
109forall x: Calgary is a fullfeatured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truthfunctional propositional logic TFL and truthtable semantics, the syntax of firstorder (predicate) logic FOL with identity (firstorder interpretations), translating (formalizing) English in TFL and FOL, and Fitchstyle natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as truthfunctional…Read more

58Evaluation of a studentoriented logic courseISSOTL 2018 Annual Meeting. 2018.In Winter 2017, the first author piloted a course in formal logic in which we aimed to (a) improve student engagement and mastery of the content, and (b) reduce maths anxiety and its negative effects on student outcomes, by adopting student oriented teaching including peer instruction and classroom flipping techniques. The course implemented a partially flipped approach, and incorporated groupwork and peer learning elements, while retaining some of the traditio…Read more

31Is Hume’s Principle analytic?Synthese 117. forthcoming.The question of the analyticity of Hume's Principle is central to the neologicist project. We take on this question with respect to Frege's definition of analyticity, which entails that a sentence cannot be analytic if it can be consistently denied within the sphere of a special science. We show that HP can be denied within nonstandard analysis and argue that if HP is taken to depend on Frege's definition of number, it isn't analytic, and if HP is taken to be primitive there is only a very nar…Read more

13Takeuti's WellOrdering Proof: Finitistically Fine?In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics The CSHPM 2017 Annual Meeting in Toronto, Ontario, Birkhäuser Basel. 2018.If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the wellordering of ordinal notations in Cantor normal form. The paper beg…Read more

33Cantor, God, and Inconsistent MultiplicitiesStudies in Logic, Grammar and Rhetoric 44 (1): 133146. 2016.The importance of Georg Cantor’s religious convictions is often neglected in discussions of his mathematics and metaphysics. Herein I argue, pace Jan ́e (1995), that due to the importance of Christianity to Cantor, he would have never thought of absolutely infinite collections/inconsistent multiplicities,as being merely potential, or as being purely mathematical entities. I begin by considering and rejecting two arguments due to Ignacio Jan ́e based on letters to Hilbert and the generating pr…Read more
University of Calgary
College of The Rockies


College of The RockiesOther (Parttime)
University of Calgary
PhD, 2018
Calgary, Alberta, Canada
Areas of Specialization
Logicism in Mathematics 