University of Calgary

Joseph McDonald

  • Master's Student

Office Hours

MondayTuesdayWednesdayThursdayFridaySaturdaySunday
12p‑1p
Logic 2
(Jan 08 - Apr 13)
-12p‑1p
Logic 2
(Jan 08 - Apr 13)
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Research Interests

Currently Teaching

Not currently teaching any courses.

Research Presentations

  • "An Introduction to the General Theory of Categories and Homomorphic Sets," University of Calgary Philosophy Graduate Colloquium, September 21, 2017.
  • "Paraconsistent Logics and Model-Theoretic Applications of LP," Meeting of the Minds Graduate Conference, University of Lethbridge, March 17-18, 2017.
  • "Paraconsistency Measurements for Preservationist Consequence Relations," University of Lethbridge Philosophy Undergraduate Conference, March 4, 2017.
  • "Paraconsistent Logics for Non-Classical Arithmetic," University of Lethbridge Philosophy Undergraduate Colloquium, November 14, 2016. 
  • "The Principles and Implications of Quantum Logic," University of Lethbridge Philosophy Undergraduate Conference, February 27, 2016. 

Thesis Project

My thesis research will cover topcis in preservationist logic, which is a recet development in paraconsistent logic. Paraconsistent logics are broadly characterized by the fact that they break the principle of explosion, which is a fundametal theorem for classical logical calculi. Unlike multi-valued paraconistent logics (such as the systems K3, LP, L3, and RM3) that extend the classical {1, 0} set of values, preservationist paraconsistent logics extend the concept of proof/model-theoretic closure under consequence itself by requiring that it preserve level, a partition-theoretic generalization of consistency. Preservationist logics draw on techniques from combinatorics, topology, graph theory, measure theory, set theory, and logic. I will explore various applications of the level function, variations on the level function, and investigate further connections to be made between preservationist logic and the other mathematical disciplines just mentioned.           

Current Studies

  • Master's Student
    Degree: Master of Arts
    Supervisor: Richard Zach
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