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The Theory of Inconsistency The Theory of InconsistencY Inconsistent Mathematics and Paraconsistent Logic C.E.Mortensen Volume I Thesis Declaration This work contains no material which has been accepted for the award of any other degree or diploma in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has bçen made in the text. I give consent for this copy of my thesis being made available in the Universþ Library. The author acknowledges that copywrite of published works contained within this thesis (as listed below) resides with the copywrite holders of those works. C.E.Mortensen 30.11.05 I The Theory of Inconsistency: Inconsistent Mathematics and Paraconsistent Logic CONTENTS Volumel Part 1: Booko Supporting DbcUmentation and Accourrt of Research Curriculum Vitae 500 word sünmary Supporting documentation Citations Reviews of lnconsistent Mathematics Invited Speaker Invited Contributions Statement of Submission Account of Research List of Publications Book Volume 2 l*t2 Fourteen Articles on Inconsistent Mathematics Part 3 Eleven Articles on Paraconsistent Logic Volume 3 Part 4 Six Articles on the Theory of Inconsistency Part 5 Ten Articles on the Philosophy of Mathematics and Physics Part 6 Three Comþuter Studies I CT]RRICT]LUMVITAE CHRISMORTENSEN Name: Christian Edward Mortensen Address: 6 Orley Ave., Stirling, SA 5152, Australia. Ph:(08)83391570 h, (08)83033814 w email : Chris. Mortens en@adelaide. edu. au, fa>r (0 8) 8 3 0 3 524I Date of birth:25.4.45, Rockharnpton, Qld, Australian Citizen. Academic Record B.A.(Honsl in Philosophy), Queensland,196T (Douglas Price Memorial Prize, also two majors in mathematics). Ph.D. in Philosoph¡ Adelaide 1976, thesis title Mental Predicates. Courses in economics and mathematical economics (part of G.Dip.Ec., ANU 1980); and computer science þart of G.Dip.Comp., Deakin 1990). Awards Fellow of the Austalian Academy of the Humanities (FAHA) 1997- Chafu of the Section of Philosophy, Religion and History of Ideas, Australian Academy ofthe Humanities, 2001-4 Australian C entenary lÙledal, 2002 Academic Positions (1) Tutor in philosophy, Adelaide 1970-1. (2) Lecturer in philosophy, Adelaide 1972 (3) Postdoctoral Fellowship in philosophy, ANU, 1977 (4) Tutor in philosophy, Adelaide,1978 (5) Lecturer in philosophy, Adelaide,7979 (6) Research Fellow in philosophy, ANU, 1980-2. (7) Lecturer in philosophy, Adelaide, 1982-5; Senior lecturer I 986-9 I ; Reader 1992-; HoD I 985-7, 1994-6, 1998-2001. Hughes Professor of Philosophy 1998-2005. Head, School of Humanities,2003 Professor Emeritus of Philosophy, 2005- Research fnterests Logic, philosophy of science and mathematics, metaphysics, Buddhism. 2 Teaching Logic, philosophy of mathematics, philosophy of mind, cognitive science, critical thinking, metaphysics, epistemology, Buddhism. Invited Papers Invited papers given at l98l AAP Annual Conference, Newcastle, NSW; 1984 Cognitive Science Conference, UNSW; 1986 Conference on Contadiction, Newcastle, NSW; 1987 Conferenceattheopeningofthe Automated Reasoning Project, ANU; 1991 Conferenceatthe closing of the Automated Reasoning Project, ANU; 1990 inaugural address at inaugural meeting of SA-Cognitive Science Society, Flinders, also 1992 talk to same body. Also invited papers given at U. of Queensland (7 times) ANU (6 times), Macquarie, Wollongong, Latrobe, Melbourne, Monash and WA. First V/orld Congress of Paraconsistency, Ghent, I[v4ay 1997 Second lMorld Congress of Paraconsistency, Sao Paulo, May 2000 Thfud World Congress of Paraconsistency, Toulouse, Aug 2003. Also many papers given at AAL and AAP conferences. Joumal Afüliations (l) Editorial Board, Australasian Journal of Philosophy,l9TT-; Assistant Editor 1977. (2) Editorial Board, Australasian Logic Teachers Journal,1980-5. (3) Associate and Commentator,The Behovioral and Brain Sciences (USA & UK), 1979'. (4) Reviewe r, Zentralblatt fur Mathematik (Gerrnany), I 980-6. (5) Reviewel Mathematical Reviews 1990-3. (6) Regular referee for The Journal of Symbolic Logic, Journal of Philosophical Logic, Notre Dame Journal of Formal Logic (all USA), Studia Logica, Bulletín of the Section of Logic of the Polish Acodemy of Sciences, (Poland) Logique et Analyse @elgium), Journal of AppliedNon-classical Logics (France). Research Grants 1985 - $12,000 Universþ of Adelaide Research Grant for Physical Topology project. 19868¿7 - $60,000 (\¡t/ith Graham Nerlich) ARGC Major Grant for same project. 1988 to present - Each year but one since I have received either a University of Adelaide Research Grant or an ARC Minor Grant for a continuing project in logic and computing, averaging $3,900 p.a. over that time. 2000 $7000 ARC Small Grant for Project "Impossible Pictures" 1993 Teaching Development Grant $2000 (with J.Pituan Maths, U.McGowan ACUE, M.Brooks Comp Sci) for project on teaching Critical Thinking to ESL and NESB students. 3 Conferences Organised Australian Association for Logic Annual Conferences 1980,81,82 (ANLI), 93,03 (Adelaide); Miniconferences on Paraconsistency (with Graham Priest), 87,89,93 (ANÐ; Conference Secretary for Australasian Association for Philosophy Annual Conference, Adelaide, 1983; First World Congress on Paraconsistency, Ghent 1997. (Organising Committee of four). Mini-conference on Logic and Topology, Adelaide 1998. University of Adelaide Committees 1983-5 Arts Faculty Staffing Committee 1986 Arts Faculty SSABSA Committee I 985-6 Education Committee l99l- Eynesbury Foundation Studies Committee (Chief Examiner for subject Critical Thinking and Logic) l99l-4 Arts Faculty Local Management Group (renamed Information Tecbnology Committee) 1993 -5 Artslladsocial Science Discipline Panel (Committee for promotion to Reader/Assoc Professor) 1993 Faculty of Science DSc Assessment Committee 1994-6, 1999- Academic Board 1994- Arts Faculty Board 1994-6 Arts Faculty Steering Committee 1995-2004 Chair, University of Adelaide Human Research Ethics Committee 1995 Arts Faculty Promotions Committee (Promotion to Lecturer B&C) 1995-6 Arts Faculty Review of Teaching 1997 Arts Faculty Rep, Board of the Faculty of Mathematical and Computer Sciences 1999- Humanities and Social Science Resea¡ch and Research Training Committee 2003 Arts Faculty Executive Miscellaneous President, Australasian Association of Philosophy, 2000. Member 1968- 4 President, Australasian Association for Logic,1993 &,2003, General Secretary 1994-02, Member 1965- President, U. of Queensland Philosophy Club, 1965-7. Member, U.of A. Philosophy Club 1971-, President l97l-4. Foundation Convenor, U of Adelaide Logic Group 1982-. Member, SA Society for Philosophy for Children, 1985-8. Member of the Board of the Second Australian Conference on Cognitive Science, UNSW, 1990. lnvited to Chair a session of IJCAI 91 (International Joint Conference on Artificial Intelligence), Sydney. My former undergraduate logic student, Dr. Greg Hjorth, was awa¡ded the inaugural Sacks Prize (best thesis on logic anywhere in the world n 1993-4), for his Berkeley PhD thesis. Foundation Honours Coordinator, joint Adelaide-Flinders Philosophy Honours School, 1990-2. External Assessor for Philosophy Major, U. of South Australia 1993. SA Convenor, Symbolic Reasoning Systems Research Project (AI project involving 7 Australian Universities, CSIRO and DSTO), 1994-. Invited Research Seminars locally in Deparhents of Computer Science (4 times), Mathematics, AI Group, Mathematical Physics, Womens'and Childrens'Hospital, Dep of General Practice, Flinders Information Science. Numerous public lectures given or organised at the University of Adelaide, including the Mitchell Centenary Lectu¡e (1994),the series Philosophy: Towards the New Millennium (1996),Mind and V/orld Tibetan Buddhist seminar (1997), Mars, Meteorites and the Meaning of Life (1997) the Gavin David Young Memorial Lectures (1998), and Buddhism: A Westem Reaction (2001) Regular fortnightly 30 min. radio spot on ABC Radio 5AN (AM 891) throughout1996, also 5AN, 5AA, 5UV, and Radio National interviews 1996-.5Al.l Regular monthly Commentator 2002- Member of Congress Organising Committee (of four) and Program Committee, First World Congress on Paraconsistency, Gent, Belgium, July 1997. Assessor for Personal Chair, 1997, U. of Sydney. Selection Committee for Boyce Gibson Chair of Philosophy, U.of Melbourne, 2000 Listowner of SAPHIL, the South Australian Philosophy List on the interret. The only academic ever to fine their Vice Chancellor for fallacious arguments and get away with it (he paid up), 5 Referees. (1) Professor Robert K. Meyer, Research School for Information Science and Engineering, Australian National University, PO Box 4, ACT 2601, Australia. email: [email protected] ph: (02)62798605w (02)62798630sec (02)62et4348h fax: (02)62798651 (2) Professor Graham Priest, Boyce Gibson Professor of Philosophy, The University of Melbourne, Parkville, Victoria Australia email : [email protected]. au ph: (03)8344711tw (03)834451 42sec (03)e344123th (3) Emeritus Professor Graham Nerlich, 29 Hañy St, Goodwood SA 5034 email: Graham.Nerlich@aÃelude.edu.au ph: (08)82711464 fax: (08)83033396 Other referees available on request. 6 MORTENSEN BTBLTOGRAPITY (1s.04.0s) 1 Books, Monographs, SymPosia 1.1 Sole Author V/orks (l) Inconsistent Mathematics, Dordrecht, Kluwer Academic Publishers, 1995. 1.2 Editorial V/orks (2) -- and Gratram Priest, Contemporary Logical Research in Australia, (edited collection, appearing as a double issue of Zogique et Analyse, vols 137-8 & 139-40).
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