
737The good, the bad and the uglySynthese 170 (3): 415441. 2009.This paper discusses the neologicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neologicist school, present …Read more

468Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der ArithmetikHistory and Philosophy of Logic 30 (4): 341348. 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

450Abstraction and identityDialectica 59 (2). 2005.A coauthored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.

152Transmission of warrantfailure and the notion of epistemic analyticityAustralasian Journal of Philosophy 83 (4). 2005.In this paper I will argue that Boghossian's explanation of how we can acquire a priori knowledge of logical principles through implicit definitions commits a transmission of warrantfailure. To this end, I will briefly outline Boghossian's account, followed by an explanation of what a transmission of warrantfailure consists in. I will also show that this charge is independent of the worry of rulecircularity which has been raised concerning the justification of logical principles and of which …Read more

146Ed Zalta's Version of NeoLogicism: a friendly letter of complaintIn Hannes Leitgeb & Alexander Hieke (eds.), Reduction – Abstraction – Analysis, Ontos. pp. 11305. 2009.In this short letter to Ed Zalta we raise a number of issues with regards to his version of NeoLogicism. The letter is, in parts, based on a longer manuscript entitled “What NeoLogicism could not be” which is in preparation. A response by Ed Zalta to our letter can be found on his website: http://mally.stanford.edu/publications.html (entry C3).

144Varieties of RiskPhilosophy and Phenomenological Research 0124. 2019.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 daytoday 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

95Adventure, climbing excellence and the practice of 'bolting'In M. 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 coauthored 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’….

84What mathematical knowledge could not beAporia 1 (1): 4670. 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 ….

74A Puzzle About Ontological CommitmentsPhilosophia Mathematica 16 (2): 209226. 2008.This paper raises and then discusses a puzzle concerning the ontological commitments of mathematical principles. The main focus here is Hume's Principle—a statement that, embedded in secondorder logic, allows for a deduction of the secondorder Peano axioms. The puzzle aims to put pressure on socalled epistemic rejectionism, a position that rejects the analytic status of Hume's Principle. The upshot will be to elicit a new and very basic disagreement between epistemic rejectionism and the neo…Read more

64What is the purpose of neologicism?Traveaux de Logique 18 3361. 2007.This paper introduces and evaluates two contemporary approaches of neologicism. Our aim is to highlight the diﬀerences between these two neologicist programmes and clarify what each projects attempts to achieve. To this end, we ﬁrst introduce the programme of the Scottish school – as defended by Bob Hale and Crispin Wright1 which we believe to be a..

49Frege's RecipeJournal of Philosophy 113 (7): 309345. 2016.In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and explain how it differs f…Read more

47Lottery judgments: A philosophical and experimental studyPhilosophical Psychology 31 (1): 110138. 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

47A Plea for RiskRoyal Institute of Philosophy Supplement 73 4564. 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 risktaking in mountaineering. Our discussion is organised around the fact that mountaineers and nonmountaineers often disagree about how risky mountaineering really is. We hope to cast some light on the nature of this disagreement – and to …Read more

42Frege on Sense Identity, Basic Law V, and AnalysisPhilosophia Mathematica 24 (1): 929. 2016.The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege di…Read more

38The convenience of the typesetter; notation and typography in Frege’s Grundgesetze der ArithmetikBulletin of Symbolic Logic 21 (1): 1530. 2015.We discuss the typography of the notation used by Gottlob Frege in his Grundgesetze der Arithmetik.

34Mountaineering and the value of selfsufficiencyIn Stephen E. Schmid (ed.), Climbing  Philosophy for Everyone: Because It's There, Wileyblackwell. 2010.

31Guillermo E. rosado Haddock. A critical introduction to the philosophy of Gottlob Frege. Aldershot, Hampshire, and burlington, Vermont: Ashgate publishing, 2006. Isbn 9780754654711. Pp. X+157 (review)Philosophia Mathematica 19 (3): 363367. 2011.Guillermo E. Rosado Haddock's critical introduction to the philosophy of Gottlob Frege is based on twentyfive years of teaching Frege's philosophy at the University of Puerto Rico. It developed from an earlier publication by Rosado Haddock on Frege's philosophy which was, however, available only in Spanish. This introduction to Frege is meant to steer a path between the two main approaches to Frege studies: on the one hand, we have interpretations of Frege which portray him as a neoKantian and…Read more

28Translators' IntroductionIn Gottlob Frege (ed.), Basic Laws of Arithmetic, Derived Using ConceptScript: Volumes I & II, Oxford University Press. 2013.

21Gottlob Frege: Basic Laws of Arithmetic (edited book)Oxford University Press. 2013.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 groundbreaking 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

20Richard G. Heck Jr. Reading Frege's Grundgesetze. Oxford: Oxford University Press, 2012. ISBN: 9780199233700 ; 9780198744375 ; 9780191655357 . Pp. xvii + 296 (review)Philosophia Mathematica 23 (2): 289293. 2015.

16The 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 wellknown 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

13Bayesian reasoning in avalanche terrain: a theoretical investigationJournal of Adventure Education and Outdoor Learning 19 (1): 8495. 2019.In this article, I explore a Bayesian approach to avalanche decisionmaking. I motivate this perspective by highlighting a version of the baserate fallacy and show that a similar pattern applies to decisionmaking in avalancheterrain. 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.

7Dummett’s Criticism of the Context PrincipleGrazer Philosophische Studien 92 (1): 2351. 2015.This paper discusses Michael Dummett’s criticism of the NeoFregean 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 NeoFregean project which might have motivated Dummett’s opposition to the NeoFregean use of the context principle. I argue that this tens…Read more

3Essays on Frege's Basic Laws of ArithmeticOxford 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 twentytwo 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

1A Framework for Implicit Definitions and the A prioriIn Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism, Oxford University Press. pp. 133160. 2016.

1Abstractionism: 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 metaontology of Abstractionism, abstractionist epistemolo…Read more

Mathematical Creation in Frege's GrundgesetzeIn Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic, Oxford University Press. pp. 325342. 2019.
University of St. Andrews
PhD, 2006
Stirling, Stirling, United Kingdom of Great Britain and Northern Ireland
Areas of Specialization
Epistemology 
Philosophy of Mathematics 
20th Century Analytic Philosophy 