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Basic Laws of Arithmetic (edited book)Oxford University Press. 1964.This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework within which his technical contributions were conceived and developed…Read more
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46Adventure, climbing excellence and the practice of boltingIn Mike J. McNamee (ed.), Philosophy, Risk and Adventure Sports, London ;routledge. pp. 56. 2007.forthcoming in M. McNamee (ed) Philosophy, Risk and Adventure Sports, Routledge The final draft of a co-authored article with Simon Robertson (Leeds). In this paper we examine a recent version of an old controversy within climbing ethics. Our organising topic is the ‘bolting’….
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19Gratuitous risk: danger and recklessness perception of adventure sports participantsJournal of the Philosophy of Sport 51 (2): 267-284. 2024.Since the 1970’s there has been a major increase in adventure sports participation but it seems that engagement in such sports comes with a stigma: adventure sports participants are often regarded as reckless ‘daredevils’. We approach the questions about people’s perception of risk and recklessness in adventure sports by combining empirical research with philosophical analysis. First, we provide empirical evidence that suggests that laypeople tend to assess the danger of adventure sports as grea…Read more
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8Basic Laws of Arithmetic (edited book)Oxford University Press UK. 2013.This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework.
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6Mountaineering and the Value of Self‐SufficiencyIn Fritz Allhoff & Stephen E. Schmid (eds.), Climbing ‐ Philosophy for Everyone, Wiley‐blackwell. 2010-09-24.This chapter contains sections titled: What is Self‐Sufficiency? The Value of Self‐Sufficiency Objections Concluding Remarks Notes.
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6Ed Zalta’s Version of Neo-Logicism – a Friendly Letter of ComplaintIn Alexander Hieke & Hannes Leitgeb (eds.), Reduction, abstraction, analysis: proceedings of the 31th International Ludwig Wittgenstein-Symposium in Kirchberg, 2008, De Gruyter. pp. 305-310. 2009.
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9Review of Kit Fine: The Limits of Abstraction (review)British Journal for the Philosophy of Science 55 (4): 791-800. 2004.Critical Notice of The Limits of abstraction by Kit Fine, Oxford: Clarendon Press, 2002, pp.216. ISBN 9780191567261
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14A Plea for Risk: Philip A. Ebert & Simon RobertsonRoyal Institute of Philosophy Supplement 73 45-64. 2013.Mountaineering is a dangerous activity. For many mountaineers, part of its very attraction is the risk, the thrill of danger. Yet mountaineers are often regarded as reckless or even irresponsible for risking their lives. In this paper, we offer a defence of risk-taking in mountaineering. Our discussion is organised around the fact that mountaineers and non-mountaineers often disagree about how risky mountaineering really is. We hope to cast some light on the nature of this disagreement – and to …Read more
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7Expert and lay judgements of danger and recklessness in adventure sportsJournal of Risk Research 26 (2): 133-146. 2023.We investigate differences in perceived danger and recklessness judgements by experts (experienced skiers, N=362) and laypeople (N=2080) about participation in adventure sports across the same judgemental task using a third person perspective. We investigate the relationship between danger and recklessness and the extent to which fatality frequency, as well as other contextual factors such as gender, dependants, competence, and motivations of the sports participant affect expert and laypeople ju…Read more
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6Frege's Concept-Script (Grundgesetze der Arithmetik)In Bruno Woltzenlogel Paleo & Giselle Reis (eds.), Encyclopedia of Proof Systems, College Publications. 2022.
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23Methodological and conceptual challenges in rare and severe event forecast verificationNatural Hazards and Earth System Science 22 (2): 539-557. 2022.There are distinctive methodological and conceptual challenges in rare and severe event (RSE) forecast verification, that is, in the assessment of the quality of forecasts of rare but severe natural hazards such as avalanches, landslides or tornadoes. While some of these challenges have been discussed since the inception of the discipline in the 1880s, there is no consensus about how to assess RSE forecasts. This article offers a comprehensive and critical overview of the many different measures…Read more
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20Safety in numbers: how social choice theory can inform avalanche risk managementJournal of Adventure Education and Outdoor Learning (#): 1-17. 2022.Avalanche studies have undergone a transition in recent years. Early research focused mainly on environmental factors. More recently, attention has turned to human factors in decision making, such as behavioural and cognitive biases. This article adds a social component to this human turn in avalanche studies. It identifies lessons for decision making by groups of skiers from the perspective of social choice theory, a sub-field of economics, decision theory, philosophy and political science that…Read more
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Contemporary Reviews of Frege’s GrundgesetzeIn Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic, Oxford University Press. pp. 637-652. 2019.
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Mathematical Creation in Frege's GrundgesetzeIn Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic, Oxford University Press. pp. 325-342. 2019.
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22Essays on Frege's Basic Laws of Arithmetic (edited book)Oxford University Press. 2019.The volume is the first collection of essays that focuses on Gottlob Frege's Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege's magnum opus. It brings together twenty-two renowned Frege scholars whose contributions discuss a wide range of topics arising from both volumes of Basic Laws of Arithmetic. The original chapters in this volume make vivid the importance and originality of Frege's masterpiece, not just for Frege scholars but for…Read more
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42Varieties of RiskPhilosophy and Phenomenological Research 101 (2): 432-455. 2020.The notion of risk plays a central role in economics, finance, health, psychology, law and elsewhere, and is prevalent in managing challenges and resources in day-to-day life. In recent work, Duncan Pritchard (2015, 2016) has argued against the orthodox probabilistic conception of risk on which the risk of a hypothetical scenario is determined by how probable it is, and in favour of a modal conception on which the risk of a hypothetical scenario is determined by how modally close it is. In this …Read more
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3Bayesian reasoning in avalanche terrain: a theoretical investigationJournal of Adventure Education and Outdoor Learning 19 (1): 84-95. 2019.In this article, I explore a Bayesian approach to avalanche decision-making. I motivate this perspective by highlighting a version of the base-rate fallacy and show that a similar pattern applies to decision-making in avalanche-terrain. I then draw out three theoretical lessons from adopting a Bayesian approach and discuss these lessons critically. Lastly, I highlight a number of challenges for avalanche educators when incorporating the Bayesian perspective in their curriculum.
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12Dummett’s Criticism of the Context PrincipleGrazer Philosophische Studien 92 (1): 23-51. 2015.This paper discusses Michael Dummett’s criticism of the Neo-Fregean concep- tion of the context principle. I will present four arguments by Dummett that purport to show that the context principle is incompatible with platonism. I discuss and ultimately reject each argument. I will close this paper by identifying what I take to be a deep rooted tension in the Neo-Fregean project which might have motivated Dummett’s opposition to the Neo-Fregean use of the context principle. I argue that this tens…Read more
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6Adventure, climbing excellence and the practice of boltingIn Mike J. McNamee (ed.), Philosophy, Risk and Adventure Sports, London ;routledge. pp. 56. 2007.forthcoming in M. McNamee (ed) Philosophy, Risk and Adventure Sports, Routledge The final draft of a co-authored article with Simon Robertson (Leeds). In this paper we examine a recent version of an old controversy within climbing ethics. Our organising topic is the ‘bolting’….
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10Abstractionism: Essays in Philosophy of MathematicsOxford University Press UK. 2016.Abstractionism, which is a development of Frege's original Logicism, is a recent and much debated position in the philosophy of mathematics. This volume contains 16 original papers by leading scholars on the philosophical and mathematical aspects of Abstractionism. After an extensive editors' introduction to the topic of abstractionism, the volume is split into 4 sections. The contributions within these sections explore the semantics and meta-ontology of Abstractionism, abstractionist epistemolo…Read more
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7Gottlob Frege: Basic Laws of Arithmetic (edited book)Oxford University Press. 1964.This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles
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21The convenience of the typesetter; notation and typography in Frege’s Grundgesetze der ArithmetikBulletin of Symbolic Logic 21 (1): 15-30. 2015.We discuss the typography of the notation used by Gottlob Frege in his Grundgesetze der Arithmetik.
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12Mountaineering and the value of self-sufficiencyIn Fritz Allhoff & Stephen E. Schmid (eds.), Climbing - Philosophy for Everyone: Because It's There, Wiley-blackwell. 2010.
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85What mathematical knowledge could not beAporia 1 (1): 46-70. 2007.This is an introductory survey article to the philosophy of mathematics. I provide a detailed account of what Benacerraf’s problem is and then discuss in general terms four different approaches to ….
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17Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der ArithmetikHistory and Philosophy of Logic 30 (4): 341-348. 2009.In 1885, Georg Cantor published his review of Gottlob Frege's Grundlagen der Arithmetik . In this essay, we provide its first English translation together with an introductory note. We also provide a translation of a note by Ernst Zermelo on Cantor's review, and a new translation of Frege's brief response to Cantor. In recent years, it has become philosophical folklore that Cantor's 1885 review of Frege's Grundlagen already contained a warning to Frege. This warning is said to concern the defect…Read more
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340Translators' IntroductionIn Gottlob Frege (ed.), Basic Laws of Arithmetic, Oxford University Press. 1893.
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5The context principle and implicit definitions : towards an account of our a priori knowledge of arithmeticDissertation, St. Andrews. 2005.This thesis is concerned with explaining how a subject can acquire a priori knowledge of arithmetic. Every account for arithmetical, and in general mathematical knowledge faces Benacerraf's well-known challenge, i.e. how to reconcile the truths of mathematics with what can be known by ordinary human thinkers. I suggest four requirements that jointly make up this challenge and discuss and reject four distinct solutions to it. This will motivate a broadly Fregean approach to our knowledge of arith…Read more
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12Mountaineering is a dangerous activity. For many mountaineers, part of its very attraction is the risk, the thrill of danger. Yet mountaineers are often regarded as reckless or even irresponsible for risking their lives. In this paper, we offer a defence of risk-taking in mountaineering. Our discussion is organised around the fact that mountaineers and non-mountaineers often disagree about how risky mountaineering really is. We hope to cast some light on the nature of this disagreement – and to …Read more
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30Lottery judgments: A philosophical and experimental studyPhilosophical Psychology 31 (1): 110-138. 2018.In this paper, we present the results of two surveys that investigate subjects’ judgments about what can be known or justifiably believed about lottery outcomes on the basis of statistical evidence, testimonial evidence, and “mixed” evidence, while considering possible anchoring and priming effects. We discuss these results in light of seven distinct hypotheses that capture various claims made by philosophers about lay people’s lottery judgments. We conclude by summarizing the main findings, poi…Read more
University of St. Andrews
PhD, 2006
Stirling, United Kingdom of Great Britain and Northern Ireland
Areas of Specialization
Epistemology |
Philosophy of Mathematics |
20th Century Analytic Philosophy |