This book builds on established ecological models that can be applied to social systems, particularly the adaptive cycle. It links these ideas to key theoretical stances from across the educational literature to create an epistemological consilience across the divide between structuralist-poststructuralist educational research literatures. It is written with a consideration of the practical moves that can be undertaken within an institution to develop a healthier environment in which sustainable pedagogies can be nurtured. Kinchin argues that the ecological university may be (...) seen as a way to 'mend' the current system so institutions can justify the use of popular terms like sustainability, inclusivity and wellbeing in an ecologically authentic and demonstrable way. (shrink)

Ethical dimensions of friendship have rarely been explicitly addressed as aspects of friendship quality in studies of children's peer relationships. This study identifies aspects of moral virtue significant for friendship, as a basis for empirically investigating the role of ethical qualities in children's friendship assessments and aspirations. We introduce a eudaimonic conception of friendship quality, identify aspects of moral virtue foundational to such quality, review and contest some grounds on which children have been regarded as not mature enough to have (...) friendships that require virtue, and report a qualitative study of the friendship assessments and aspirations of children aged nine and ten. In focus group sessions conducted in ten schools across Great Britain, moral qualities figured prominently in children's assessments of friendship quality. The findings provide evidence of children having friendships exhibiting mutual respect, support, and valuing of each other's good character. (shrink)

Luck permeates our lives, and this raises a number of pressing questions: What is luck? When we attribute luck to people, circumstances, or events, what are we attributing? Do we have any obligations to mitigate the harms done to people who are less fortunate? And to what extent is deserving praise or blame a ected by good or bad luck? Although acquiring a true belief by an uneducated guess involves a kind of luck that precludes knowledge, does all luck undermine (...) knowledge? And how accurate are our luck attributions anyway? The academic literature has seen growing, interdisciplinary interest in luck, and this volume brings together and explains the most important areas of this research. It consists of 39 newly commissioned chapters, written by an internationally acclaimed team of philosophers and psychologists, for a readership of students and researchers. Its coverage is divided into six sections: (i) The History of Luck, (ii) The Nature of Luck, (iii) Moral Luck, (iv) Epistemic Luck, (v) The Psychology of Luck, and (vi) Future Research. The chapters in these sections cover a wide range of topics, from the problem of moral luck, to anti-luck epistemology, to the relationship between luck attributions and cognitive biases, to meta-questions regarding the nature of luck itself, to a range of other theoretical and empirical questions currently being investigated by ethicists, epistemologists, and psychologists. By bringing this research together, the Handbook serves as both a touchstone for understanding the relevant issues and a first port of call for future philosophical and psychological research on luck. (shrink)

An ω-model (a model in which all natural numbers are standard) of the predicative fragment of Quine's set theory "New Foundations" (NF) is constructed. Marcel Crabbe has shown that a theory NFI extending predicative NF is consistent, and the model constructed is actually a model of NFI as well. The construction follows the construction of ω-models of NFU (NF with urelements) by R. B. Jensen, and, like the construction of Jensen for NFU, it can be used to construct α-models for (...) any ordinal α. The construction proceeds via a model of a type theory of a peculiar kind; we first discuss such "tangled type theories" in general, exhibiting a "tangled type theory" (and also an extension of Zermelo set theory with Δ 0 comprehension) which is equiconsistent with NF (for which the consistency problem seems no easier than the corresponding problem for NF (still open)), and pointing out that "tangled type theory with urelements" has a quite natural interpretation, which seems to provide an explanation for the more natural behaviour of NFU relative to the other set theories of this kind, and can be seen anachronistically as underlying Jensen's consistency proof for NFU. (shrink)

Two intellectual vices seem to always tempt us: arrogance and diffidence. Regarding the former, the world is permeated by dogmatism and table-thumping close-mindedness. From politics, to religion, to simple matters of taste, zealots and ideologues all too often define our disagreements, often making debate and dialogue completely intractable. But to the other extreme, given a world with so much pluralism and heated disagreement, intellectual apathy and a prevailing agnosticism can be simply all too alluring. So the need for intellectual humility, (...) open-mindedness, and a careful, humble commitment to the truth are apparent. In this book, Dr Church and Dr Samuelson explicate a robust and vibrant account of the philosophy and science of this most valuable virtue, and they highlight how it can be best applied and personally developed. (shrink)

We analyze the representation of binary relations in general, and in particular of functions and of total antisymmetric relations, in monadic third order logic, that is, the simple typed theory of sets with three types. We show that there is no general representation of functions or of total antisymmetric relations in this theory. We present partial representations of functions and of total antisymmetric relations which work for large classes of these relations, and show that there is an adequate representation of (...) cardinality in this theory. The relation of our work to similar work by Henrard and Allen Hazen is discussed. This work can be understood as part of a program of assessing the capabilities of weak logical frameworks: our results are applicable for example, to the framework in David Lewis’s Parts of Classes. (shrink)

This book examines the dominant discourses in higher education. From the moment academics enter higher education, they are met with binaries such as teaching vs. research, quantitative vs. qualitative research, and constructivists vs. positivists. When embarking upon a teaching career in a university there are further binaries that immediately present themselves, with deep vs. surface learning probably being the most pervasive. Kinchin and Gravett contend that this presents a distorted view and contributes to the disconnect between the aims and observable (...) practice of higher education. Rather than celebrating difference, dominant discourses tend to seek similarities in an attempt to simplify and manage the environment, in what the authors perceive as a less than scholarly mode. In order to break down the barriers between 'structuralist' or 'traditional' academics and those who are more familiar with poststructuralist, critical perspectives, the authors explore the overlaps between these perspectives to offer a richer and more inclusive interrogation of the dominant discourses that pervade higher education. Offering methodological approaches to explore these perspectives, the authors bring together academics working in different parts of the university and examine the concept of a 'rich cartography', exploring how this can offer meaning within higher education research and practice. (shrink)

This paper will be broken down into four sections. In §1, I try to assuage a worry that intellectual humility is not really an intellectual virtue. In §2, we will consider the two dominant accounts of intellectual humility in the philosophical literature—the low concern for status account the limitations-owing account—and I will argue that both accounts face serious worries. Then in §3, I will unpack my own view, the doxastic account of intellectual humility, as a viable alternative and potentially a (...) better starting place for thinking about this virtue. And I’ll conclude in §4 by trying to defend the doxastic account against some possible objections. (shrink)

This paper discusses a sequence of extensions ofNFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16].The original theoryNFof Quine continues to present difficulties. After 60 years of intermittent investigation, it is still not known to be consistent relative to any set theory in which we have confidence. Specker showed in [20] thatNFdisproves Choice (and so proves Infinity). Even if one assumes the consistency ofNF, one is hampered by the lack of powerful methods for proofs of consistency and (...) independence such as are available for use withZFC; very clever work has been done with permutation methods, starting with [18] and [5], and exemplified more recently by [14], but permutation methods can only be applied to show the consistency or independence of unstratified sentences (see the definition ofNFUbelow for a definition of stratification). For example, there is no method available to determine whether the assertion “the continuum can be well-ordered” is consistent with or independent ofNF. There is one substantial independence result for an assertion with nontrivial stratified consequences, using metamathematical methods: this is Orey's proof of the independence of the Axiom of Counting fromNF(see below for a statement of this axiom).We mention these difficulties only to reassure the reader of their irrelevance to the present work. Jensen's modification of “New Foundations” (in [13]), which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements, has almost magical effects. (shrink)

This paper presents an exposition of subsystems and of Quine's , originally defined and shown to be consistent by Crabbé, along with related systems and of type theory. A proof that (and so ) interpret the ramified theory of types is presented (this is a simplified exposition of a result of Crabbé). The new result that the consistency strength of is the same as that of is demonstrated. It will also be shown that cannot be finitely axiomatized (as can and (...) ). (shrink)

This paper discusses a sequence of extensions ofNFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16].The original theoryNFof Quine continues to present difficulties. After 60 years of intermittent investigation, it is still not known to be consistent relative to any set theory in which we have confidence. Specker showed in [20] thatNFdisproves Choice (and so proves Infinity). Even if one assumes the consistency ofNF, one is hampered by the lack of powerful methods for proofs of consistency and (...) independence such as are available for use withZFC; very clever work has been done with permutation methods, starting with [18] and [5], and exemplified more recently by [14], but permutation methods can only be applied to show the consistency or independence of unstratified sentences (see the definition ofNFUbelow for a definition of stratification). For example, there is no method available to determine whether the assertion “the continuum can be well-ordered” is consistent with or independent ofNF. There is one substantial independence result for an assertion with nontrivial stratified consequences, using metamathematical methods: this is Orey's proof of the independence of the Axiom of Counting fromNF(see below for a statement of this axiom).We mention these difficulties only to reassure the reader of their irrelevance to the present work. Jensen's modification of “New Foundations” (in [13]), which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements, has almost magical effects. (shrink)

Related Works: Original Paper: M. Randall Holmes. Strong Axioms of Infinity in NFU. J. Symbolic Logic, Volume 66, Issue 1 , 87--116. Project Euclid: euclid.jsl/1183746361.

In this paper I add credence to Linda Zagzebski's (1994) diagnosis of Gettier problems (and the current trend to abandon the standard analysis) by analyzing the nature of luck. It is widely accepted that the lesson to be learned from Gettier problems is that knowledge is incompatible with luck or at least a certain species thereof. As such, understanding the nature of luck is central to understanding the Gettier problem. Thanks by and large to Duncan Pritchard's seminal work, Epistemic Luck, (...) a great deal of literature has been developed recently concerning the nature of luck and anti-luck epistemology. The literature, however, has yet to explore the very intuitive idea that luck comes in degrees. I propose that once luck is recognized to admit degrees even the slightest non-zero degree (of the relevant sort) precludes knowledge. Connecting this to Zagzebski's thesis, I propose that a given theory of warrant must guarantee truth in order to avoid Gettier counterexamples (or subsequently deny that warrant bears any relationship to the truth whatsoever), simply because a sufficient standard analysis of knowledge cannot allow for knowledge that is even marginally lucky. (shrink)

We critique two popular philosophical definitions of intellectual humility: the “low concern for status” and the “limitations-owning.” accounts. Based upon our analysis, we offer an alternative working definition of intellectual humility: the virtue of accurately tracking what one could non-culpably take to be the positive epistemic status of one’s own beliefs. We regard this view of intellectual humility both as a virtuous mean between intellectual arrogance and diffidence and as having advantages over other recent conceptions of intellectual humility. After defending (...) this view, we sketch remaining questions and issues that may bear upon the psychological treatment of intellectual humility such as whether evidence will help determine how this construct relates to general social humility on the one hand, and intellectual traits such as open-mindedness, curiosity, and honesty on the other. (shrink)

Systems TRC and TRCU of illative combinatory logic are introduced and shown to be equivalent in consistency strength and expressive power to Quine's set theory ‘New Foundations’ and the fragment NFU + Infinity of NF described by Jensen, respectively. Jensen demonstrated the consistency of NFU + Infinity relative to ZFC; the question of the consistency of NF remains open. TRC and TRCU are presented here as classical first-order theories, although they can be presented as equational theories; they are not constructive.

If the history of the Gettier Problem has taught us anything, it is to be skeptical regarding purported solutions. Nevertheless, in “Manifest Failure: The Gettier Problem Solved” (2011), that is precisely what John Turri offers us. For nearly fifty years, epistemologists have been chasing a solution for the Gettier Problem but with little to no success. If Turri is right, if he has actually solved the Gettier Problem, then he has done something that is absolutely groundbreaking and really quite remarkable. (...) Regrettably, however, while Turri’s account is both intuitive and elegant—improving upon many seminal projects within contemporary epistemology—I argue in this paper that any success against Gettier counterexamples it affords is merely fleeting. Straightforwardly, this is done in two sections. In §1, I briefly sketch Turri’s proposed solution to the Gettier Problem. Then, in §2, I level a counterexample against it. Unfortunately for Turri and his solution, in this paper we will see history repeat itself. (shrink)

This paper described a formal theory of type judgments for propositional logic notations of PM; I felt the need of my own automated type checker to check their examples. The type checker I wrote did indeed serve to help me referee the paper, but also took a rather different approach to notation and typing for propositional functions of PM, which proved worth writing up independently in our own paper: Holmes, M. Randall, “Polymorphic type– checking for the ramified theory of (...) types of Principia Mathematica”, in Fairouz Kamareddine, ed., Thirty–five Years of Automating Mathematics, Kluwer, 2003, pp. 173-215. (shrink)

Experimental philosophy of religion is the project of taking the tools and resources of the human sciences—especially psychology and cognitive science—and bringing them to bear on issues within philosophy of religion toward explicit philosophical ends. This paper introduces readers to experimental philosophy of religion. §1 explores the contours of experimental philosophy of religion by contrasting it with a few related fields: the psychology of religion and cognitive science of religion, on the one hand, and natural theology, on the other. §2 (...) offers a brief history of experimental philosophy of religion. The goal in this section is to highlight the ancient pedigree of this emerging area of research; as the contemporary experimental philosophy of religion literature expands and proliferates, it’s important to remember that this field has deep historical roots. Then, §3 focuses on the following questions: Why should we care about experimental philosophy of religion? And why is it needed? (shrink)

The usual construction of models of NFU (New Foundations with urelements, introduced by Jensen) is due to Maurice Boffa. A Boffa model is obtained from a model of (a fragment of) Zermelo–Fraenkel with Choice (ZFC) with an automorphism which moves a rank: the domain of the Boffa model is a rank that is moved. “Most” elements of the domain of the Boffa model are urelements in terms of the interpreted NFU. The main result of this paper is that the restriction (...) of the membership relation of the original model of set theory with automorphism to the domain of the Boffa model is first-order definable in the language of NFU. In particular, all information about the extensions in the original model of the urelements of the model of NFU is definable in terms of NFU. A corollary (answering a question of Thomas Forster) is that the urelements in a Boffa model are not homogeneous. (shrink)

The primary aim of this paper is to highlight, at least in short, how the resources of experimental philosophy could be fruitfully applied to the evidential problem of evil. To do this, we will consider two of the most influential and archetypal formulations of the problem: William L. Rowe’s article, “The Problem of Evil and Some Varieties of Atheism” (1979). and Paul Draper’s article, “Pain and Pleasure: An Evidential Problem for Theists” (1989). We will consider the relevance of experimental philosophy (...) to Rowe’s 1979 argument in §1 and to Draper’s 1989 argument in §2. But in addition to exploring how the resources of experimental philosophy might apply to the problem of evil, it is also worth exploring what broader empirical factors might contribute to people having the intuitions that have—from someone’s affective state to someone’s need for closure. In §3, we want to very briefly elucidate a few areas where the psychology of philosophy might be productively explored in future empirical research. (shrink)

We show in (the usual set theory without Choice) that for any set X, the collection of sets Y such that each element of the transitive closure of is strictly smaller in size than X (the collection of sets hereditarily smaller than X) is a set. This result has been shown by Jech in the case (where the collection under consideration is the set of hereditarily countable sets).

This paper extends the results of an earlier paper by the author . New subsystems of the combinatory logic TRC shown in that paper to be equivalent to NF are introduced; these systems are analogous to subsystems of NF with predicativity restrictions on set comprehension introduced and shown to be consistent by Crabbé. For one of these systems, an exact equivalence in consistency strength and expressive power with the analogous subsystem of NF is established.

The character of the current controversy over geneticallymodified (GM) agriculture, typified by protesters' use of emotivesymbolism, has been largely inspired by the Green movement'snon-governmental organizations and political parties. This articleexplores the deeper philosophical and spiritual motivations of the Greenmovement, to inquire why it is implacably opposed to GM agriculture. TheGreen movement's anti-capitalism, exemplified by the hate-symbol statusof Monsanto as the company pioneering GM crops, is viewed within thewider context of alienation in the modern era. A complex of meanings isseen in (...) Frankenstein as the focal symbol of GM protests, includingperceptions of risk, fears of the remixing of living identities seen ingenetic engineering, and resentment at the spiritual nihilism of thereduction of life to the digital code of DNA. By contrast, RobertGoodin's Green Theory of Value, which postulates the deep psychologicalimportance of nature in locating the self in a meaningful context largerthan ourselves, can explain the power of the Green symbol of thethreatened environment, Gaia. The advent of GM agriculture seems toimply that capitalism and technology can now enframe nature itself,leaving a world devoid of natural myth or meaning, with no escape fromthe alienation and nihilism of modernity. The central question posed forprotagonists of the GM debate is whether their agenda is based on thesepowerful but mythical conceptions of the environment, or whetherpreservation of the real environment is their primary ethic. (shrink)

The Oxford University Studies in the Enlightenment series, previously known as SVEC (Studies on Voltaire and the Eighteenth Century), has published over 500 peer-reviewed scholarly volumes since 1955 as part of the Voltaire Foundation at the University of Oxford. International in focus, Oxford University Studies in the Enlightenment volumes cover wide-ranging aspects of the eighteenth century and the Enlightenment, from gender studies to political theory, and from economics to visual arts and music, and are published in English or French.

A common objection to Quine's set theory "New Foundations" is that it is inadequately motivated because the restriction on comprehension which appears to avert paradox is a syntactical trick. We present a semantic criterion for determining whether a class is a set which motivates NF.

Andrzej Kisielewicz has proposed three systems of double extension set theory of which we have shown two to be inconsistent in an earlier paper. Kisielewicz presented an argument that the remaining system interprets ZF, which is defective: it actually shows that the surviving possibly consistent system of double extension set theory interprets ZF with Separation and Comprehension restricted to 0 formulas. We show that this system does interpret ZF, using an analysis of the structure of the ordinals.

This research addresses equity in geographic access to financial services. As financial products and services continue to become more accessible and affordable, many low‐ to moderate‐income Americans remain unbanked and underbanked, relying instead upon informal, alternative financial service providers, including check cashing outlets and payday lenders. While geographic access to affordable financial products and services assists in the successful asset building strategies of economically vulnerable households, concerns that access to financial services is uneven persist. This article uses geographic information systems (...) and spatial binary logistic regression analysis to test the hypothesis that sociodemographic characteristics and mortgage lending variables have a predictive relationship on the presence of financial deserts—census tracts where check cashing outlets are more prevalent than banks—in southeastern Pennsylvania. Results of comparison of means and regression analysis reveal that these tracts are associated with higher than average population density, lower levels of median household income, a higher proportion of Black and Latinx residents, and higher levels of mortgage application denial. This article contributes to the ongoing debate over the emergence of a two‐tiered or dual financial service delivery system, whereby financial products and services are bifurcated based on socioeconomic status and geography. (shrink)

Three systems of double extension set theory have been proposed by Andrzej Kisielewicz in two papers. In this paper, it is shown that the two stronger systems are inconsistent, and that the third, weakest system does not admit extensionality for general sets or the use of general sets as parameters in its comprehension scheme. The parameter-free version of the comprehension principle of double extension set theory is also shown to be inconsistent with extensionality. The definitions of the systems and a (...) self-contained exposition of their properties is given, sufficient to develop the inconsistency proofs. (shrink)

Ian Fraser assesses the human qualities of the three saints who are celebrated for their contribution to Christianity in Britain. He also examines some contemporary issues related to their struggle to live faith fully.

This is a brief report on results reported at length in our paper [2], made for the purpose of a presentation at the workshop to be held in November 2011 in Cambridge on the Principia Mathematica of Russell and Whitehead ([?], hereinafter referred to briefly as PM ). That paper grew out of a reading of the paper [3] of Kamareddine, Nederpelt, and Laan. We refereed this paper and found it useful for checking their examples to write our own independent (...) computer type-checker for the type system of PM ([1]), which led us to think carefully about formalization of the language and the type system of PM A modern mathematical logician reading PM finds that it is not completely formalized in a modern sense. The type theory in particular is inarguably not formalized, as no notation for types is given at all! In PM itself, the only type annotations which appear are occasional numerical indices indicating order; the type notation we use here extends one introduced later by Ramsey. The authors of PM regard the absence of explicit indications of type as a virtue of their system: they call it “systematic ambiguity”; modern computer scientists refer to this as “polymorphism”. The language of PM is also not completely formalized, and it is typographically inconvenient for computer software to which ASCII input is to be given. The notation of PM for abstractions (propositional functions) does not use head binders; the order of the arguments of a complex expression is determined by the alphabetical order of the bound variables. For example ˆa < ˆb is the “less than” relation while ˆb < ˆa is the “greater than” relation (this is indicated by the alphabetical order of the variables). In PM , the fact that a variable is bound in a propositional function is indicated by circumflexing it. Variables bound by quantifiers are not circumflexed. A feature of the notation of [3], carried over into ours, is that no circumflexes are used: notations for propositions and the corresponding propositional functions are identical.. (shrink)

A common objection to Quine’s set theory “New Foundations” is that it is inadequately motivated because the restriction on comprehension which appears to avert paradox is a syntactical trick. We present a semantic criterion for determining whether a class is a set (a kind of symmetry) which motivates NF.

David B. Wong’s 2006 monograph, Natural Moralities: A Defense of Pluralistic Relativism,1 presents and defends a sophisticated and nuanced form of moral relativism that has been in development since his 1984 work, Moral Relativity. The present volume, Moral Relativism and Chinese Philosophy, is a collection of six critical essays focused on Natural Moralities, which are followed by Wong’s responses to each of his critics. I see the greater contribution of this volume, when we consider the title’s conjuncts, to be the (...) discussion of moral relativism, so in this review I will leave aside the debates over how best to interpret various Chinese philosophers.In Natural Moralities, Wong draws... (shrink)

While experimental philosophy has fruitfully applied the tools and resources of psychology and cognitive science to debates within epistemology, metaphysics, and ethics, relatively little work has been done within philosophy of religion. And this isn’t due to a lack of need! Philosophers of religion frequently rely on empirical claims that can be either verified or disproven, but without exploring whether they are. And philosophers of religion frequently appeal to intuitions which may vary wildly according to education level, theological background, etc., (...) without concern for whether or not the psychological mechanisms that underwrite those intuitions are broadly shared or reliable. In this chapter, I explore some of the fruit and possibilities for the emerging field of experimental philosophy of religion. First, in Section 1, I will elucidate some of the historical grounding for experimental philosophy of religion. Then in Section 2, I briefly consider how the tools and resources of experimental philosophy might be fruitfully applied to a seminal topic within philosophy of religion, namely, the problem of evil. In Section 3, we’ll sketch some broader applications of experimental philosophy of religion. (shrink)

In this chapter, we will explore the luck at issue in Gettier-styled counterexamples and the subsequent problem it poses to any viable reductive analysis of knowledge. In the 1st section, we will consider the specific species of luck that is at issue in Gettier counterexamples, then, in the next section, I will briefly sketch a diagnosis of the Gettier Problem and try to explain why the relevant species of luck has proven to be extremely difficult to avoid. And finally, I (...) will consider a prominent objection to the proposed diagnosis of the Problem. (shrink)