Staff profile

Dr Ross Thomas Brady

Reader and Associate Professor

Faculty of Humanities and Social Sciences

School of Communication, Arts and Critical Enquiry

HU2 309, Melbourne (Bundoora)

 

Qualifications

BSc (Hons-Sydney), MA (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 interests

Philosophy of the Mind

- Applications to Set Theory and Arithmetic

- Paradoxes

- Relevant Logic

Teaching Units

PHI 2/3LOG - Logic. PHI 2/3TWP - The Ways of Paradox. PHI 1CRT - Critical Thinking.

Recent Publications

  • 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.
  • Universal Logic, The Centre for the Study of Language and Information (CSLI) Publications, Stanford, 346pp, 2006.
  • “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.
  • "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.
  • “Semantic Decision Procedures for Some Relevant Logics”, Australasian Journal of Logic, Vol.1 (2003), pp.4-27.
  • "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.
  • (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.
  • (With Penelope Rush) “Four Basic Logical Issues”, Review of Symbolic Logic, Vol.2 (2009), pp.488-508. 

 

Research projects

  • The Consistency and Completeness of Arithmetic
  • Simple semantics for relevant logics
  • A new Formalist foundation for mathematics