•  737
    The good, the bad and the ugly
    Synthese 170 (3): 415-441. 2009.
    This paper discusses the neo-logicist 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" neo-logicist school, present …Read more
  •  468
    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
  •  450
    Abstraction and identity
    Dialectica 59 (2). 2005.
    A co-authored 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.
  •  152
    Transmission of warrant-failure and the notion of epistemic analyticity
    Australasian 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 warrant-failure. To this end, I will briefly outline Boghossian's account, followed by an explanation of what a transmission of warrant-failure consists in. I will also show that this charge is independent of the worry of rule-circularity which has been raised concerning the justification of logical principles and of which …Read more
  •  146
    Ed Zalta's Version of Neo-Logicism: a friendly letter of complaint
    In Hannes Leitgeb & Alexander Hieke (eds.), Reduction – Abstraction – Analysis, Ontos. pp. 11--305. 2009.
    In this short letter to Ed Zalta we raise a number of issues with regards to his version of Neo-Logicism. The letter is, in parts, based on a longer manuscript entitled “What Neo-Logicism 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).
  •  144
    Varieties of Risk
    with Martin Smith and Ian Durbach
    Philosophy and Phenomenological Research 01-24. 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 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
  •  95
    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’….
  •  84
    What mathematical knowledge could not be
    Aporia 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 ….
  •  74
    A Puzzle About Ontological Commitments
    Philosophia Mathematica 16 (2): 209-226. 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 second-order logic, allows for a deduction of the second-order Peano axioms. The puzzle aims to put pressure on so-called 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
  •  64
    What is the purpose of neo-logicism?
    Traveaux de Logique 18 33-61. 2007.
    This paper introduces and evaluates two contemporary approaches of neo-logicism. Our aim is to highlight the differences between these two neo-logicist 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..
  •  49
    Frege's Recipe
    Journal of Philosophy 113 (7): 309-345. 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
  •  47
    Lottery judgments: A philosophical and experimental study
    with Martin Smith and Ian Durbach
    Philosophical 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
  •  47
    A Plea for Risk
    Royal 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
  •  42
    Frege on Sense Identity, Basic Law V, and Analysis
    Philosophia Mathematica 24 (1): 9-29. 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
  •  38
    The convenience of the typesetter; notation and typography in Frege’s Grundgesetze der Arithmetik
    with Jim J. Green and Marcus Rossberg
    Bulletin of Symbolic Logic 21 (1): 15-30. 2015.
    We discuss the typography of the notation used by Gottlob Frege in his Grundgesetze der Arithmetik.
  •  31
    Guillermo E. Rosado Haddock's critical introduction to the philosophy of Gottlob Frege is based on twenty-five 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 neo-Kantian and…Read more
  •  21
    Gottlob 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 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
  •  19
    Frege's Theorem (review)
    Philosophical Quarterly 64 (254): 166-169. 2014.
  •  16
    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
  •  13
    Bayesian reasoning in avalanche terrain: a theoretical investigation
    Journal 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.
  •  7
    Dummett’s Criticism of the Context Principle
    Grazer 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
  •  7
    Going to ground with concepts
    Metascience 19 (2): 217-220. 2010.
  •  3
    Essays on Frege's Basic Laws of Arithmetic
    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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  •  1
    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