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Profile: Ryan Brady
  1. Ross Brady (2006). Universal Logic. CSLI Publications.
    Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic. But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes. _Universal Logic _begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes. It is the first text to demonstrate how the main set-theoretic and semantic paradoxes can be solved in (...)
     
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  2. Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady (1982). Relevant Logics and Their Rivals. Ridgeview.
     
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  3. Jc Beall, Ross Brady, J. Michael Dunn, A. P. Hazen, Edwin Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney & Richard Sylvan (2012). On the Ternary Relation and Conditionality. Journal of Philosophical Logic 41 (3):595 - 612.
    One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...)
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  4.  81
    JC Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall (2006). Relevant Restricted Quantification. Journal of Philosophical Logic 35 (6):587 - 598.
    The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.
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  5.  13
    Ross T. Brady & Andrea Meinander (2013). Distribution in the Logic of Meaning Containment and in Quantum Mechanics. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer 223--255.
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  6.  37
    R. T. Brady & P. A. Rush (2008). What is Wrong with Cantor's Diagonal Argument? Logique Et Analyse 51 (1):185-219..
    We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...)
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  7. Ross T. Brady (1984). Reply to Priest on Berry's Paradox. Philosophical Quarterly 34 (135):157-163.
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  8.  17
    Ross T. Brady (1991). Gentzenization and Decidability of Some Contraction-Less Relevant Logics. Journal of Philosophical Logic 20 (1):97 - 117.
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  9. Ross T. Brady (1989). The Non-Triviality of Dialectical Set Theory. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag 437--470.
     
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  10.  15
    Ross T. Brady (1983). The Simple Consistency of a Set Theory Based on the Logic ${\Rm CSQ}$. Notre Dame Journal of Formal Logic 24 (4):431-449.
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  11.  31
    Ross T. Brady (2014). The Simple Consistency of Naive Set Theory Using Metavaluations. Journal of Philosophical Logic 43 (2-3):261-281.
    The main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of the (...)
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  12.  15
    Ross T. Brady (1971). The Consistency of the Axioms of Abstraction and Extensionality in a Three-Valued Logic. Notre Dame Journal of Formal Logic 12 (4):447-453.
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  13. Ross T. Brady (forthcoming). Simplified Gentzenizations for Contraction-Less Logics. Logique Et Analyse.
     
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  14. R. T. Brady (1984). Natural deduction systems for some quantified relevant logics. Logique Et Analyse 27 (8):355.
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  15. Ross Brady (2008). Negation in Metacomplete Relevant Logics. Logique Et Analyse 51.
     
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  16.  35
    Ross Thomas Brady (2010). Free Semantics. Journal of Philosophical Logic 39 (5):511 - 529.
    Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic (...)
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  17.  19
    Ross T. Brady (1984). Depth Relevance of Some Paraconsistent Logics. Studia Logica 43 (1-2):63 - 73.
    The paper essentially shows that the paraconsistent logicDR satisfies the depth relevance condition. The systemDR is an extension of the systemDK of [7] and the non-triviality of a dialectical set theory based onDR has been shown in [3]. The depth relevance condition is a strengthened relevance condition, taking the form: If DR- AB thenA andB share a variable at the same depth, where the depth of an occurrence of a subformulaB in a formulaA is roughly the number of nested ''s (...)
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  18.  41
    Ross T. Brady (1996). Relevant Implication and the Case for a Weaker Logic. Journal of Philosophical Logic 25 (2):151 - 183.
    We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for $DJ^{d}$ with respect (...)
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  19.  8
    Ross T. Brady (1990). The Gentzenization and Decidability of RW. Journal of Philosophical Logic 19 (1):35 - 73.
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  20. Ross T. Brady (2012). The Consistency of Arithmetic, Based on a Logic of Meaning Containment. Logique Et Analyse 55 (219).
  21.  11
    Ross T. Brady (2006). Normalized Natural Deduction Systems for Some Relevant Logics I: The Logic DW. Journal of Symbolic Logic 71 (1):35 - 66.
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  22.  1
    J. C. Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall (2006). Relevant Restricted Quantification. Journal of Philosophical Logic 35 (6):587-598.
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  23.  31
    Ross T. Brady (1994). Rules in Relevant Logic - I: Semantic Classification. [REVIEW] Journal of Philosophical Logic 23 (2):111 - 137.
    We provide five semantic preservation properties which apply to the various rules -- primitive, derived and admissible -- of Hilbert-style axiomatizations of relevant logics. These preservation properties are with respect to the Routley-Meyer semantics, and consist of various truth- preservations and validity-preservations from the premises to the conclusions of these rules. We establish some deduction theorems, some persistence theorems and some soundness and completeness theorems, for these preservation properties. We then apply the above ideas, as best we can, to the (...)
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  24.  15
    Robert K. Meyer, Steve Giambrone & Ross T. Brady (1984). Where Gamma Fails. Studia Logica 43 (3):247 - 256.
    A major question for the relevant logics has been, “Under what conditions is Ackermann's ruleγ from -A ∨B andA to inferB, admissible for one of these logics?” For a large number of logics and theories, the question has led to an affirmative answer to theγ problem itself, so that such an answer has almost come to be expected for relevant logics worth taking seriously. We exhibit here, however, another large and interesting class of logics-roughly, the Boolean extensions of theW — (...)
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  25.  16
    Richard Sylvan & Ross Brady (eds.) (1982). Relevant Logics and Their Rivals. Ridgeview Pub. Co..
    Relevant Logics and their Rivals, Volume II extends the material of the first volume in two ways.
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  26.  66
    Ross Brady & Penelope Rush (2009). Four Basic Logical Issues. Review of Symbolic Logic 2 (3):488-508.
    Four Basic Logical Issues: The paper addresses what we see as the four major issues in logic. The overriding issue is that of the choice of logic. We start with some discussion of the preliminary issue of whether there is such a 'one true logic,' but we reserve the main discussion for the first issue of 'classical logic versus nonclassical logic.' Here, we discuss the role of meaning and truth, the relation between classical logic and classical negation, and whether and, (...)
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  27. R. T. Brady (1982). Completeness Proofs for RM3 and BN4. Logique Et Analyse 25:9-32.
     
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  28. Ross T. Brady (1982). Completeness proofs for the systems RM3 and BN4. Logique Et Analyse 25 (97):9.
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  29. Richard Routley, Robert K. Meyer, Val Plumwood & Ross T. Brady (1988). Relevant Logics and Their Rivals: Part 1. The Basic Philosophical and Semantical Theory. Studia Logica 47 (2):169-172.
     
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  30. Ross Brady (2003). Semantic Decision Procedures for Some Relevant Logics. Australasian Journal of Philosophy 1:4-27.
    This paper proves decidability of a range of weak relevant logics using decision procedures based on the Routley-Meyer semantics. Logics are categorized as F-logics, for those proved decidable using a filtration method, and U-logics, for those proved decidable using a direct method. Both of these methods are set out as reductio methods, in the style of Hughes and Cresswell. We also examine some extensions of the U-logics where the method fails and infinite sequences of worlds can be generated.
     
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  31.  13
    Ross T. Brady (1996). Gentzenizations of Relevant Logics Without Distribution. II. Journal of Symbolic Logic 61 (2):379-401.
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  32.  31
    Ross T. Brady (1993). Rules in Relevant Logic — II: Formula Representation. Studia Logica 52 (4):565 - 585.
    This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A 1 .A 2 . ... .A n B, the conjunctive form,A 1&A 2 & ...A n (...)
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  33.  10
    Ross T. Brady (1996). Gentzenizations of Relevant Logics Without Distribution. I. Journal of Symbolic Logic 61 (2):353-378.
  34.  12
    Ross Brady & Richard Routley (1973). Don't Care Was Made to Care. Australasian Journal of Philosophy 51 (3):211 – 225.
  35.  36
    R. Brady (2010). On Preserving: Essays on Preservationism and Paraconsistent Logic * Edited by Peter Schotch, Bryson Brown and Raymond Jennings. Analysis 70 (2):382-383.
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  36.  2
    Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady (1989). Relevant Logics and Their Rivals. Part I. The Basic Philosophical and Semantical Theory. Journal of Symbolic Logic 54 (1):293-296.
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  37.  12
    Ross Brady (2004). 2003 Annual Conference of the Australasian Association for Logic: Sponsored by the Association for Symbolic Logic, Adelaide, Australia July 5-6, 2003. [REVIEW] Bulletin of Symbolic Logic 10 (2):290-294.
  38. Richard Sylvan & Ross Brady (2005). Relevant Logics and Their Rivals, Volume II. Bulletin of Symbolic Logic 11 (1):70-72.
     
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  39.  17
    Ross T. Brady (1989). A Routley-Meyer Affixing Style Semantics for Logics Containing Aristotle's Thesis. Studia Logica 48 (2):235 - 241.
    We provide a semantics for relevant logics with addition of Aristotle's Thesis, ∼(A→∼A) and also Boethius,(A→B)→∼(A→∼B). We adopt the Routley-Meyer affixing style of semantics but include in the model structures a regulatory structure for all interpretations of formulae, with a view to obtaining a lessad hoc semantics than those previously given for such logics. Soundness and completeness are proved, and in the completeness proof, a new corollary to the Priming Lemma is introduced (c.f.Relevant Logics and their Rivals I, Ridgeview, 1982).
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  40. Ronald H. Brady (1998). The Idea in Nature: Rereading Goethe's Organics. In David Seamon & Arthur Zajonc (eds.), Goethe's Way of Science: A Phenomenology of Nature. State University of New York Press 83--111.
     
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  41.  11
    Rob Brady (1981). Verdictives, Self-Presentation, and Self-Knowledge. Southern Journal of Philosophy 19 (1):11-20.
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  42.  5
    Ross T. Brady (1996). Simple Gentzenizations for the Formal Formulae of Contraction-Less Logics. Journal of Symbolic Logic 61 (4):1321-1346.
  43.  2
    Ross T. Brady (1972). The Relative Consistency of the Class Axioms of Abstraction and Extensionality and the Axioms of NBG in a Three-Valued Logic. Notre Dame Journal of Formal Logic 13 (2):161-176.
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  44.  2
    Ross Brady (2000). Australasian Association for Logic 1999 Annual Conference Co-Sponsored by the Association for Symbolic Logic. Bulletin of Symbolic Logic 6 (2):248-255.
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  45.  10
    Ross T. Brady (1989). A Content Semantics for Quantified Relevant Logics. II. Studia Logica 48 (2):243 - 257.
    In part I, we presented an algebraic-style of semantics, which we called “content semantics,” for quantified relevant logics based on the weak systemBBQ. We showed soundness and completeness with respect to theunreduced semantics ofBBQ. In part II, we proceed to show soundness and completeness for extensions ofBBQ with respect to this type of semantics. We introducereduced semantics which requires additional postulates for primeness and saturation. We then conclude by showing soundness and completeness forBB d Q and its extentions with respect (...)
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  46.  4
    Ross Brady & Conrad Asmus (2010). The 2009 Annual Conference of the Australasian Association for Logic. Bulletin of Symbolic Logic 16 (3):445-449.
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  47.  10
    Ross T. Brady (1988). A Content Semantics for Quantified Relevant Logics. I. Studia Logica 47 (2):111 - 127.
    We present an algebraic-style of semantics, which we call a content semantics, for quantified relevant logics based on the weak system BBQ. We show soundness and completeness for all quantificational logics extending BBQ and also treat reduced modelling for all systems containing BB d Q. The key idea of content semantics is that true entailments AB are represented under interpretation I as content containments, i.e. I(A)I(B) (or, the content of A contains that of B). This is opposed to the truth-functional (...)
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  48.  11
    Ross T. Brady (1992). Hierarchical Semantics for Relevant Logics. Journal of Philosophical Logic 21 (4):357 - 374.
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  49.  8
    Ross T. Brady (1996). Gentzenizations of Relevant Logics with Distribution. Journal of Symbolic Logic 61 (2):402-420.
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  50.  2
    Ross T. Brady (1980). Significance Range Theory. Notre Dame Journal of Formal Logic 21 (2):319-345.
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