
77Logical pluralism and normativityInquiry: An Interdisciplinary Journal of Philosophy 122. 2017.We are logical pluralists who hold that the right logic is dependent on the domain of investigation; different logics for different mathematical theories. The purpose of this article is to explore the ramifications for our pluralism concerning normativity. Is there any normative role for logic, once we give up its universality? We discuss Florian Steingerger’s “Frege and Carnap on the Normativity of Logic” as a source for possible types of normativity, and then turn to our own proposal, which po…Read more

66Logical Pluralism from a Pragmatic PerspectiveAustralasian Journal of Philosophy 96 (3): 578591. 2018.This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the QuestionUnderDiscussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Ques…Read more

57A New Interpretation of Carnap’s Logical PluralismTopoi 38 (2): 305314. 2019.Rudolf Carnap’s logical pluralism is often held to be one in which corresponding connectives in different logics have different meanings. This paper presents an alternative view of Carnap’s position, in which connectives can and do share their meaning in some contexts. This reinterpretation depends crucially on extending Carnap’s linguistic framework system to include metalinguistic frameworks, those frameworks which we use to talk about linguistic frameworks. I provide an example that shows h…Read more

57Typically, a logic consists of a formal or informal language together with a deductive system and/or a modeltheoretic semantics. The language is, or corresponds to, a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record which inferences are correct for the given language, and the semantics is to capture, codify, or record the meanings, or truthconditions, or possible truth conditions, for at least part of the language.

42Restall’s ProofTheoretic Pluralism and Relevance LogicErkenntnis 81 (6): 12431252. 2016.Restall :279–291, 2014) proposes a new, prooftheoretic, logical pluralism. This is in contrast to the modeltheoretic pluralism he and Beall proposed in Beall and Restall :475–493, 2000) and in Beall and Restall. What I will show is that Restall has not described the conditions on being admissible to the prooftheoretic logical pluralism in such a way that relevance logic is one of the admissible logics. Though relevance logic is not hard to add formally, one critical component of Restall’s plu…Read more

25A Reply to Heathcote’s: On the Exhaustion of Mathematical Entities by StructuresAxiomathes 25 (3): 345357. 2015.In this article I respond to Heathcote’s “On the Exhaustion of Mathematical Entities by Structures”. I show that his ontic exhaustion issue is not a problem for ante rem structuralists. First, I show that it is unlikely that mathematical objects can occur across structures. Second, I show that the properties that Heathcote suggests are underdetermined by structuralism are not so underdetermined. Finally, I suggest that even if Heathcote’s ontic exhaustion issue if thought of as a problem of refe…Read more

23Metalinguistic negotiation and logical pluralismSynthese 112. forthcoming.Logical pluralism is the view that there is more than one right logic. A particular version of the view, what is sometimes called domainspecific logical pluralism, has it that the right logic and connectives depend somehow on the domain of use, or context of use, or the linguistic framework. This type of view has a problem with crossframework communication, though: it seems that all such communication turns into merely verbal disputes. If two people approach the same domain with different logi…Read more

22Ante Rem Structuralism and the NoNaming ConstraintPhilosophia Mathematica 24 (1): 117128. 2016.Tim Räz has presented what he takes to be a new objection to Stewart Shapiro's ante rem structuralism. Räz claims that ARS conflicts with mathematical practice. I will explain why this is similar to an old problem, posed originally by John Burgess in 1999 and Jukka Keränen in 2001, and show that Shapiro can use the solution to the original problem in Räz's case. Additionally, I will suggest that Räz's proposed treatment of the situation does not provide an argument for the in re over the ante re…Read more

6Logical pluralism and normativityInquiry: An Interdisciplinary Journal of Philosophy 63 (34): 389410. 2020.We are logical pluralists who hold that the right logic is dependent on the domain of investigation; different logics for different mathematical theories. The purpose of this article is to explore the ramifications for our pluralism concerning normativity. Is there any normative role for logic, once we give up its universality? We discuss Florian Steingerger’s “Frege and Carnap on the Normativity of Logic” as a source for possible types of normativity, and then turn to our own proposal, which po…Read more


Old Dominion UniversityAssistant Professor
Norfolk, VA, United States of America
Areas of Specialization
Philosophy of Language 
Logic and Philosophy of Logic 
Philosophy of Mathematics 