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, pointing to future research, and comparing our findings to (...) recent studies by Turri and Friedman. (shrink)

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 article, we use Pritchard’s discussion as a springboard for a more wide-ranging discussion of the notion of risk. We introduce three different conceptions of risk: the standard probabilistic conception, Pritchard’s modal conception, and a normalcy conception that is new (though it has some precursors in the psychological literature on risk perception). Ultimately, we argue that the modal conception is ill-suited to the roles that a notion of risk is required to play and explore the prospects for a form of pluralism about risk, embracing both the probabilistic and the normalcy conceptions. (shrink)

In a recent paper in this journal Duncan Pritchard responds to an objection to the modal account of risk pressed by Ebert, Smith and Durbach ( 2020 ). In this paper, I expand upon the objection and argue that it still stands. I go on to consider a more general question raised by this exchange – whether risk is ‘objective’, or whether it is something that varies from one perspective to another.

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 argue that (...) mountaineering may actually be worthwhile because of the risks it involves. Section 1 introduces the disagreement and, in doing so, separates out several different notions of risk. Sections 2–4 then consider some explanations of the disagreement, showing how a variety of phenomena can skew people's risk judgements. Section 5 then surveys some recent statistics, to see whether these illuminate how risky mountaineering is. In light of these considerations, however, we suggest that the disagreement is best framed not simply in terms of how risky mountaineering is but whether the risks it does involve are justified. The remainder of the paper, sections 6–9, argues that risk-taking in mountaineering often is justified – and, moreover, that mountaineering can itself be justified by and because of the risks it involves. (shrink)

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 tension does (...) give rise to a legitimate concern, yet it does not affect the Neo-Fregean conception of the context principle. (shrink)

This chapter contains sections titled: What is Self‐Sufficiency? The Value of Self‐Sufficiency Objections Concluding Remarks Notes.

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 arithmetic and mathematics in general. (...) Pursuing this strategy appeals to the context principle which, it is proposed, underwrites a form of Platonism and explains how reference to and object-directed thought about abstract entities is, in principle, possible. I discuss this principle and defend it against different criticisms as put forth in recent literature. Moreover, I will offer a general framework for implicit definitions by means of which - without an appeal to a faculty of intuition or purely pragmatic considerations - a priori and non-inferential knowledge of basic mathematical principles can be acquired. In the course of this discussion, I will argue against various types of opposition to this general approach. Also, I will highlight crucial shortcomings in the explanation of how implicit definitions may underwrite a priori knowledge of basic principles in broadly similar conceptions. In the final part, I will offer a general account of how non-inferential mathematical knowledge resulting from implicit definitions is best conceived which avoids these shortcomings. (shrink)

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 epistemology, the mathematics of Abstractionis, and finally, Frege's application constraint within an abstractionist (...) setting. (shrink)

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.

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 Boghossian is fully aware. My (...) argument comes in two steps: firstly, I will argue for the insufficiency of Boghossian's template which is meant to explain how a subject can acquire a warrant for logical principles. I will show however that this insufficiency of his template can be remedied by adopting what I call the Disquotational Step. Secondly, I will argue that incorporating this further step makes his template subject to a transmission of warrant-failure, assuming that certain rather basic and individually motivated principles hold. Thus, Boghossian's account faces a dilemma: either he adopts the Disquotational Step and subjects his account to the charge of a transmission of warrant-failure, or he drops this additional step leaving the account confronted with explaining the gap that has previously been highlighted. I will then suggest various rejoinders that Boghossian might adopt but none of which - I will argue - can resolve the dilemma. Lastly, I will raise and briefly discuss the question whether this worry generalizes to other accounts, such as Hale and Wright's that aim to explain our knowledge of logic and/or mathematics in virtue of implicit definitions. (shrink)

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-Fregeans, defenders of the analytic status of (...) Hume's Principle, which will provide a new angle from which properly to assess and re-evaluate the current debate. (shrink)

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 the study of the history (...) of logic, mathematics, and philosophy. (shrink)

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 (...) did not hold the relevant sense-identity claim regarding basic law V. (shrink)

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 ….

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 used to capture the (...) quality of categorical, binary RSE forecasts – forecasts of occurrence and non-occurrence – and argues that of skill scores in the literature there is only one adequate for RSE forecasting. We do so by first focusing on the relationship between accuracy and skill and showing why skill is more important than accuracy in the case of RSE forecast verification. We then motivate three adequacy constraints for a measure of skill in RSE forecasting. We argue that of skill scores in the literature only the Peirce skill score meets all three constraints. We then outline how our theoretical investigation has important practical implications for avalanche forecasting, basing our discussion on a study in avalanche forecast verification using the nearest-neighbour method (Heierli et al., 2004). Lastly, we raise what we call the “scope challenge”; this affects all forms of RSE forecasting and highlights how and why working with the right measure of skill is important not only for local binary RSE forecasts but also for the assessment of different diagnostic tests widely used in avalanche risk management and related operations, including the design of methods to assess the quality of regional multi-categorical avalanche forecasts. (shrink)

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 judgements respectively. Experienced skiers gave lower overall danger and recklessness ratings than non-skiers. (...) Experienced skiers’ judgements were also more sensitive than non-skiers’ to variations in the fatality rate of the activity and the competence level of the participant, yet were less sensitive to whether the event was done for external benefit such as a charity. Recklessness judgements were overall more sensitive to changes in activity descriptions than danger judgements. Our findings support the emerging picture of adventure sports participants as rational and sensitive to risk-relevant features rather than somehow pathological in their risk perception. (shrink)

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 greater than more mundane sports and judge adventure (...) sports participants as more reckless than participants in non-adventure sports. We contextualise these findings within existing psychological risk perception paradigms and outline new philosophical explanations of the identified pattern in laypeople’s risk perception. (shrink)

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.

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.

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 defectiveness (...) of Frege's notion of extension. The exact scope of such speculations varies and sometimes extends as far as crediting Cantor with an early hunch of the paradoxical nature of Frege's notion of extension. William Tait goes even further and deems Frege 'reckless' for having missed Cantor's explicit warning regarding the notion of extension. As such, Cantor's purported inkling would have predated the discovery of the Russell-Zermelo paradox by almost two decades. In our introductory essay, we discuss this alleged implicit (or even explicit) warning, separating two issues: first, whether the most natural reading of Cantor's criticism provides an indication that the notion of extension is defective; second, whether there are other ways of understanding Cantor that support such an interpretation and can serve as a precisification of Cantor's presumed warning. (shrink)

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 thus (...) as some kind of idealist; on the other, we have writings like those of Dummett in which Frege is portrayed as a type of ‘philosophical Adam’, i.e., as completely separated from his philosophical tradition. Rosado Haddock succeeds in placing Frege's thinking into a broader philosophical context — mainly by reference to his contemporary Edmund Husserl — while also avoiding a Kantian reading of Frege's work.The structure of the book follows Frege's writing chronologically. In this way, Rosado Haddock leads the reader through the whole of Frege's philosophy while highlighting important changes and developments in Frege's thought from the Begriffsschrift to his Grundgesetze and other later writings. Chapter 1 introduces us to the core philosophical themes of Frege's Begriffsschrift with a special emphasis on Frege's notions of ‘conceptual content’ and ‘judgeable content’. Here, Rosado Haddock anticipates further discussion and points towards changes and developments of Frege's core notions of ‘identity’, ‘function’, and ‘content’. Chapters 2 and 3 focus on Frege's Grundlagen der Arithmetik. Chapter 2 discusses Frege's methodological principles as outlined in Frege's introduction and his criticisms of psychological, naturalistic, and Kantian approaches to the philosophy of mathematics. Chapter 3 focuses exclusively on Frege's own logicist account of arithmetic while emphasizing differences between Frege's views and Kantian …. (shrink)

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..

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 investigates voting methods and other forms of (...) collective decision making. In the first part, we outline the phenomenon of wisdom of crowds, where groups make better decisions than their individual members. Drawing on the conceptual apparatus of social choice theory and using idealised scenarios, we identify conditions under which wisdom of crowds arises and also explain how and when deciding together can instead result in worse decisions than may be expected from individual group members. In the second part, we use this theoretical understanding to offer practical suggestions for decision making in avalanche terrain. Finally, we make several suggestions for risk management in other outdoor and adventure sports and for outdoor sports education. (shrink)

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 from the role played by extensions in his earlier book “Die Grundlagen der Arithmetik”. Lastly, we will demonstrate that this hitherto neglected yet foundational aspect of Frege’s use of Basic Law V helps to resolve a number of important interpretative challenges in recent Frege scholarship, while also shedding light on some important differences between Frege’s logicism and recent neo-logicist approaches to the foundations of mathematics. (shrink)

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.

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’….

Critical Notice of The Limits of abstraction by Kit Fine, Oxford: Clarendon Press, 2002, pp.216. ISBN 9780191567261.

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 39.4 (2005) 1-2 [Access article in PDF] A Personal Tribute to Nellie McCaslin: 20 August 1914–28 February 2005 Nellie McCaslin, pioneer in creative drama and educational theatre, passed away earlier this year in New York City at age 90. Having obtained a bachelor's degree from Western Reserve University in 1936 and a master's degree in 1937, she went on to study improvisation with Maria (...) Ouspenskaya, of the Moscow Art Theatre, in California. In 1957, she received a Ph.D. from the School of Education at New York University (NYU). A longtime Greenwich Village resident, she became associate dean at the Gallatin School of Individualized Study and for over thirty years was an adjunct faculty member at NYU's Program in Educational Theatre.Her publications include Theatre for Children in the United States: A History (1971), Children and Drama (1975), Theatre for Young Audiences (1978), and Creative Drama in the Classroom and Beyond (2006), forthcoming in its eighth edition. She will be fondly remembered by her colleagues and friends for her keynote speeches delivered at conferences and events from Canada to Switzerland, from Israel to Taiwan. Throughout her career, she enthusiastically encouraged imagination and creativity through creative drama and the arts. In 1977, she was elected to the American College of Fellows. She received an honorary Doctor of Humanities from Ferrum College, Virginia, in 1986. Nellie's outstanding contribution to educational theatre was recognized with a Lifetime Achievement Award from the American Alliance of Theatre and Education in 1996 and with a Medallion Award from the Children's Theatre Foundation in 2001.At the Program in Educational Theatre at NYU, she taught courses in Theatre for Young Audiences and Creative Drama. She would also invite [End Page 1] friends and acquaintances to attend seminars at her church, First Presbyterian in the Village, and afterwards we might return to her apartment on 10th Street, where she would introduce us to fellow artists. Nellie found time to volunteer at church and at the local animal shelter, Bide-A-Wee. Her tireless energy and compassion were expressions of her love of living. She had begun to act again and each summer would travel south to take part in the Blue Ridge Dinner Theatre. Artistic Director Rex Stephenson said recently, "She's the only person that could cash a check from New York in Rocky Mount, Virginia, because everybody knew who she was."1 People were drawn to Nellie, as if by her luminous presence; she always had time to listen. Active to the end, she wrote the article that appears in this issue of the Journal of Aesthetic Education. Before she died, Nellie was working with NYU students to create a new play. At St. Vincent's in Manhattan, she was rehearsing her lines by telephone from her hospital bed. She will be deeply missed. Alistair Martin-Smith Endnote 1. Margalit Fox, "Nellie McCaslin, Professor and Children's Theater Authority, Dies at 90," New York Times, 12 March 2005.Photo by Maya Ishiura... (shrink)

This stunning paperback volume showcases the winners and best entries for the International Garden Photographer of the Year competition and accompanies a major exhibition at the Royal Botanic Gardens, Kew, in May 2011 and touring the UK and USA thereafter. ‘The contemporary camera maybe a technological marvel but it can’t take photographs, only the photographer can do that. To succeed it involves making an incredible complex of choices and only one chance in the entire history of time to make them (...) as close to perfect as possible. A carefree snap - easy, a composed and considered picture, well, that requires a synergy of skills and perhaps a dash of genius. So that's why this album is such a treat to revel in, its a feast of the worlds best gardens, gardeners, the plants and animals growing and living in them in the very best photographic forms. The images will 'wow' you, make you wish you had been there, wish it was your garden in the picture or wish you had squeezed the button. It’s a testament to a huge array of skills and a catalogue of remarkable beauty’. Chris Packham – BBC Presenter and photographer. (shrink)

Virtue of Civility in the Practice of Politics is a book at the intersection of ethical theory, political philosophy and Christian belief. The book argues that there is a true political virtue: civility. Civility is a virtue that is directed toward the political opponent. MacIntyre's schema for understanding a virtue is used to show how civility contributes to better human living in a variety of contexts: business, family life, church life, and public affairs.