
Should Theories of Logical Validity SelfApply?Erkenntnis. forthcoming.Some philosophers argue that a theory of logical validity should not interpret its own language, because a Russellian argument shows that selfapplicability is inconsistent with the ability to capture all the interpretations of its own language. First, I set up a formal system to examine the Russellian argument. I then defend the need for selfapplicability. I argue that selfapplicability seems to be implied by generality, and that the Russellian argument rests on a test for meaning that is bia…Read more

Probability and DangerAmherst Lecture in Philosophy. 2009.What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantummechanical blips threaten the idea that competent deduction is a way of extending our knowledge. Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma between scepticism and abandoning MPC is false. In extr…Read more

A Philosophical Introduction to Higherorder LogicsRoutledge. 2023.This is the first comprehensive textbook on higher order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higherorder languages  their model theory and proof theory, the theory of λabstraction and its generalizations  and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on nonextensional higherorder logics, makin…Read more

Logical methodsThe MIT Press. 2023.

NeoLogicism and Gödelian IncompletenessMind 131 (524): 10551082. 2023.There is a longstanding gap in the literature as to whether Gödelian incompleteness constitutes a challenge for NeoLogicism, and if so how serious it is. In this paper, I articulate and address the challenge in detail. The NeoLogicist project is to demonstrate the analyticity of arithmetic by deriving all its truths from logical principles and suitable definitions. The specific concern raised by Gödel’s first incompleteness theorem is that no single sound system of logic syntactically implies…Read more

A simple solution to the collapse argument for logical pluralismInquiry: An Interdisciplinary Journal of Philosophy. forthcoming.Many philosophers have argued that logical pluralism is not compatible with the normativity of logic. They developed different versions of the collapse argument: if two logics are correct, then the weaker one will be normatively irrelevant. In this paper, I argue that the collapse argument is based on a controversial premise: the assumption that every logic can be characterized by the same bridge principle. I provide a solution to the collapse argument based on the modification of this premise, …Read more

Mathematics and MetaphilosophyCambridge University Press. 2022.This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the problem of explaining the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the problem of explaining their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book sh…Read more

Proofs and Models in Philosophical LogicCambridge University Press. 2022.This Element is an introduction to recent work proofs and models in philosophical logic, with a focus on the semantic paradoxes the sorites paradox. It introduces and motivates different proof systems and different kinds of models for a range of logics, including classical logic, intuitionistic logic, a range of threevalued and fourvalued logics, and substructural logics. It also compares and contrasts the different approaches to substructural treatments of the paradox, showing how the structu…Read more

Does rationality demand higherorder certainty?Synthese 198 (12): 1156111585. 2020.Should you always be certain about what you should believe? In other words, does rationality demand higherorder certainty? First answer: Yes! Higherorder uncertainty can’t be rational, since it breeds at least a mild form of epistemic akrasia. Second answer: No! Higherorder certainty can’t be rational, since it licenses a dogmatic kind of insensitivity to higherorder evidence. Which answer wins out? The first, I argue. Once we get clearer about what higherorder certainty is, a view emerges …Read more

Good GuessesPhilosophy and Phenomenological Research 105 (3): 581618. 2021.This paper is about guessing: how people respond to a question when they aren’t certain of the answer. Guesses show surprising and systematic patterns that the most obvious theories don’t explain. We argue that these patterns reveal that people aim to optimize a tradeoff between accuracy and informativity when forming their guess. After spelling out our theory, we use it to argue that guessing plays a central role in our cognitive lives. In particular, our account of guessing yields new theories…Read more

University of CopenhagenPostdoctoral Fellow
St Andrews, United Kingdom of Great Britain and Northern Ireland
Areas of Specialization
Logic and Philosophy of Logic 
Epistemology 