There was a methodological revolution in the mathematics of the nineteenth century, and philosophers have, for the most part, failed to notice.2 My objective in this chapter is to convince you of this, and further to convince you of the following points. The philosophy of mathematics has been informed by an inaccurately narrow picture of the emergence of rigour and logical foundations in the nineteenth century. This blinkered vision encourages a picture of philosophical and logical foundations as essentially disengaged from (...) ongoing mathematical practice. Frege is a telling example: we have misunderstood much of what Frege was trying to do, and missed the intended significance of much of what he wrote, because our received stories underestimate the complexity of nineteenth-century mathematics and mislocate Frege’s work within that context. Given Frege’s perceived status as a paradigmatic analytic philosopher, this mislocation translates into an unduly narrow vision of the relation between mathematics and philosophy. This chapter surveys one part of a larger project that takes Frege as a benchmark to fix some of the broader interest and philosophical significance of nineteenth-century developments. To keep this contribution to a manageable.. (shrink)

A cluster of recent papers on Frege have urged variations on the themethat Frege’s conception of logic is in some crucial way incompatible with‘metatheoretic’ investigation. From this observation, significant consequencesfor our interpretation of Frege’s understanding of his enterprise are taken tofollow. This chapter aims to critically examine this view, and to isolate whatI take to be the core of truth in it. However, I will also argue that once wehave isolated the defensible kernel, the sense in which Frege was committedto (...) rejecting ‘metatheory’ is too narrow and uninteresting to support the con-clusions drawn from the thesis by its proponents. (shrink)

A selection of essays dedicated to Hans Herzberger with affection and gratitude for both his profound work and his lasting example. Contributors: I. Levi (on whether and how a rational agent should be seen as a maximizer of some cognitive value), C. Normore (on medieval accounts of logical validity), J. P. Tappenden (on the local influences on Frege's doctrines), A. Urquhart (on the inexpressible), A. C. Varzi (on dimensionality and the sense of possibility), and S. Yablo (on content and (...) carvings, and from there to mathematical realism). (shrink)

Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the view proposed (...) by Philip Kitcher and Michael Friedman of explanation or understanding as involving the unification of theories that had antecedently appeared heterogeneous. For the second narrowing, I’ll take up one specific feature (among many) of theories and their basic concepts that is sometimes taken to make the theories and concepts preferred: in some fields, for some problems, what is counted as understanding a problem may involve finding a way to represent the problem so that it (or some aspect of it) can be visualized. The final section develops a case study which exemplifies the way that this consideration – the potential for visualizability – can rationally inform decisions as to what the proper framework and axioms should be. The discussion of unification (in sections 3 and 4) leads to a mathematical analogue of Goodman’s problem of identifying a principled basis for distinguishing grue and green. Just as there is a philosophical issue about how we arrive at the predicates we should use when making empirical predictions, so too there is an issue about what properties best support many kinds of mathematical reasoning that are especially valuable to us. The issue becomes pressing via an examination of some physical and mathematical cases that make it seem unlikely that treatments of unification can be as straightforward as the philosophical literature has hoped. Though unification accounts have a grain of truth (since a phenomenon (or cluster of phenomena) called “unification” is in fact important in many cases) we are far from an analysis of what “unification” is.. (shrink)

This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry and (...) the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer. (shrink)

A cluster of recent papers on Frege have urged variations on the theme that Frege’s conception of logic is in some crucial way incompatible with ‘metatheoretic’ investigation. From this observation, significant consequences for our interpretation of Frege’s understanding of his enterprise are taken to follow. This chapter aims to critically examine this view, and to isolate what I take to be the core of truth in it. However, I will also argue that once we have isolated the defensible kernel, the (...) sense in which Frege was committed to rejecting ‘metatheory’ is too narrow and uninteresting to support the con-. (shrink)

This paper uses the strengthened liar paradox as a springboard to illuminate two more general topics: i) the negation operator and the speech act of denial among speakers of English and ii) some ways the potential for acceptable language change is constrained by linguistic meaning. The general and special problems interact in reciprocally illuminating ways. The ultimate objective of the paper is, however, less to solve certain problems than to create others, by illustrating how the issues that form the topic (...) of this paper are more intricate than previously realised, and that they are related in delicate and somewhat surprising ways. (shrink)

It is widely believed that some puzzling and provocative remarks that Frege makes in his late writings indicate he rejected independence arguments in geometry, particularly arguments for the independence of the parallels axiom. I show that this is mistaken: Frege distinguished two approaches to independence arguments and his puzzling remarks apply only to one of them. Not only did Frege not reject independence arguments across the board, but also he had an interesting positive proposal about the logical structure of correct (...) independence arguments, deriving from the geometrical principle of duality and the associated idea of substitution invariance. The discussion also serves as a useful focal point for independently interesting details of Frege's mathematical environment. This feeds into a currently active scholarly debate because Frege's supposed attitude to independence arguments has been taken to support a widely accepted thesis (proposed by Ricketts among others) concerning Frege's attitude toward metatheory in general. I show that this thesis gains no support from Frege's puzzling remarks about independence arguments. (shrink)

The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.

The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.

Setting out to understand Frege, the scholar confronts a roadblock at the outset: We just have little to go on. Much of the unpublished work and correspondence is lost, probably forever. Even the most basic task of imagining Frege's intellectual life is a challenge. The people he studied with and those he spent daily time with are little known to historians of philosophy and logic. To be sure, this makes it hard to answer broad questions like: 'Who influenced Frege?' But (...) the information vacuum also creates local problems of textual interpretation. Say we encounter a sentence that may be read as alluding to a scientific dispute. Should it be read that way? To answer, we'd need to address prior questions. Is it .. (shrink)

I’ll use an extension of the “smidget” example Soames sets out on pages 165-172 to bring out the point. Groups A and B are disjoint and satisfy certain regularity conditions. Recall that the extension and anti-extension are specified by a pair of sufficient conditions. We specify: every member of group A is a smidget and every member of group B is not a smidget. No decision is made about persons that are outside groups A and B. It is, of course, (...) crucial that the smidgethood of the indeterminate cases is genuinely left open. What is the cash value of the difference between leaving a case unsettled and settling a case as indeterminate? Here is one difference: when a case is left unsettled, speakers of the language can resolve it later, if there is some reason to do so. This provides a simple model of key features of legal stipulations, at least in circumstances like U.S. constitutional law, where a single body can introduce an expression and stipulate how it is to be interpreted. (shrink)

I’ll use an extension of the “smidget” example Soames sets out on pages 165-172 to bring out the point. Groups A and B are disjoint and satisfy certain regularity conditions. Recall that the extension and anti-extension are specified by a pair of sufficient conditions. We specify: every member of group A is a smidget and every member of group B is not a smidget. No decision is made about persons that are outside groups A and B. It is, of course, (...) crucial that the smidgethood of the indeterminate cases is genuinely left open. What is the cash value of the difference between leaving a case unsettled and settling a case as indeterminate? Here is one difference: when a case is left unsettled, speakers of the language can resolve it later, if there is some reason to do so. This provides a simple model of key features of legal stipulations, at least in circumstances like U.S. constitutional law, where a single body can introduce an expression and stipulate how it is to be interpreted. (shrink)

I’ll use an extension of the “smidget” example Soames sets out on pages 165-172 to bring out the point. Groups A and B are disjoint and satisfy certain regularity conditions. Recall that the extension and anti-extension are specified by a pair of sufficient conditions. We specify: every member of group A is a smidget and every member of group B is not a smidget. No decision is made about persons that are outside groups A and B. It is, of course, (...) crucial that the smidgethood of the indeterminate cases is genuinely left open. What is the cash value of the difference between leaving a case unsettled and settling a case as indeterminate? Here is one difference: when a case is left unsettled, speakers of the language can resolve it later, if there is some reason to do so. This provides a simple model of key features of legal stipulations, at least in circumstances like U.S. constitutional law, where a single body can introduce an expression and stipulate how it is to be interpreted. (shrink)

Le choix de définitions « naturelles » ou « correctes » est un aspect fondamental de la recherche mathématique qui a été négligé dans l’étude de la connaissance mathématique. L’une des raisons qui expliquent cet abandon tient au sentiment qu’ont eu de nombreux auteurs que la préférence pour une définition au détriment d’une autre ne pouvait être que « simplement psychologique » ou « subjective » en sorte que de tels jugements ne pouvaient pas être philosophiquement intéressants. Je discute ici (...) d’un sens minimal du terme « objectif » selon lequel on pourrait de manière défendable argumenter que de tels choix de définitions préférées sont objectivement corrects, en dépit des raisons apparemment « esthétiques » qui soutiennent un tel jugement.Choosing « natural » or « correct » definitions is a fundamental aspect of mathematical research that has been neglected in studies of mathematical knowledge. One reason for this neglect may be a sense that many writers seem to have that a preference for one definition over another can only be « merely psychological » and « subjective » in a way that prevents such judgments from being philosophically interesting. I discuss a minimal sense of « objective » according to which such choices of preferred definitions can be defensibly argued to be objectively correct, despite the seemingly « aesthetic » grounds for the judgement. (shrink)

Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the view proposed (...) by Philip Kitcher and Michael Friedman of explanation or understanding as involving the unification of theories that had antecedently appeared heterogeneous. For the second narrowing, I’ll take up one specific feature (among many) of theories and their basic concepts that is sometimes taken to make the theories and concepts preferred: in some fields, for some problems, what is counted as understanding a problem may involve finding a way to represent the problem so that it (or some aspect of it) can be visualized. The final section develops a case study which exemplifies the way that this consideration – the potential for visualizability – can rationally inform decisions as to what the proper framework and axioms should be. The discussion of unification (in sections 3 and 4) leads to a mathematical analogue of Goodman’s problem of identifying a principled basis for distinguishing grue and green. Just as there is a philosophical issue about how we arrive at the predicates we should use when making empirical predictions, so too there is an issue about what properties best support many kinds of mathematical reasoning that are especially valuable to us. The issue becomes pressing via an examination of some physical and mathematical cases that make it seem unlikely that treatments of unification can be as straightforward as the philosophical literature has hoped. Though unification accounts have a grain of truth (since a phenomenon (or cluster of phenomena) called “unification” is in fact important in many cases) we are far from an analysis of what “unification” is.. (shrink)

In this work, Jamie Mayerfeld undertakes a careful inquiry into the meaning and moral significance of suffering. Understanding suffering in hedonistic terms as an affliction of feeling, he claims that it is an objective psychological condition, amenable to measurement and interpersonal comparison, although its accurate assessment is never easy. Mayerfeld goes on to examine the content of the duty to prevent suffering and the weight it has relative to other moral considerations. He argues that the prevention of suffering is (...) morally more important than the promotion of happiness, and that the duty to relieve suffering is much stronger than most of us acknowledge. (shrink)

In reference to the philosophical theology of medieval Islamic theologian Ibn Taymiyya, this paper outlines a parallel between Taymiyyan thought and Alvin Plantinga’s thesis of ‘Reformed Epistemology’. In critiquing a previous attempt to build an account of ‘Islamic externalism’, the Taymiyyan model offers an account that can be seen as wholly ‘Plantingan’.

In this article, I consider how the epistemic problem of religious disagreement has been viewed within the Islamic tradition. Specifically, I consider two religious epistemological trends within the tradition: Islamic Rationalism and Islamic Traditionalism. In examining the approaches of both trends toward addressing the epistemic problem, I suggest that neither is wholly adequate. Nonetheless, I argue that both approaches offer insights that might be relevant to building a more adequate response. So, I attempt to combine insights from both by drawing (...) a distinction between inferential and noninferential reflective responsibility. Given this distinction, I argue that it may be possible for a theist to remain steadfast in upholding their tradition-specific theistic belief, without having to hold that belief by way of inference; but nevertheless, having to be sufficiently reflectively responsible in forming their theistic belief noninferentially. (shrink)

Amongst intellectuals and activists, neoliberalism has become a potent signifier for the kind of free-market thinking that has dominated politics for the past three decades. Forever associated with the conviction politics of Ronald Reagan and Margaret Thatcher, the free-market project has since become synonymous with the 'Washington consensus' on international development policy and the phenomenon of corporate globalization, where it has come to mean privatization, deregulation, and the opening up of new markets. But beyond its utility as a protest slogan (...) or buzzword as shorthand for the political-economic Zeitgeist, what do we know about where neoliberalism came from and how it spread? Who are the neoliberals, and why do they studiously avoid the label? Constructions of Neoliberal Reason presents a radical critique of the free-market project, from its origins in the first half of the 20th Century through to the recent global economic crisis, from the utopian dreams of Friedrich von Hayek through the dogmatic theories of the Chicago School to the hope and hubris of Obamanomics. The book traces how neoliberalism went from crank science to common sense in the period between the Great Depression and the age of Obama. Constructions of Neoliberal Reason dramatizes the rise of neoliberalism and its uneven spread as an intellectual, political, and cultural project, combining genealogical analysis with situated case studies of formative moments throughout the world, like New York City's bankruptcy, Hurricane Katrina, and the Wall Street crisis of 2008. The book names and tracks some of neoliberalism's key protagonists, as well as some of the less visible bit-part players. It explores how this adaptive regime of market rule was produced and reproduced, its logics and limits, its faults and its fate. (shrink)

This investigation is motivated by the lack of scholarship examining the content of what firms are communicating to various stakeholders about their commitment to socially responsible behaviors. To address this query, a qualitative study of the legal, ethical and moral statements available on the websites of Forbes Magazine''s top 50 U.S. and top 50 multinational firms of non-U.S. origin were analyzed within the context of stakeholder theory. The results are presented thematically, and the close provides implications for social responsibility among (...) managers of global organizations as well as researchers interested in business ethics. (shrink)

Despite the prominence of person‐centred care (PCC) in nursing, there is no general agreement on the assumptions and the meaning of PCC. We sympathize with the work of others who rethink PCC towards relational, embedded, and temporal selfhood rather than individual personhood. Our perspective addresses criticism of humanist assumptions in PCC using critical posthumanism as a diffraction from dominant values We highlight the problematic realities that might be produced in healthcare, leading to some people being more likely to be disenfranchised (...) from healthcare than others. We point to the colonial, homo‐ and transphobic, racist, ableist, and ageist consequences of humanist traditions that have influenced the development of PCC. We describe the deep rooted conditions that structurally uphold inequality and undermine nursing practice that PCC reproduces. We advocate for the self‐determination of patients and emphasize that we support the fundamental mechanisms of PCC enabling patients' choice; however, without critical introspection, these are limited to a portion of humans. Last, we present limitations of our perspective based on our white*‐cisheteropatriarchy** positionality. We point to the fact that any reimagining of models such as PCC should be carefully done by listening, following, and ceding power to people with diversity dimensions*** and the lived experience or expertise that exists from diverse perspectives. We point towards Black, queer feminism, and critical disabilities studies to contextualize our point of critique with humanism and PCC to amplify equity for all people and communities. Theory and philosophy are useful to understand restrictive factors in healthcare delivery and to inform systematic strategies to improve the quality of care so as not to perpetuate the oppression of groups of people with diversity dimensions. *We purposely capitalize Black and use lower case for white to decentre whiteness and as an intentional act of antiracism (see White Homework a podcast series by Tori W. Douglas). **Cisheteropatriarchy describes people with intersecting identities of dominant social groups; cisgender is the gender identity that aligns with the gender you were assigned at birth, hetero means heterosexual, and patriarchy refers to structural systems of power based on maleness where women are often excluded and hold less power. ***With diversity dimensions, we refer to subjective lived experience and material realities of people that exist outside the ‘dominant minorities' of white‐cisheteropatriarchy, meaning groups of people in society who historically and currently hold more power and through this, structurally dominate the norms and possibilities of living for other people. (shrink)

This paper offers a defence of the distinction between agent-neutral and agent-relative reasons for action from scepticism aired by Toni Rønnow-Rasmussen. In response it is argued that the Nagelian notion of an agent-neutral reason is not incomprehensible, and that agent-neutral reasons can indeed be understood as obtaining states of affairs that count in favour of anyone and everyone performing the action they favour. Furthermore, I argue that a distinction drawn between agent-neutral and agent-relative reason-statements that express the salient features of (...) reason-constitutive states of affairs is neither reductive in the sense of reducing normative reasons to the propositional content of an agent’s mental state, nor trivial in the sense of locating the distinction merely in an agent’s description of the world. (shrink)

This thesis examines the hogbacks and hammerhead crosses of Viking Age Strathclyde and Northumbria. Both are Insular forms of carved stone sculpture often found in Christian contexts. This thesis aims to highlight the significance of these carved stones within a contemporary landscape dominated by a complex historical and archaeological narrative, with the overall aim of ascribing them functions, beyond those of funerary. The approach this thesis takes is theoretical in its construct, both methodologically and analytically, and is grounded in the (...) phenomenological principles of Maurice Merleau-Ponty. It is hoped that this thesis will break down the perceived barrier imposed on research by the modern Scotland-England border, thus potentially alleviate the implied disconnect between Viking Age Strathclyde and Northumbria. While acknowledging the current art-historical work, this thesis archaeologically reappraises hogbacks and provides an original and detailed archaeological treatise of hammerhead crosses. Additionally, this thesis espouses a conceptual framework for approaching, analysing and interpreting carved stones, which considers the idea of what makes space become a place. This framework involves the adoption of a reflexive phenomenological approach to the recording of carved stone monuments in the landscape, and, in approaching material, the adoption and adaption of the concepts of hybrid practice, supervenience, Deleuzian difference, common difference, the third space, and art and agency. In integrating these approaches and concepts, the idea of place-making emerges, discerned via non-dialectical interrelationships between people, material, and space. It is conceptualised here in abstract form as the person/object/place framework. In applying this framework to postulate the functions of hogbacks and hammerhead crosses in the landscape, the following, non-mutually exclusive, themes are considered: commemorative space, economic space, biblical space, mythological space, political space, and sacred space. Considering these themes in the application of the conceptual framework to approaching notable carved stones gives rise to the concept of functional landscapes. These abstract landscapes emerge and are understood through a network of functional places, developing out of particular carved stone monuments inhabiting specific spaces. Ascribing functions to Viking Age carved stones allows for interpretation beyond the traditional and uncritical narrative that hogbacks and hammerhead crosses are simply Viking ‘calling cards’ or gravestones. Furthermore, in considering the Christian context and syncretic nature of many hogbacks, this thesis challenges the common idea that their origins and models often lie solely in Scandinavian paganism and culture. (shrink)

Ethicists, policy-makers, and the general public have questioned whether artificial entities such as robots warrant rights or other forms of moral consideration. There is little synthesis of the research on this topic so far. We identify 294 relevant research or discussion items in our literature review of this topic. There is widespread agreement among scholars that some artificial entities could warrant moral consideration in the future, if not also the present. The reasoning varies, such as concern for the effects on (...) artificial entities and concern for the effects on human society. Beyond the conventional consequentialist, deontological, and virtue ethicist ethical frameworks, some scholars encourage “information ethics” and “social-relational” approaches, though there are opportunities for more in-depth ethical research on the nuances of moral consideration of artificial entities. There is limited relevant empirical data collection, primarily in a few psychological studies on current moral and social attitudes of humans towards robots and other artificial entities. This suggests an important gap for psychological, sociological, economic, and organizational research on how artificial entities will be integrated into society and the factors that will determine how the interests of artificial entities are considered. (shrink)