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42The incompleteness of RGLStudia Logica 65 (3): 315-322. 2000.RGLis a version of the modal logic GLbased on the relevant logic R. It is shown that the class of RKframes that verify all theorems of RGLalso verify a scheme that we call (!). If RGLhas (!) as a theorem, however, it is not a relevant logic. I go on to show that not all instances of (!) are theorems of RGL, hence this logic is not complete over any class of RKframes.
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41An informational interpretation of weak relevant logic and relevant property theorySynthese 199 (Suppl 3): 547-569. 2017.This paper extends the theory of situated inference from Mares to treat two weak relevant logics, B and DJ. These logics are interesting because they can be used as bases for consistent naïve theories, such as naïve set theory. The concepts of a situation and of information that are employed by the theory of situated inference are used to justify various aspects of these logics and to give an interpretation of the notion of set that is represented in the naïve set theories that are based on them…Read more
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37CE is not a conservative extension of EJournal of Philosophical Logic 29 (3): 263-275. 2000.The logic CE (for "Classical E") results from adding Boolean negation to Anderson and Belnap's logic E. This paper shows that CE is not a conservative extension of E
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35Classically complete modal relevant logicsMathematical Logic Quarterly 39 (1): 165-177. 1993.A variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule γ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them “classically complete”. MSC: 03B45, 03B46
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35Advances in modal logic, Volume 1, edited by Marcus Kracht, Maarten de Rijke, Heinrich Wansing, and Michael Zakharyaschev, CSLI lecture notes, no. 87, Center for the Study of Language and Information, Stanford 1998, also distributed by Cambridge University Press, New York, xvi + 392 pp (review)Bulletin of Symbolic Logic 8 (1): 95-97. 2002.
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34Review: Marcus Kracht, Maarten de Rijke, Heinrich Wansing, Michael Zakharyaschev, Advances in Modal Logic (review)Bulletin of Symbolic Logic 8 (1): 95-97. 2002.
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28Logical Modalities from Aristotle to Carnap: The Story of Necessity (edited book)Cambridge University Press. 2016.Interest in the metaphysics and logic of possible worlds goes back at least as far as Aristotle, but few books address the history of these important concepts. This volume offers new essays on the theories about the logical modalities held by leading philosophers from Aristotle in ancient Greece to Rudolf Carnap in the twentieth century. The story begins with an illuminating discussion of Aristotle's views on the connection between logic and metaphysics, continues through the Stoic and mediaeval…Read more
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28Even dialetheists should hate contradictionsAustralasian Journal of Philosophy 78 (4). 2000.This Article does not have an abstract
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27Realism and Anti-RealismRoutledge. 2006.There are a bewildering variety of ways the terms "realism" and "anti-realism" have been used in philosophy and furthermore the different uses of these terms are only loosely connected with one another. Rather than give a piecemeal map of this very diverse landscape, the authors focus on what they see as the core concept: realism about a particular domain is the view that there are facts or entities distinctive of that domain, and their existence and nature is in some important sense objective a…Read more
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25Boolean Conservative Extension Results for some Modal Relevant LogicsAustralasian Journal of Logic 8 (5): 31-49. 2011.This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.
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25A Lewisian Semantics for S2History and Philosophy of Logic 34 (1): 53-67. 2013.This paper sets out a semantics for C.I. Lewis's logic S2 based on the ontology of his 1923 paper ‘Facts, Systems, and the Unity of the World’. In that article, worlds are taken to be maximal consistent systems. A system, moreover, is a collection of facts that is closed under logical entailment and conjunction. In this paper, instead of defining systems in terms of logical entailment, I use certain ideas in Lewis's epistemology and philosophy of logic to define a class of models in which system…Read more
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24Editor's Introduction to C.I. Lewis and C.H. Langford 'A Note on Strict Implication'History and Philosophy of Logic 35 (1): 1-6. 2014.The article ‘A Note on Strict Implication’ was submitted for publication by C.I. Lewis and C.H. Langford but withdrawn in proof. The paper is, according to notes and letters by both Lewis and Langford, largely by Lewis. It constitutes an early attempt by Lewis to give meanings for the modal connectives using abstract objects. To be necessary, for example, is for a statement to have the same intension as a truth-functional tautology. This theory prefigures the view of Lewis's 1946 book, Analysis …Read more
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22Fictional Objects and Fregean SinneIn Werner Stelzner (ed.), Philosophie Und Logik: Frege-Kolloquien 1989 Und 1991, De Gruyter. pp. 65-72. 1993.
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22Introduction to Special Issue in Honour of Robert GoldblattAustralasian Journal of Logic 17 (2): 81. 2020.This is a brief introduction to the special issue.
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22The Semantics of R4Journal of Philosophical Logic 22 (1): 95-110. 1993.The Logic R4 is obtained by adding the axiom □ → to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.
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18The logic of entailment and its history[Cambridge University Press]. 2024.This book provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. Its fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.
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17Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs (edited book)Springer Verlag. 2021.This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to …Read more
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14Edwin D. Mares, Relevant Logic—A Philosophical Interpretation: Cambridge University Press, 2004, x + 229 pp., £ 45.00, ISBN-13: 9780521829236, ISBN-10: 0521829232, hardback (review)Studia Logica 85 (3): 419-424. 2007.
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14A General Semantics for Quantified Modal LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 227-246. 1998.This paper uses an "admissible set semantics" to treat quantification in quantified modal logics. The truth condition for the universal quantifier states that a universally quantified statement (x)A(x) is true at a world w if and only if there is some proposition true at that world that entails every instance of A(x). It is shown that, for any canonical propositional modal logic the corresponding admissible set semantics characterises the quantified version of that modal logic.
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13C. I. Lewis’s Intensional SemanticsNotre Dame Journal of Formal Logic 64 (3): 329-352. 2023.This paper begins with a discussion of C. I. Lewis’s theory of meaning in his book, An Analysis of Knowledge and Valuation (1946) and his pragmatic theory of analyticity and necessity. I bring this theories together with some remarks that he makes in an appendix to the second edition of Symbolic Logic to construct an algebraic semantics for his logics S2 and S3. These logics and their semantics are compared and evaluated with regard to how well they implement Lewis’s theories of meaning and anal…Read more
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13A PrioriRoutledge. 2011.In recent years many influential philosophers have advocated that philosophy is an a priori science. Yet very few epistemology textbooks discuss a priori knowledge at any length, focusing instead on empirical knowledge and empirical justification. As a priori knowledge has moved centre stage, the literature remains either too technical or too out of date to make up a reasonable component of an undergraduate course. Edwin Mares book aims to rectify this. This book seeks to make accessible to stud…Read more
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12From Iff to Is: Some New Thoughts on Identity in Relevant LogicsIn Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 343-363. 2019.In this paper, I set out a semantics for identity in relevant logic that is based on an analogy between the biconditional and identity. This analogy supports the semantics that Priest has set out for identity in basic relevant logic and it motivates a version of the Routley–Meyer semantics in which identities can be viewed as constraints on the ternary relation that is used to treat implication.
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12I. The problem of Molinist conditionalsIn Ken Perszyk (ed.), Molinism: The Contemporary Debate, Oxford University Press. pp. 96. 2011.
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11Truth and Meaning (review)Dialogue 39 (2): 412-413. 2000.I have found in teaching courses on philosophy of language that one can concentrate either on the problem of reference or the problem of meaning, not on both and still teach a coherent course. Kenneth Taylor’s Truth and Meaning provides further confirmation of this view. It is a very good textbook for a course on the theory of meaning and attempts to say relatively little about reference. It is clear and well written. It presents a wide range of rather difficult material perhaps as clearly and e…Read more
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11Papers From Advances In Modal Logic, Volume 1 (review)Bulletin of Symbolic Logic 8 (1): 95-96. 2002.
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Victoria University of WellingtonSchool of History, Philosophy, Political Science and International RelationsProfessor
Wellington, Wellington, New Zealand