This second edition encourages the integration of technology into a pedagogically sound learning sequence for primary mathematics.

A plea for natural philosophy --On the question of realism --Hume and Reid --Moore's hands --Wittgenstein on hinges --A note on truth and reference --The philosophy of logic --A Second Philosophy of logic --Psychology and the a priori sciences --Do numbers exist? --Enhanced if-thenism.

Professor Deutscher studies Beauvoir's philosophy on "otherness" not just through her famous views on gender (in her celebrated 1949 work The...

The enthusiastic reception for the first edition of this book has prompted us to produce a second. We were delighted by the interest from people thinking about and working in public services beyond health care, although the book had been unapologetically health focused. Eight years have passed, and although the issues we addressed are still very much with us, times have changed. 'Austerity' has bitten hard into the UK's public services, especially social care. Developments in policy, technology, organisation and practice (...) have affected health and social care, separately and together. Mindful of this, we have extended our reach to consider both sectors and, to an extent, the wider world of 'welfare'. Hence our new subtitle: 'rehabilitating the welfare state'. We have expanded our narratives, case studies and references accordingly, believing that the issues and perspectives in each field illustrate important points for all. (shrink)

Juliette Kennedy’s new book brims with intriguing ideas. I don’t understand all of them, and I’m not convinced that the ones I do understand all fit together, b.

Since the fourteenth century, Eastern Woodlands tribes have used delicate purple and white shells called “wampum” to form intricately woven belts. These wampum belts depict significant moments in the lives of the people who make up the tribes, portraying everything from weddings to treaties. Wampum belts can be used as a form of currency, but they are primarily used as a means to record significant oral narratives for future generations. In Reading the Wampum, Kelsey provides the first academic consideration of (...) the ways in which these sacred belts are reinterpreted into current Haudenosaunee tradition. While Kelsey explores the aesthetic appeal of the belts, she also provides insightful analysis of how readings of wampum belts can change our understanding of specific treaty rights and land exchanges. Kelsey shows how contemporary Iroquois intellectuals and artists adapt and reconsider these traditional belts in new and innovative ways. Reading the Wampum conveys the vitality and continuance of wampum traditions in Iroquois art, literature, and community, suggesting that wampum narratives pervade and reappear in new guises with each new generation. (shrink)

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical (...) realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

Sleep enhances integration across multiple stimuli, abstraction of general rules, insight into hidden solutions and false memory formation. Newly learned information is better assimilated if compatible with an existing cognitive framework or schema. This article proposes a mechanism by which the reactivation of newly learned memories during sleep could actively underpin both schema formation and the addition of new knowledge to existing schemata. Under this model, the overlapping replay of related memories selectively strengthens shared elements. Repeated reactivation of memories in (...) different combinations progressively builds schematic representations of the relationships between stimuli. We argue that this selective strengthening forms the basis of cognitive abstraction, and explain how it facilitates insight and false memory formation. (shrink)

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Ludwig Wittgenstein gave priority to aesthetics over other disciplines due to its invaluable capacities for revealing certain aspects of the nature of human understanding and for guiding our actions toward an ethical life. Although Wittgenstein did not focus on these issues in a systematic way, these worries were present in his philosophy during his lifetime. That is why I use a very wide range of his writings, from the Tractatus to letters and diaries. Aesthetic inquiries can throw light upon the (...) existence of an intransitive understanding–that is, a kind of knowledge that cannot be expressed by language shared by all competent users of a language. I also discuss Wittgenstein’s conception of ethics in order to explain the close relationship that he proposed between ethics and aesthetics. I hope this will clarify why he believed there was so much to learn from paintings, films, music, poems, or novels. I compare works of art and religious belief and how the former can help us to guide our lives as the latter does. I do this while extending the scope and claiming the importance of aesthetic education, given that it can help us to deal with our nature and with our history. (shrink)

“I can’t read. Show me” is a student’s cry heard by teachers of the arts in all kinds of classes. Demonstrating a particular process one on one is a very effective way to learn, but sometimes teachers need a way for students to take notes or follow a guide to aid in remembering a complex technique. Notation systems have developed as the educational solution to this need.1 Adela Bay, a private piano teacher, relates in her book’s dedication the reason she (...) developed a notation system for her music students, saying they were “intimidated by traditional music instruction.”2 In the arts, written notations are available from places and times that most people cannot visit in order to learn a particular technique.3 .. (shrink)

The human microbiome has become one of the dominant biomedical frameworks of the contemporary moment that may be understood to be post-Pasteurian. The recognitions the human microbiome opens up for thinking about the biological self and the individual have ontological and epistemological ramifications for considering what and who the human being is. As this article illustrates, the microbiopolitics of the human microbiome challenges the immunitarian Pasteurian model in which the organismic self shores itself up and defends itself against a microbial (...) non-self or other. Instead, this theory presents the human organism as comprised of multiple ecosystems and as a multitude, suggesting that the thanatopolitical attempts to wipe out microbial others (evident in the overuse and misuse of antibiotics, for example) are giving way to an affirmative microbiopolitics grounded in generative multispecies relationality. This article sets out to make the case for this affirmative microbiopolitics. (shrink)

Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In Second Philosophy, Penelope Maddy describes and practices a particularly austere form of naturalism called "Second Philosophy". Without a definitive criterion for what counts as "science" and what doesn't, Second Philosophy can't be specified directly ("trust only the methods of science" for example), so Maddy proceeds instead by illustrating the behaviors of an idealized inquirer she calls the "Second (...) Philosopher". mhis Second Philosopher begins from perceptual common sense experimentation, theory formation and testing, working all the while to asses, correct and improve her methods as she goes. Second Philosophy is then the result of the Second Philosopher's investigations. Maddy delineates the Second Philosopher's approach by tracing her reactions to various familiar skeptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing her methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. She then undertakes to practice Second Philosophy in her reflections on the ground of logical truth, the methodology, ontology and epistemology of mathematics, and the general prospects for metaphysics naturalized. (shrink)

This paper interrogates the status of the Malthusian couple and the policing and government of reproduction in the first volume of Foucault's History of Sexuality, Volume I ( HS1), and the associated Collège de France lectures. Presented by Foucault as one of the four ‘strategic ensembles’ of the 18th century through which knowledge and power became centered on sex, what Foucault calls the socialization of procreative sexuality ( HS1: 104) also constitutes a largely invisible hinge between the trajectories in HS1: (...) biopolitics (vector of governmentality, management, administration and intensification of life) and sex (vector through which the repressive hypothesis is rejected). Particularly because it is one of the least discussed figures in Foucauldian commentary, my argument is that a reading of HS1 through the prism of its Malthusian couple produces unexpected results. A text that can be interpreted from the perspective of (a) its debate with psychoanalysis, or (b) its potential debate with those for whom sexual rights belong to a sexual subject, or (c) its status as a watershed text for biopolitical theory, enters into a fourth dialogue with the history of reproduction as politicized and biopoliticized, a problematic to date taken up most directly by Ann Stoler in Race and the Education of Desire. This allows for a revisiting of the complex relationship between the vectors of ‘sex’ and ‘life’ in HS1. Although reproductive sex, and reproductive life, are not the themes of the strongest importance in HS1, they serve as the invisible hinge at the interface of biopolitics and sex in HS1. Considering the status of reproductive life from this perspective becomes a departure point for reconsidering the reproductive woman, in her historical role as part of the problematized Malthusian couple and at the intersection of biopolitics and thanatopolitics. (shrink)

Many philosophers claim to be naturalists, but there is no common understanding of what naturalism is. Maddy proposes an austere form of naturalism called 'Second Philosophy', using the persona of an idealized inquirer, and she puts this method into practice in illuminating reflections on logical truth, philosophy of mathematics, and metaphysics.

We adopt and extend the concept of ‘noncooperative space’ to analyze how (aspirant) black women intellectual activists attempt to sustain their efforts within settings that publicly endorse racial equality, while, in practice, the contexts remain deeply racist. Noncooperative spaces reflect institutional, organizational, and social environments portrayed by powerful white agents as conducive to anti-racism work and promoting racial equality but, indeed, constrain individuals who challenge racism. Our work, which is grounded in intersectionality, draws on an autoethnographic account of racially motivated (...) domestic violence suffered by our lead author. Our analysis suggests that (aspirant) black women intellectual activists must develop courage to sustain their ‘voice’ within noncooperative spaces. However, the three interlinked dimensions of noncooperative spaces—namely, deceiving design, hegemonic actors’ indifference to racism, and (some assimilated gatekeepers’) false equivalence—may gradually erode a black female scholar’s courage. This forces her ‘voice’ to vanish temporarily, or even permanently. Courage is thus fragile and depletable. Yet, courage can be regenerated, resulting in regaining voice. Consequently, we propose courageous collective action by white allies and black and brown individuals who voluntarily and officially cooperate within and across various spaces to achieve racial equality. (shrink)

Lack of supportive workplaces may be depriving babies and mothers of the health advantages of breastfeeding. This citizen science pilot project set out to engage women in photographing and sharing information on the available facilities for breastfeeding and expressing and storing breastmilk in Australian workplaces. While some useful insights were gained, the project failed in the sense that 234 people ‘liked’ the project Facebook page set up to recruit participants, but only nine photographs were submitted. The heaviest loss of participation (...) occurred after the ethics committee requirements were explained, in particular, the requirement for employer consent to take a photograph, or alternatively, for a participant to agree to bear the risk of taking a photo without permission. The ethics committee also made stipulations about the formality of language to be used. Thus, the project’s potential role as an enabler for health action was neutered. We argue that the ethics requirements worked contrary to our purpose and possibly acted to reinforce the powerlessness some women experience at work. (shrink)

This ambitious book explores the relationship between time and history and shows how an appreciation of long-term time helps to make sense of the past. The book is devoted to a wide-ranging analysis of the way different societies have conceived and interpreted time, and it develops a theory of the threefold roles of continuity, gradual change, and revolution which together form a "braided" history. Linking the interpretative chapters are intriguing brief expositions on time travel, time cycles, time lines, and time (...) pieces, showing the different ways in which human history has been located in time. In its global approach the book is part of the new shift toward “big history,” in which traditional period divisions are challenged in favor of looking at the entire past of the world from start to end. The approach is thematic. The result is a view of world history in which outcomes are shown to be explicable, once they happen, but not necessarily predictable before they do. This book will inform the work of historians of all periods and at all levels, and contributes to the current reconsideration of traditional period divisions (such as Modernity and Postmodernity), which the author finds outmoded. (shrink)

This paper discusses an asymmetry in the way that we think about causation. Put roughly, the asymmetry is this. We tend to regard hastening some event or result as a way of causing it, whereas we do not tend to regard delaying an event or result as a way of causing it. In the first two sections of this paper, I illustrate the asymmetry with some examples, characterize it more precisely, and explain why I think it is puzzling. In the (...) third section I discuss some responses to the puzzle that I take to be inadequate. In the following sections I present my own solution. I argue that the key to the asymmetry puzzle is a difference in the ways in which delaying and hastening are related to preventing. My explanation is compatible with the view that, in general, what delays an event or result is not among its causes. But it is also compatible with the view (to which I incline) that although delayers really are always causes of what they delay, there are pragmatic reasons why it is, in general, odd or unnatural so to describe them. (shrink)

I argue that David Lewis’s attempt, in his ‘Counterfactual Dependence and Time’s Arrow’, to explain the fixity of the past in terms of counterfactual independence is unsuccessful. I point out that there is an ambiguity in the claim that the past is counterfactually independent of the present (or, more generally, that the earlier is counterfactually independent of the later), corresponding to two distinct theses about the relation between time and counterfactuals, both officially endorsed by Lewis. I argue that Lewis’s attempt (...) is flawed for a variety of reasons, including the fact that his own theory about the evaluation of counterfactuals requires too many exceptions to the general rule that the past is counterfactually independent of the present. At the end of the paper, I consider a variant of Lewis’s strategy that attempts to explain the fixity of the past in terms of causal, rather than counterfactual, independence. I conclude that, although this variant avoids some of the objections that afflict Lewis’s account, it nevertheless seems to be incapable of giving a satisfactory explanation of the notion of the fixity of the past. (shrink)

Non-suicidal self-injury is a complex behaviour, routinely engaged for emotion regulatory purposes. As such, a number of theoretical accounts regarding the aetiology and maintenance of NSSI are grounded in models of emotion regulation; the role that cognition plays in the behaviour is less well known. In this paper, we summarise four models of emotion regulation that have repeatedly been related to NSSI and identify the core components across them. We then draw on social cognitive theory to unite models of cognition (...) and models of emotion in developing a new cognitive-emotional model of NSSI. Our model articulates how emotion regulation and cognition can work in concert to govern NSSI, and offers several new research questions that can be addressed within this framework. (shrink)

A novel treatment of an issue central to much current work in metaphysics: the distinction between the essential and accidental properties of individuals. Mackie challenges widely held views, and arrives at what she calls "minimalist essentialism," an unorthodox theory according to which ordinary individuals have relatively few interesting essential properties. Mackie's clear and accessible discussions of issues surrounding necessity and essentialism mean that the book will appeal as much to graduate students as it will to seasoned metaphysicians.

This paper is about a puzzle concerning the metaphysics of material objects: a puzzle generated by cases where material objects appear to coincide, sharing all their matter. As is well known, it can be illustrated by the example of a statue. In front of me now, sitting on my desk, is a statue – a statue of a lion. The statue is made of clay. So in front of me now is a piece of clay. But what is the relation (...) between the statue and the piece of clay? Are they identical, or are they distinct? (shrink)

Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of (...) the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments. (shrink)