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.

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)

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)

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 (in part) by and because of the risks it involves. (shrink)

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

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)

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 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)

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 ….

Guillermo E. Rosado Haddock. A Critical Introduction to the Philosophy of Gottlob Frege. Aldershot, Hampshire, and Burlington, Vermont: Ashgate Publishing, 2006. ISBN 978-0-7546-5471-1. Pp. x+157.

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.

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)

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 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 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 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)

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)

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)

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)

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 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).

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)

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.

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..

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)

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)

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

We discuss the typography of the notation used by Gottlob Frege in his Grundgesetze der Arithmetik.

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 a generic form (...) of the Bad Company objection and introduce an epistemic issue connected to this general problem that will be the focus of the rest of the paper. In the third section, we present an alternative approach within philosophy of mathematics, a view that emerges from Hilbert's Grundlagen der Geometrie (1899, Leipzig: Teubner; Foundations of geometry (trans.: Townsend, E.). La Salle, Illinois: Open Court, 1959.). We will argue that Bad Company-style worries, and our concomitant epistemic issue, also affects this conception and other foundationalist approaches. In the following sections, we then offer various ways to address our epistemic concern, arguing, in the end, that none resolves the issue. The final section offers our own resolution which, however, runs against the foundationalist spirit of the Scottish neo-logicist program. (shrink)

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’….

EbertPhilip A and RossbergMarcus, eds.* * _ Essays on Frege’s Basic Laws of Arithmetic_. Oxford: Oxford University Press, 2019. Pp. xii + 673. ISBN: 978-0-19-871208-4 ; 978-0-19-102005-6, 978-0-19-178024-0. doi: 10.1093/oso/9780198712084.001.0001.

Western society is steeped in a legacy of white supremacy and colonialism--a worldview that pits humans against nature and that has created numerous pressing social and environmental challenges. So great are these challenges that many of us have come to believe that our species is fundamentally flawed and that our story is destined to be nasty, brutish, and short. In Finding Our Niche I explore these tragedies of western society while offering the makings of an alternative: a set of metaphors (...) and examples that can guide us in reconciling our settler-colonial histories in favor of a new and more sustainable vision for humanity and our natural world. Drawing on a variety of compelling stories from my personal life and research experiences around the world, I bring the reader through the difficult journey of reconciliation, a journey that leads to a more optimistic understanding of human nature and the prospects for our future. Drawing from my fifteen years of experience as an anthropologist and ecologist working with people around the world, I share exceptional stories of local people rejecting the oppressive, industrial logic of progress and creating win-win scenarios, where both people and nature thrive together. These stories include cattle ranching on the Burren in Ireland, clam gardening in coastal British Columbia, and the conservation of an accidental wetland in Northwest Mexico. I structure my telling of these stories with a series of ecological metaphors--including keystone, engineer, and sentinel--that collectively provide a basis for more sustainable ways of living. In tandem with these stories, I weave a series of personal vignettes, drawing from my own struggle to reconcile my identity as a white settler on stolen Indigenous lands. As a whole, the book develops a thesis about how we can reimagine our nature and identity, and in so doing, address issues like climate change, biodiversity loss, and food insecurity by building more healthful and fulfilling relationships with our neighbors and the land- and seascapes around us. Finding our Niche is a timely piece that offers confidence in a time when the realities of ecological disaster are becoming a daily reminder that something has to give. It engages with the critical but thorny problems of sustainability, white supremacy, capitalism, and colonialism in a fresh and productive way, making it a perfect fit for Fernwood's portfolio and critical readership. At once a primer on paradigm shift, it is an accessible and personal book that seeks to offer tangible examples of hope to the countless people who are concerned about the sustainability and future of our societies and planet. (shrink)

While examples of bacteria benefiting eukaryotes are increasingly documented, studies examining effects of eukaryote hosts on microbial fitness are rare. Beneficial bacteria are often called “mutualistic” even if mutual reciprocity of benefits has not been demonstrated and despite the plausibility of other explanations for these microbes' beneficial effects on host fitness. Furthermore, beneficial bacteria often occur in diverse communities, making mutualism both empirically and conceptually difficult to demonstrate. We suggest reserving the terms “mutualism” and “parasitism” for pairwise interactions where the (...) relationship is largely independent of other species and can be verified by measuring the fitness effect experienced by both partners. In hosts with diverse microbial communities, we propose re‐formulating some of the essential questions of symbiosis research – e.g. concerning specificity, transmission mode, and common evolutionary fates – as questions of community ecology and ecosystem function, allowing important biological interactions to be investigated without making assumptions about reciprocity. Understanding the fitness of host‐associated bacteria is a crucial component of investigations into the role of microbes in eukaryote evolution. (shrink)

Abstract In this essay, a new approach for the ethical study of emerging technology ethics will be presented, called anticipatory technology ethics (ATE). The ethics of emerging technology is the study of ethical issues at the R&D and introduction stage of technology development through anticipation of possible future devices, applications, and social consequences. I will argue that a major problem for its development is the problem of uncertainty, which can only be overcome through methodologically sound forecasting and futures studies. I (...) will then consider three contemporary approaches to the ethics of emerging technologies that use forecasting: ethical technology assessment, the techno-ethical scenarios approach and the ETICA approach, and I considered their strengths and weaknesses. Based on this critical study, I then present my own approach: ATE. ATE is a conceptually and methodologically rich approach for the ethical analysis of emerging technologies that incorporates a large variety of ethical principles, issues, objects and levels of analysis, and research aims. It is ready to be applied to contemporary and future emerging technologies. Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s11569-012-0141-7 Authors Philip A. E. Brey, Department of Philosophy, School of Behavioral Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Journal NanoEthics Online ISSN 1871-4765 Print ISSN 1871-4757. (shrink)

In recent years, interest has increased in regenerative practices as a strategy for transforming food systems and solving major environmental problems such as biodiversity loss and climate change. However, debates persist regarding these practices and how they ought to be defined. This paper presents a framework for exploring the regenerative potential of food systems, focusing on how food systems activities and technologies are organized rather than the specific technologies or practices being employed. The paper begins with a brief review of (...) debates over sustainable food systems and the varying ways that regenerative food systems have been defined and theorized. Then, it provides the theoretical backing of the framework—the conservation of change principle—which is an interpretation of the laws of thermodynamics and theories of adaptive change as relevant to the regenerative capacity of living systems. Next, the paper introduces the framework itself, which comprises two independent but intersecting dimensions of food systems organization: resource diversity and livelihood flexibility. These two dimensions result in four archetypical regimes for food systems: degenerative, regenerative, impoverished, and coerced. The paper defines each and offers real-world examples. Finally, the paper concludes with a discussion of pathways for transforming food systems and opportunities for additional research. (shrink)

In this essay, a new approach to the ethics of emerging information technology will be presented, called anticipatory technology ethics (ATE). The ethics of emerging technology is the study of ethical issues at the R&D and introduction stage of technology development through anticipation of possible future devices, applications, and social consequences. In the essay, I will first locate emerging technology in the technology development cycle, after which I will consider ethical approaches to emerging technologies, as well as obstacles in developing (...) such approaches. I will argue that any sound approach must centrally include futures studies of technology. I then present ATE and some applications of it to emerging information technologies. In ATE, ethical analysis is performed at three levels, the technology, artifact and application levels, and at each levels distinct types of ethical questions are asked. ATE analyses result in the identification and evaluation of a broad range of ethical issues that can be anticipated in relation to an emerging information technology. This ethical analysis can then be used for ethical recommendations for design or governance. (shrink)

McCullough and colleagues draw an historical line from the writings of Percival, who found himself resolving arguments (sometimes violent) between physicians, surgeons and apothecaries, to the concept of civility as a professional virtue and duty. The authors show that civility is a prerequisite to effective cooperation, which itself underpins patient safety and positive clinical outcomes—desirable endpoints of any discussion about healthcare. They exhort academic leaders to teach, role model and reward correct behaviours.1 Why then, as a clinician manager with a (...) deep interest in fostering civility and psychological safety, am I not satisfied? Three reasons: the paper does not adequately explore the reasons why, its focus is largely restricted to academic institutions, and it does not encompass the non-clinical workforce; as a result, its proposed solutions appear ungrounded. Why are ‘good people’, who were attracted to careers that demand altruism and empathy, uncivil in the workplace? What are the competing goals that result in curt, disrespectful or downright rude exchanges? This has been studied. Leape et al concluded that endogenous factors such as personality, insecurity, anxiety, depression, narcissism and responses to prior …. (shrink)