Here are two significant volumes that arose from conferences I organized with colleagues. The first, "Non-Classicality: Logic, Mathematics, Philosophy" (2017), co-edited with Maarten McKubre-Jordens and Zach Weber, explores non-classical methodologies for logic, mathematics, and philosophy. The second, "Dynamic Formal Epistemology" (2011), co-edited with Olivier Roy and Mathieu Marion, delves into dynamic aspects of knowledge and belief, showcasing contributions from a conference focused on dynamic epistemic logic. Both books reflect collaborative efforts to advance discussions in these evolving fields.

1. Girard, Patrick. Logic in the Wild. Montreal: McGill-Queen’s University Press, 2024.

2. Girard, Patrick, Maarten McKubre-Jordens, and Zach Weber. “Non-Classicality: Logic, Mathematics, Philosophy.” Special Issue of The Australasian Journal of Logic 14, no. 1 (2017).

3. Girard, Patrick, Olivier Roy, and Mathieu Marion. Dynamic Formal Epistemology. Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science; 351. Dordrecht: Springer Science+Business Media B.V., 2011. https://doi.org/10.1007/978-94-007-0074-1.

Traditionally, non-classical logics are analyzed using classical meta-theory, but my interest lies in adopting a paraconsistent logic throughout. This approach allows me to explore and establish new foundations in logic, philosophy, and mathematics from this non-classical standpoint. By challenging the conventional boundaries and embracing contradictions, my research aims to redefine understanding and application in these fields, demonstrating how a paraconsistent framework can lead to innovative and meaningful insights.

I’m The Modal Madman.

1. Girard, Patrick, and Koji Tanaka. “Against Classical Paraconsistent Metatheory.” Analysis 83, no. 2 (2023): 285–94. https://doi.org/10.1093/analys/anac093.

2. Girard, Patrick, Guillermo Badia, and Zach Weber. “Paraconsistent Metatheory: New Proofs with Old Tools.” Journal of Philosophical Logic 51 (2022): 825–856. https://doi.org/10.1007/s10992-022-09651-x.

3. Girard, Patrick, and Zach Weber. “Modal Logic Without Contraction in a Metatheory Without Contraction.” The Review of Symbolic Logic 12, no. 4 (2019): 685-701. https://doi.org/10.1017/S1755020319000030.

4. Girard, Patrick. “Dialetheic Conditional Modal Logic.” In Graham Priest on Dialetheism and Paraconsistency, edited by Can Başkent and Thomas Macaulay Ferguson, 18:271–84. Cham: Springer International Publishing, 2019. https://doi.org/10.1007/978-3-030-25365-3_14.

5. Girard, Patrick, Guillermo Badia, and Zach Weber. “What is an Inconsistent Truth Table.” Australasian Journal of Philosophy 94, no. 3 (2016): 533-548. https://doi.org/10.1080/00048402.2015.1093010.

6. Girard, Patrick, and Zach Weber. “Bad Worlds.” Thought: A Journal of Philosophy 4, no. 2 (2015): 93-101. https://doi.org/10.1002/tht3.162.

I’ve developed a modal logic analysis of ‘ceteris paribus’ (all other things being equal) reasoning. This involves creating a logical framework that captures the nuances of inferences where certain factors are held constant while others vary. My approach uses modal logic to systematically represent and analyze scenarios where ceteris paribus clauses are crucial. This is particularly important in fields like philosophy, economics, and the social sciences, where such conditional statements are frequently employed to simplify complex systems by focusing on the effects of specific variables in isolation. My work provides a clearer understanding of these conditions, offering a more rigorous and structured way to handle the often ambiguous ceteris paribus clauses, and making significant contributions to the logical foundations of reasoning under assumed conditions.

1. Girard, Patrick, and Marcus A. Triplett. “Prioritised Ceteris Paribus Logic for Counterfactual Reasoning.” Synthese 195, no. 4 (2018): 1681-1703. https://doi.org/10.1007/s11229-016-1296-5.

2. Girard, Patrick, and Marcus Anthony Triplett. “Ceteris Paribus Logic in Counterfactual Reasoning.” In Proceedings of the 15th Conference on Theoretical Aspects of Rationality and Knowledge, 2015. https://doi.org/10.48550/arXiv.1606.07522.

3. Girard, Patrick, and Jeremy Seligman. “Flexibility in Ceteris Paribus Reasoning.” The Australasian Journal of Logic 10 (2011): 67-99. https://doi.org/10.26686/ajl.v10i0.1826.

4. Girard, Patrick, Johan van Benthem, and Olivier Roy. “Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences.” Journal of Philosophical Logic 38, no. 1 (2009): 83-125. https://doi.org/10.1007/s10992-008-9085-3.

   Paper selected for the 2009 Philosopher’s annual, republished in : Grim, P., Charlow, N., Gallow D., Herold, D. (ed.) The Philosopher's annual.

I use dynamic logic to delve into the evolving nature of beliefs and preferences within communities. This field allows me to explore how beliefs change, how information is updated, and the ways individual and collective preferences shift over time. My focus is on understanding the logical structure of belief revision, using formal epistemological methods to model and analyze these dynamic processes. I investigate scenarios where new information may contradict existing beliefs, necessitating modifications in belief systems, and scrutinize the logical outcomes of such changes. Additionally, my research encompasses the social dynamics of knowledge and belief, examining how interactions within communities and their structures influence the evolution of collective understandings. This work not only deepens our comprehension of the fluidity inherent in knowledge and belief systems but also highlights the complex interplay between logic, information, and social dynamics.

1. Girard, Patrick, Liu Fenrong, and Jeremy Seligman. “Logical Dynamics of Belief Change in the Community.” Synthese 191, no. 11 (2014): 2403–31. https://doi.org/10.1007/s11229-014-0432-3.

2. Girard, Patrick. “Logic of Promotion and Demotion.” In The Cognitive Foundations of Group Attitudes and Social Interaction, edited by Andreas Herzig and Emiliano Lorini, 107-120. Springer, 2015. https://doi.org/10.1007/978-3-319-21732-1_5.

3. Girard, Patrick, Liu Fenrong, and Jeremy Seligman. “Facebook and the Epistemic Logic of Friendship.” In TARK 2013 - Proceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge, edited by Burkhard Schipper, 2013. https://doi.org/10.48550/arXiv.1310.6440.

4. Girard, Patrick, Liu Fenrong, and Jeremy Seligman. “Knowledge, Friendship and Social Announcements.” In Logic Across the University: Foundations and Applications: Proceedings of the Tsinghua Logic Conference, Beijing, 2013, edited by Johan van Benthem and Fenrong Liu. London, UK: College Publications, 2013.

5. Girard, Patrick, Liu Fenrong, and Jeremy Seligman. “General Dynamic Dynamic Logic.” In Advances in Modal Logic: Volume 9, edited by Thomas Bolander, Torben Braüner, Silvio Ghilardi, and Lawrence Moss, 239-260. London, UK: College Publications, 2012. http://www.aiml.net/volumes/volume9/Girard-Seligman-Liu.pdf.

6. Girard, Patrick. “Modal Logic for Lexicographic Preference Aggregation.” In Games, Norms and Reasons, edited by Johan van Benthem, Amitabha Gupta, and Eric Pacuit, 97-117. Springer Verlag, 2011. https://doi.org/10.1007/978-94-007-0714-6_6.

7. Girard, Patrick, Liu Fenrong, and Jeremy Seligman. “Logic in the Community.” Proceedings of the Fourth Indian Conference in Logic and Applications, 178-188, 2011. https://doi.org/10.1007/978-3-642-18026-2_15.

8. Girard, Patrick, and Jeremy Seligman. “An Analytic Logic of Aggregation.” In Logic and Its Applications, Chennai, 146-161, 2009. https://doi.org/10.1007/978-3-540-92701-3_10.

In my research on belief revision, I apply the methodology of dynamic epistemic logic to explore how beliefs are updated in response to new information. This approach allows me to delve into the logical structures that underpin the process of belief change, particularly focusing on how individuals adjust their beliefs when confronted with new, sometimes conflicting, evidence. Dynamic epistemic logic provides a robust framework for modeling the evolution of belief systems, enabling me to investigate the criteria and mechanisms that guide rational modifications of beliefs. By using this methodology, I examine the consistency and coherence of belief systems both before and after they undergo revision. My work contributes significantly to our understanding of cognitive processes in belief change, shedding light on rational decision-making and the maintenance of logical consistency amidst evolving information. This approach offers valuable insights into the dynamics of knowledge and belief, particularly in the context of how individuals and communities process and adapt to new information.

1. Girard, Patrick, and Koji Tanaka. “Paraconsistent Dynamics.” Synthese 193, no. 1 (2016): 1-14. https://doi.org/10.1007/s11229-015-0740-.

2. Girard, Patrick, and Hans Rott. “Belief Revision and Dynamic Logic.” In Johan Van Benthem on Logic and Information Dynamics, edited by Alexandru Baltag and Sonja Smets, 203-233. Springer, 2014. https://doi.org/10.1007/978-3-319-06025-5_8.

3. Girard, Patrick. “From Onions to Broccoli: Generalizing Lewis' Counterfactual Logic.” Journal of Applied Non-Classical Logic 17, no. 2 (2007): 213-229. https://doi.org/10.3166/jancl.17.213-229.

While metaphysics is not my primary area of expertise, my proficiency in logic equips me to contribute significantly as a logician in philosophical inquiries. Whenever logical analysis and reasoning become pivotal in philosophical investigations, I am keen to offer my skills and insights. My logical acumen is especially valuable in dissecting complex philosophical arguments, providing clarity and structure to abstract concepts. I am always ready to apply my logical expertise to assist in unraveling the nuances of metaphysical discussions or any philosophical domain where logic plays a crucial role.

1. Girard, Patrick, Rohan French, and Dave Ripley. “Classical Counterpossibles.” The Review of Symbolic Logic (2020): 1-17. https://doi.org/10.1017/S1755020319000637.

2. Girard, Patrick, and Luca Moretti. “Antirealism and the Conditional Fallacy: The Semantic Approach.” Journal of Philosophical Logic 43, no. 4 (2014): 761-783. https://doi.org/10.1007/s10992-013-9288-0.

My academic focus in teaching philosophy largely revolves around the domain of critical thinking, with a particular interest in its evolution and relevance in the 21st century. To contribute to the growth of this discipline, I have engaged with feminist critiques of critical thinking, exploring their insights to deepen the framework. Additionally, I have dedicated significant thought to developing methodologies for teaching foundational concepts of logical and critical thinking to adolescents. This aspect of my work aims to adapt and modernise critical thinking education to be more inclusive and effective for younger learners in today’s context.

Textbook on Formal Logic: The “Auckland Remix” of forall x

Together with colleagues Andrew Withy and Jeremy Seligman, I contributed to a “remix” of the open-source textbook forall x from the Open Logic Project, adapting it for students at the University of Auckland. forall x is a comprehensive, full-featured textbook on formal logic, covering foundational topics such as truth-functional propositional logic (TFL), first-order predicate logic (FOL) with identity, and Fitch-style natural deduction proof systems. Our remix has been revised with content and examples relevant to Auckland students, tailored for both accessibility and engagement.

The textbook can be downloaded here: Download Auckland Remix PDF.

Selected Publications

1. Girard, Patrick, Adam Dalgleish, and Maree Davies. “Critical Thinking, Bias and Feminist Philosophy: Building a Better Framework through Collaboration.” Informal Logic 37, no. 4 (2017): 351-369. https://doi.org/10.22329/il.v37i4.4794.

2. Girard, Patrick, Maree Davies, and Simon Esling. “Street Smarts: A Developing Critical Thinking Talk Framework for Adolescents.” In Dialogic Pedagogy: Discourse in Contexts from Pre-School to University, edited by Anne Thwaite, Alyson Simpson, and Pauline Jones. Routledge Research in Education. London; New York: Routledge, Taylor & Francis Group, 2023.

Accessible Logic Teaching Methods

Together with my late friend and colleague Jonathan McKeown-Green, we crafted a practical method for teaching logic to visually impaired students. This approach utilises Polish notation, providing an accessible and effective way to engage with logical concepts for those with visual impairments.

Girard, Patrick, and Jonathan McKeown-Green. “Teaching Logic to Blind Students.” https://philpapers.org/rec/GIRTLT.