Staff profile

Dr Ross Thomas Brady

Adjunct Reader and Associate Professor

College of Arts, Social Sciences and Commerce
Humanities and Social Sciences
Department of Politics and Philosophy

Melbourne (Bundoora)

Qualifications

BSc (Hons)(Syd), MA (Hons)(UNE), PhD (St Andrews)

Membership of professional associations

Australasian Association for Logic, Association of Symbolic Logic, Australian Academy of Humanities.

Area of study

Philosophy

Brief profile

Dr Ross Brady has worked extensively on the consistency of naïve set theory and its extension to higher order predicate theory, thus providing a logical solution to the set-theoretic and semantic paradoxes. He has subsequently worked on the proof theory of relevant logics, especially Gentzen systems and natural deduction. He has more recently specialized in the logic MC of meaning containment, setting it up as the logic of choice. He has studied metacompleteness and its associated logics, establishing properties for them that significantly diverge from those of classical logic. Indeed, he has recently proved the simple consistency of arithmetic by finitary methods, in contrast with Godel’s celebrated Second Theorem.

Research specialisation

- Formal Logic

Recent publications

  • "History of Relevant Logic in Australasia", in A History of Philosophy in Australia and New Zealand, ed. by Graham Oppy, Lynda Burns, Fiona Leigh and Nick Trakakis, Springer Publishing, Dordrecht, 2014. 
  • "A General History of Logic in Australasia", in A History of Philosophy in Australia and New Zealand, ed. by Graham Oppy, Lynda Burns, Fiona Leigh and Nick Trakakis, Springer Publishing, Dordrecht, 2014.  
  • "History of Modal Logic in Australasia", in A History of Philosophy in Australia and New Zealand, ed. by Graham Oppy, Lynda Burns, Fiona Leigh and Nick Trakakis, Springer Publishing, Dordrecht, 2014.
  • “The Simple Consistency of Naïve Set Theory using Metavaluations”, Journal of Philosophical Logic, Vol.43 (2014), pp.261-281.
  • "Distribution in the Logic of Meaning Containment and in Quantum Mechanics" (with Andrea Meinander), in Paraconsistency: Logic and Applications, ed. by Koji Tanaka, Franz Berto, Edwin Mares and Francesco Paoli, Springer Publishing, Dordrecht, 2013, pp.223-255. 
  • "On the Ternary Relation and Conditionality" (with JC Beall, J. Michael Dunn, Allen Hazen, Edwin Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney and Richard Sylvan (formerly Routley)), Journal of Philosophical Logic, Vol.41 (2012), pp.595-612. 
  • "The Consistency of Arithmetic, Based on a Logic of Meaning Containment", Logique et Analyse, Vol. 55, pp.353-383, 2012.
  • "Metavaluations, Naive Set Theory and Inconsistency", in J-Y. Beziau and M.E..Coniglio (eds.) Logic without Frontiers, Festschrift for Walter Alexandre Carnielli on the occasion of his 60th Birthday, College Publications, London, pp.339-360, 2011.
  • "Free Semantics", Journal of Philosophical Logic, Vol.39 (2010), pp.511-529.  [DOI: 10.1007/s10992-010-9129-3]
  • "Extending Metacompleteness to Classical Systems", Australasian Journal of Logic, Vol.8 (2010), pp.9-30.
  • "The Australasian Association for Logic", in A Companion to Philosophy in Australia and New Zealand, ed. by Graham Oppy and Nick Trakakis, Monash University Publishing, Melbourne, 2010, pp.48-49.
  • (With Penelope Rush) “Four Basic Logical Issues”, Review of Symbolic Logic, Vol.2 (2009), pp.488-508. 
  • (With Penelope Rush) "What is Wrong with Cantor's Diagonal Argument?" Logique et Analyse, Vol.51 (2008), pp.185-219.
  • "A Rejection System for the First-Degree Formulae of some Relevant Logics", Australasian Journal of Logic, Vol.6 (2008), pp.55-69.
  • "Negation in Metacomplete Relevant Logics", Logique et Analyse, Vol.51 (2008), pp.331-354.
  • "Entailment Logic - A Blueprint", in J-Y. Beziau, W. Carnielli and D. Gabbay (eds.) Handbook of Paraconsistency, College Publications, King’s College, London, pp.127-151, 2007.
  • Universal Logic, The Centre for the Study of Language and Information (CSLI) Publications, Stanford, 346pp, 2006.
  • "Normalized Natural Deduction Systems for Some Relevant Logics I: The Logic DW", The Journal of Symbolic Logic, Vol.71 (2006), pp.35-66.
  • (With J.C. Beall, A. Hazen, G. Priest and G. Restall) "Relevant Restricted Quantification", Journal of Philosophical Logic, Vol.35 (2006), pp.587-598.

Older publications

  • “On the Formalization of the Law of Non-Contradiction”, in G. Priest, JC Beall and B. Armour-Garb (eds.) The Law of Non-Contradiction: New Philosophical Essays, Oxford U.P., pp.41-48, 2004.
  • Relevant Logics and their Rivals, Vol.2, A Continuation of the Work of Richard Sylvan, Robert Meyer, Val Plumwood and Ross Brady (also ed.), Ashgate, pp.425, 2003.
  • “Semantic Decision Procedures for Some Relevant Logics”, Australasian Journal of Logic, Vol.1 (2003), pp.4-27.
  • “Ordering Properties for the Routley-Meyer Relation R”, Journal of Applied Non-Classical Logics, Vol.12 (2002), pp.85-98.
  • “Entailment, Negation and Paradox Solution”, in Frontiers of Paraconsistent Logic, ed. by D. Batens, C. Mortensen, G. Priest, J.-P. van Bendegem, Research Studies Press, Baldock, 2000, pp.113-135.
  • “Simple Gentzenizations for the Normal Formulae of Contraction-less Logics”, Journal of Symbolic Logic, Vol. 61 (1996), pp. 1321-1346.
  • “Gentzenizations of Relevant Logics with Distribution”, Journal of Symbolic Logic, Vol. 61 (1996), pp. 402-420.
  • “Gentzenizations of Relevant Logics Without Distribution - II”, Journal of Symbolic Logic, Vol. 61 (1996), pp. 379-401.
  • "Gentzenizations of Relevant Logics Without Distribution - I”, Journal of Symbolic Logic, Vol. 61 (1996), pp. 353-378.
  • “Relevant Implication and the Case for a Weaker Logic”, Journal of Philosophical Logic, Vol. 25 (1996), pp. 151-1
  • “Rules in Relevant Logic - I: Semantic Classification”, Journal of Philosophical Logic, Vol. 23 (1994), pp. 111-137.
  • “Rules in Relevant Logic - II: Formula Representation”, Studia Logica, Vol. 52 (1993), pp. 565-585.

Research projects

  • The History of Metavaluations.
  • The Consistency of Set Theory.
  • Partial Meaning and Consistency in the General Application of Logic.
  • Logical Contents and Information.
  • Decidability of Non-Classical Predicate Logics.
  • Logical Representation of Definitions in the Derivation of Paradoxes.