Ed Mares’s Web Page

 

I am originally from Toronto, Canada. I have retained my Canadian accent (or so my Kiwi friends tell me when they can’t understand what I’m saying) and the (probably futile) hope that the Maple Leafs will again win the Stanley Cup some day. After leaving Toronto, I moved around a bit, living in the States, Australia, and on both ends of Canada before settling in New Zealand. Now I live in lovely Wellington and teach at Victoria University.

 

Victoria is a wonderful place to do logic. We have a Centre for Logic, Language and Computation, which has members from our maths, philosophy, computer science, and linguistics programmes. There is a lot of interesting work going on here on modal logic, non-classical logics, model theory, algebraic logic, recursion theory, complexity theory, and set theory.

 

My current research is on relevant logic, Bertrand Russell, and on the logic of belief revision. My interest in Russell is to reconstruct his view ca. 1913 to make a coherent epistemology and philosophy of mathematics. I started down this road by reading Bernie Linsky’s book, Russell’s Metaphysical Logic. This project is just beginning but it promises to be long and difficult but fun.

 

My work on belief revision started with the question of how we should amend traditional epistemologies given the view that it is sometimes legitimate to believe in a contradiction. I realised early on that even if we think that to believe the negation of a proposition does not preclude believing the proposition itself, we may still hold that there are some propositions that we find abhorrent, that we want to preclude believing. These abhorrent propositions are those that we reject. The theory of belief revision has us revise our beliefs and rejections in response to new information to retain a coherent (although perhaps inconsistent) whole, in which the set of beliefs do not entail (disjunctions of) any of the propositions that are rejected. This project has also led me to think and write about paraconsistency, negation, and rejection.

 

My work on relevant logic has been both formal and philosophical. The philosophical ideas, as they currently stand, are in my book. For some years I have been thinking about provability predicates in a form of Peano arithmetic based on relevant logic.

 

I have also done some joint work about the use of critical thinking in management and the public service. Bob Cavana of Victoria’s Management School and I have been working on a project linking critical thinking with systems thinking in the analysis of processes in the private and public sector. We have a paper on this forthcoming in the journal, Systems Dynamics Review.

 

I have a Rough Collie named “Zermela”. “Zermela” is the feminine form of “Zermelo”. She is named after the mathematician, Ernst Zermelo. Zermelo was one of the founders of modern set theory, having provided it with an early axiomatisation. Zermelo was also responsible for the first explicit formulation of the axiom of choice and for the discovery of large cardinals. Zermelo even discovered Russell’s paradox four years before Russell (at least according to Hilbert).

 

If you look at the pictures below and take into account Zermelo’s mathematical achievements, you will understand why I named my Collie puppy after him.

 

 

 

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This is Zermela the Collie as a puppy.

 

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And this is Ernst Zermelo the set theorist.

 

 

 

Ed Mares’s Publications

 

 

Book

 

Relevant Logic: A Philosophical Interpretation, Cambridge: Cambridge University Press, 2004

 

 

Book Contract

 

(co-authored with Stuart Brock), Realism versus Anti-Realism, under contract to Acumen Press

 

 

 

Published Articles and Book Chapters

 

  1. (with André Fuhrmann) "Relevant Theories of Counterfactuals" in Ross Brady (ed.), Relevant Logics and their Rivals, Volume II, Aldershot: Ashgate Publishing, 2003
  2. "A Paraconsistent Theory of Belief Revision" Erkenntnis 56 (2002) pp 229-246
  3. "Relevance Logic" in Dale Jacquette (ed.), A Companion to Philosophical Logic, Oxford: Blackwell, 2002, pp 609-627
  4. (with Robert K. Meyer*) "Relevant Logics" in Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Oxford: Blackwell, 2001, pp 280-308
  5. "The Incompleteness of RGL" Studia Logica 65 (2000) pp 315-322
  6. "CE is not a Conservative Extension of E" Journal of Philosophical Logic 29 (2000) pp 263-275
  7. "Disjunctive Information" in Larry Moss, Jonathan Ginzburg and Maarten de Rijke (eds.), Logic, Language and Computation, Volume 2, Stanford: CSLI Press, 1998
  8. "Paraconsistent Probability Theory and Paraconsistent Bayseanism" Logique et analyse 160 (1997) pp 375-384
  9. "Who's Afraid of Impossible Worlds?" Notre Dame Journal of Formal Logic 38 (1997) pp 516-526
  10. (with Paul McNamara) "Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours" Studia Logica 57 (1997) pp 397-415
  11. "Relevant Logic and the Theory of Information" Synthese 109 (1997) pp 345-360
  12. "Mostly Meyer Modal Models" Logique et analyse 146 (1994) pp 119-128
  13. (With A. Fuhrmann) "A Relevant Theory of Conditionals" Journal of Philosophical Logic 24 (1995) pp 645-665
  14. "A Star-Free Semantics for R" The Journal of Symbolic Logic 61 (1995) pp 579-590
  15. (With C.G. Morgan) "Conditionals, Probability, and Non-Triviality" Journal of Philosophical Logic 24 (1995) pp 455-467
  16. "Why We Need a Relevant Theory of Conditionals" Topoi 13 (1994) pp 31-36
  17. (With A. Fuhrmann) "On S" Studia Logica 53 (1994) pp 75-91
  18. "Fictional Objects and Fregean Sinne" in W. Stelzner (ed.), Philosophie und Logik, Berlin: Walter de Gruyter, 1993, pp 65-72
  19. (With R.K. Meyer) "The Semantics of Entailment 0" in Kosta Došen and Peter Schröder-Heister (eds.), Substructural Logics, Oxford: Oxford University Press, 1993, pp 239-258
  20. "Classically Complete Modal Relevant Logics" Mathematical Logic Quarterly 39 (1993), pp 165-177
  21. (With R.K. Meyer) "The Semantics of R4" Journal of Philosophical Logic 22 (1993) pp 95-110
  22. (With R.K. Meyer) "The Admissibility of γ in R4" Notre Dame Journal of Formal Logic 33, no. 2 (1992), pp 197-206
  23. "The Semantic Completeness of RK" Reports on Mathematical Logic 26 (1992) pp 3-10
  24. "Andersonian Deontic Logic" Theoria 58 (1992) pp 75-91
  25. "Semantics for Relevance Logic with Identity" Studia Logica 51 (1992), no. 1, pp 1-20

 

Articles Forthcoming

 

  1. "Relevant Implication and the Indicative Conditional" Synthese
  2. "Semantic Dialetheism" in Graham Priest, J.C. Beall, and Bradley Armour Garb (eds.), The Law of Non-Contradiction, Oxford: Oxford University Press,
  3. "A ‘Four-Valued’ Semantics for R" Journal of Philosophical Logic
  4. “Halldén-Completeness and Modal Relevant Logic” Logique et analyse
  5. “The Semantics of Denial” in Bryson Brown (ed.), Essays in Memory of Hughes Leblanc, Dordrecht: Reidel
  6. (With Bob Cavana) “Linking critical and systems thinking: From premises to causal loops” Systems Dynamics Review

 

 

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