better qualified to crticize. Rather, I have rephrased my analysis of Booms and Busts in terms of liquidity, and come to the sceptical conclusion that often the best that governements can do is nnothing. Most government interventions increase nuncertrainty, and hence demand for liquidity, thereby discouraging investment and enterprise. A second sceptical note ends my Prolegomenon. It is widely asumed that full employment and ever-increasing economic is the proper goal for society. But solitary activities and social actifities not undertaken to earn money are also valuable,, and a good sociey is one in which these figure prominenly, and not only those in which money changes hands. What I am putting on the web is work in progress, not finished work or a book prepared for publication. There are still several repetitions and duplications needing to be ironed out, and undoubtedly many errors. It is just a draft I am sending to my co-author for his comments, crticisms and corrections. In putting it on the web, I am exposing it to your comments, criticisms and corrections too. But that is one of the advantages of the web: it makes comment, criticism and correction possible before publication, instead of only after it.

    January 31st, 2011 I am still working on the first part, eliminating typos, duplications and the like. I am having heretical thoughts about money in the second part, and need to think more about it. Meanwhile I put A three-page synopsis of the arguments against there being any place for moral arguments in economics, and the counters to them.
    February 14th, 2011 Chapter One of Economics as a Moral Science
    February 24th, 2011 Chapter Two of Economics as a Moral Science

    The Conceptual Roots of Mathematics was published by Routledge on Friday, October 15th, 1999.
    It is dedicated to

    David Bostock


    all my colleagues

    I have had many colleagues, and have been greatly helped by them, some of them unknown to me. I dedicated an earlier work, Space, Time and Causality to Eric James and all my teachers, and wrote to those I could and told them so. I dedicated Responsibility to all my pupils, and put their names on the book-jacket. I have listed in colour the names of those in Merton with whom I have shared pupils, those I have given lectures and seminars with, and those with whom I have worked on other projects in Oxford, Cambridge, Leeds, Edinburgh, the British Society for the Philosophy of Science, and elsewhere. But there are many others whose names could well appear here, to whom also the book is dedicated with grateful thanks.

    Corrigenda to The Conceptual Roots of Mathematics,


    I am grateful to someone from Greece who telephoned me on the morning of January 20th, 2005, to tell me of another misprint in The Conceptual Roots of Mathematics. He gave me his E-mail address, but it bounced, as his to me had earlier. Will he please accept this as my thanks for his correction, and my apology for not having got back to him within half an hour, as I said I would. If he writes to me by snail-mail, I shall gratefully and apologetically respond.

    I had an E-mail from a schoolgirl in Australia, asking for details about myself. An abridged version of her letter and my response gives some information about me. More recently I had another one from California, which I give in me2.

    This page was devised on May 31st, 1996, and most recently revised on December 9th, 2018

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