•  918
    Antirealism and the Conditional Fallacy: The Semantic Approach
    Journal of Philosophical Logic 43 (4): 761-783. 2014.
    The expression conditional fallacy identifies a family of arguments deemed to entail odd and false consequences for notions defined in terms of counterfactuals. The antirealist notion of truth is typically defined in terms of what a rational enquirer or a community of rational enquirers would believe if they were suitably informed. This notion is deemed to entail, via the conditional fallacy, odd and false propositions, for example that there necessarily exists a rational enquirer. If these cons…Read more
  •  589
    Paraconsistent dynamics
    Synthese 193 (1): 1-14. 2016.
    It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic operations of belief revision in a paraconsistent setting
  •  495
    Against Classical Paraconsistent Metatheory
    Analysis 83 (2): 285-294. 2023.
    There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it is desi…Read more
  •  433
    Teaching Logic to blind students
    with Jonathan McKeown-Green
    This paper is about teaching elementary logic to blind or visually impaired students. The targeted audience are teachers who all of sudden have a blind or visually impaired student in their introduction to logic class, find limited help from disability centers in their institution, and have no idea what to do. We provide simple techniques that allow direct communication between a teacher and a visually impaired student. We show how the use of what is known as Polish notation simplifies communic…Read more
  •  112
    What Is an Inconsistent Truth Table?
    Australasian Journal of Philosophy 94 (3): 533-548. 2016.
    ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears …Read more
  •  92
    Classical counterpossibles
    with Rohan French and David Ripley
    Review of Symbolic Logic 15 (1): 259-275. 2022.
    We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent n…Read more
  •  91
    Bad Worlds
    with Zach Weber
    Thought: A Journal of Philosophy 4 (2): 93-101. 2015.
    The idea of relevant logic—that irrelevant inferences are invalid—is appealing. But the standard semantics for relevant logics involve baroque metaphysics: a three-place accessibility relation, a star operator, and ‘bad’ worlds. In this article we propose that these oddities express a mismatch between non-classical object theory and classical metatheory. A uniformly relevant semantics for relevant logic is a better fit
  •  90
    Logical dynamics of belief change in the community
    Synthese 191 (11): 2403-2431. 2014.
    In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under various dynamical situations. We also cons…Read more
  •  62
    From onions to broccoli: generalizing Lewis' counterfactual logic
    Journal of Applied Non-Classical Logics 17 (2): 213-229. 2007.
    We present a generalization of Segerberg's onion semantics for belief revision, in which the linearity of the spheres need not occur. The resulting logic is called broccoli logic. We provide a minimal relational logic, with a bi-modal neighborhood semantics. We then show that broccoli logic is a well-known conditional logic, the Burgess-Veltman minimal conditional logic
  •  49
    Modal Logic Without Contraction in a Metatheory Without Contraction
    with Zach Weber
    Review of Symbolic Logic 12 (4): 685-701. 2019.
    Standard reasoning about Kripke semantics for modal logic is almost always based on a background framework of classical logic. Can proofs for familiar definability theorems be carried out using anonclassical substructural logicas the metatheory? This article presents a semantics for positive substructural modal logic and studies the connection between frame conditions and formulas, via definability theorems. The novelty is that all the proofs are carried out with anoncontractive logicin the back…Read more
  •  48
    Critical Thinking, Bias and Feminist Philosophy: Building a Better Framework through Collaboration
    with Adam Dalgleish and Maree Davies
    Informal Logic 37 (4): 351-369. 2017.
    In the late 20th century theorists within the radical feminist tradition such as Haraway highlighted the impossibility of separating knowledge from knowers, grounding firmly the idea that embodied bias can and does make its way into argument. Along a similar vein, Moulton exposed a gendered theme within critical thinking that casts the feminine as toxic ‘unreason’ and the ideal knower as distinctly masculine; framing critical thinking as a method of masculine knowers fighting off feminine ‘unrea…Read more
  •  36
    Paraconsistent Metatheory: New Proofs with Old Tools
    with Guillermo Badia and Zach Weber
    Journal of Philosophical Logic 51 (4): 825-856. 2022.
    This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-captur…Read more
  •  32
    Prioritised ceteris paribus logic for counterfactual reasoning
    with Marcus A. Triplett
    Synthese 195 (4): 1681-1703. 2018.
    The semantics for counterfactuals due to David Lewis has been challenged by appealing to miracles. Miracles may skew a given similarity order in favour of those possible worlds which exhibit them. Lewis responded with a system of priorities that mitigates the significance of miracles when constructing similarity relations. We propose a prioritised ceteris paribus analysis of counterfactuals inspired by Lewis’ system of priorities. By analysing the couterfactuals with a ceteris paribus clause one…Read more
  •  16
    Dialetheic Conditional Modal Logic
    In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 271-284. 2019.
    Standard modal logic for alethic modalities analyses modalities as ranging over all possible worlds. This leaves very little room in the space of worlds to entertain impossible things. My proposal is to liberate the Leibnizian universe and reinforce the relative aspect of possibility; worlds are possible with respect to some worlds, and impossible for others. The central idea is to isolate relative possibility from conditionality. To accommodate counterpossibles, I provide a dialetheic condition…Read more
  •  16
    General Dynamic Dynamic Logic
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 239-260. 1998.
  •  15
    Dynamic Formal Epistemology (edited book)
    Springer. 2010.
    This volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call “dynamic epistemology”. It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge…Read more
  •  14
    Flexibility in Ceteris Paribus Reasoning
    Australasian Journal of Logic 10. 2011.
    Ceteris Paribus clauses in reasoning are used to allow for defeaters of norms, rules or laws, such as in von Wright’s example “I prefer my raincoat over my umbrella, everything else being equal”. In earlier work, a logical analysis is offered in which sets of formulas Γ, embedded in modal operators, provide necessary and sufficient conditions for things to be equal in ceteris paribus clauses. For most laws, the set of things allowed to vary is small, often finite, and so Γ is typically infinite.…Read more
  •  12
    Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences
    Journal of Philosophical Logic 38 (1): 83-125. 2009.
    This paper presents a new modal logic for ceteris paribus preferences understood in the sense of “all other things being equal”. This reading goes back to the seminal work of Von Wright in the early 1960’s and has returned in computer science in the 1990’s and in more abstract “dependency logics” today. We show how it differs from ceteris paribus as “all other things being normal”, which is used in contexts with preference defeaters. We provide a semantic analysis and several completeness theore…Read more
  •  9
    Front Matter
    Australasian Journal of Logic 14 (1). 2017.
    Editors' Introduction and List of Contributors
  •  9
    General Dynamic Dynamic Logic
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 239-260. 1998.