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)

This article offers an overview of philosophical methodologies. In an attempt to avoid a certain circularity, the article itself tries to avoid consciously or solely deploying and engaging with any current standard notion of what constitutes a philosophical method or philosophy itself. It hopes to find some of the possible places in which philosophy occurs, and this turns out to include such endeavours as literature, art, poetry, and linguistics. From here it considers how almost anything—for example, conversation, everyday life, and (...) love—can also be philosophy. An attempt is made to identify some characteristic feature of philosophy as it occurs in all such forms. In the end, the simultaneous enacting of a peculiar optimism and particular humility both, in the search for knowledge, is put forward as potentially sufficient to at least begin to identify philosophy across its many guises. (shrink)

ABSTRACTGrounded in Emotional Cascade Theory, we explored whether rumination and multisensory imagery-based cognitions moderated the relationships between affect and both odds of non-suicidal self-injury, and frequency of the behaviour. A sample of 393 university students completed self-report questionnaires assessing the constructs of interest. Contrary to expectations, rumination did not emerge as a significant moderator of the affect-NSSI relationship. However, the relationship between affect and frequency of NSSI was moderated by the use of imagery. Further, the relationship between negative affect and (...) NSSI was moderated by positive affect, underscoring the need to consider both negative and positive affect in models of NSSI. Most youth who self-injured reported thinking in images while the urge to self-injure was strong, with 53% thinking in images at least half the time. Future work is needed to explore how positive and negative affect work in concert to govern NSSI, and how imagery might eit... (shrink)

Richard L. Epstein with Carolyn Kerbrger, Critical Thinking, 3rd Edition, Advanced Reasoning Forum, 2012, 464 pp., ISBN-10: 1938421000, ISBN-13: 978-1938421006.Richard L. Epstein, The Pocket Guide to Critical Thinking, 4th Edition, Advanced Reasoning Forum, 2011, 162 pp., paperback ISBN-13: 9780981550770, ISBN-10: 0981550770, ebook ISBN-13: 9780981550787.

Fifty years on from its first publication, The Concept of Law is still the starting point for the study of legal philosophy and is widely heralded as a classic work of modern philosophy. This third edition features a new introduction by Leslie Green, looking at Hart's work from the perspective of modern jurisprudence.

IntroductionAcademic integrity policy that is inaccessible, ambiguous or confusing is likely to result in inconsistent policy enactment. Additionally, policy analysis and development are often undertaken as top down processes requiring passive acceptance by users of policy that has been developed outside the context in which it is enacted. Both these factors can result in poor policy uptake, particularly where policy users are overworked, intellectually critical and capable, not prone to passive acceptance and hold valuable grass roots intelligence about policy enactment.Case (...) descriptionThe case study presented in this paper describes the actions of a community of practice at a regional Australian university to deconstruct and translate ambiguous academic integrity policy into a suite of accessible academic integrity resources that were intelligible to staff and students, and which assisted academic staff to consistently enact policy. The paper narrates the formation of the CoP, the tangible and intangible value it created, the social learning practices enacted by its members, its grassroots policy work and the material resources produced from that work.Discussion and evaluationAn evaluation of the CoP was conducted using a value creation framework to explore its immediate value, potential value, applied value, realised value, and reframing value. These values were considered at each stages of the CoP’s lifespan. The evaluation was a useful process that demonstrated the wide-ranging value created by the CoP. Six insights were drawn from the evaluation which promote understanding of the value created for a university by a CoP, particularly in contributing to academic integrity culture over a sustained period of time.ConclusionsThis paper contributes to a research gap on specific examples of discretion within rule-based systems. It illustrates how academics and members of the CoP used their discretion to interpret and enact academic integrity policy within a higher education setting. Drawing from the evaluation of the CoP we argue for greater understanding of the grass-roots contribution of academic and professional staff to academic integrity policy translation and enactment. (shrink)

Sexual difference as a basis of equality : an introduction to Irigarayan politics -- Irigaray on language : from the speech of dementia to the problem of sexual indifference -- Rethinking the politics of recognition : the declaration of Irigarayan sexuate rights -- Irigarayan performativity : is this a question of can saying it make it so? -- Sexuate genre : ethics and politics for improper selves -- Anticipating sexual difference : mediation, love, and divinity -- Interrogating an unasked question (...) : is there sexual difference? -- The impossible friend : traversing the heterosocial, the homosocial, and the successes of failure -- Sexed discourse and the language of the philosophers : to be two -- Effacement redoubled? : between the Orient and the Occident. (shrink)

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)

ABSTRACTThis paper argues that decolonial theory can offer a distinctive and valuable ethical lens. Decolonial perspectives give rise to an ethics that is fundamentally global but distinct from, and critical of, moral cosmopolitanism. Decolonial ethics shares with cosmopolitanism a refusal to circumscribe normative commitments on the basis of existing political and cultural boundaries. It differs from cosmopolitanism, though, by virtue of its rejection of the individualism and universalism of cosmopolitan thought. Where cosmopolitan approaches tend to articulate abstract principles developed from (...) within a particular Western tradition, decolonial approaches reject abstract global designs in favour of inter-cultural dialogue amongst multiple people, including peoples who deem collective and non-human entities to be of fundamental moral importance. In addition, decolonial global ethics rejects universality in favour of ‘pluriversality’. (shrink)

Penelope Deutscher reconsiders the role of procreation in Foucault's thought, especially its proximity to risk, mortality, and death. Foucault's Futures brings together his work on sexuality and biopolitics to provide new insights into the conflicted political status of reproductive conduct and what it means for feminism and critical theory.

I discuss a thesis that I call ‘The Appearance of Mind-Independence’, to the effect that, to the subject of an ordinary perceptual experience, it seems that the experience involves the awareness of a mind-independent world. Although this thesis appears to be very widely accepted, I argue that it is open to serious challenge. Whether such a challenge can be maintained is especially relevant to the assessment of any theory, such as Berkeley’s idealism, according to which the only objects of which (...) we are aware in perception are mind-dependent. But the issue is of significance for the philosophy of perception more generally. In the course of my sceptical discussion, I argue that recent work by Campbell and Cassam may be flawed by a failure to take sufficiently seriously the requirements for genuine mind-independence. (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)

It’s often said that set theory provides a foundation for classical mathematics because every classical mathematical object can be modeled as a set and every classical mathematical theorem can be proved from the axioms of set theory. This is obviously a remarkable mathematical fact, but it isn’t obvious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring (...) to what extent they do these same jobs, and to what extent they might do other jobs also reasonably regarded as foundational. (shrink)

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.

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.

Traditional accounts of the feminist history of philosophy have viewed reason as associated with masculinity and subsequent debates have been framed by this assumption. Yet recent debates in deconstruction have shown that gender has never been a stable matter. In the history of philosophy 'female' and 'woman' are full of ambiguity. What does deconstruction have to offer feminist criticism of the history of philosophy? _Yielding Gender_ explores this question by examining three crucial areas; the issue of gender as 'troubled'; deconstruction; (...) and feminist criticism of the history of philosophy. The first part of the book discusses the work of Judith Butler, Jacques Derrida, and contemporary French feminist philosophy including key figures such as Luce Irigiray. Particular attention is given to the possibilities offered by deconstruction for understanding the history of philosophy. The second part considers and then challenges feminist interpretations of some key figures in the history of philosophy. Penelope Deutscher sketches how Rousseau, St. Augustine and Simone de Beauvoir have described gender and argues that their readings of gender are in fact empowered by gender's own contradiction and instability rather than limited by it. (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)

Existing research on the formation of employee ethical climate perceptions focuses mainly on organization characteristics as antecedents, and although other constructs have been considered, these constructs have typically been studied in isolation. Thus, our understanding of the context in which ethical climate perceptions develop is incomplete. To address this limitation, we build upon the work of Rupp to develop and test a multi-experience model of ethical climate which links aspects of the corporate social responsibility, ethics, justice, and trust literatures and (...) helps to explain how employees’ ethical climate perceptions form. We argue that in forming ethical climate perceptions, employees consider the actions or characteristics of a complex web of actors. Specifically, we propose that employees look outward at how communities are impacted by their organization’s actions, upward to make inferences about the ethicality of leaders in their organizations, and inward at their own propensity to trust others as they form their perceptions. Using a multiple-wave field study conducted at a privately held US corporation, we find substantial evidence in support of our model. (shrink)

Available from UMI in association with The British Library. Requires signed TDF. ;The main part of the thesis concerns how things, in the sense of individuals, might have been. The topic is what limits there are on the counterfactual possibilities for individuals: in other words, what essential properties, if any, they have. ;In Chapters 3-6 three answers to this question that have been given in recent philosophical literature are examined. They are: that each thing has a unique individual essence ; (...) that there are features of the origin of an individual without which it could not possibly have existed ; and, finally, that there are sortal concepts that represent essential properties of the things that fall under them . ;All of these answers, and many of the arguments that have been given for them, are criticised. Sometimes the criticism takes the form of pointing to unpalatable consequences that result from the acceptance of the doctrine in question. Sometimes the criticism consists in pointing to difficulties or inadequacies in the arguments that have been presented in its favour. ;A preliminary chapter prepares the ground by setting out the conceptual framework, and the chief formal characteristics, of the essentialism discussed in the later chapters. Chapter 2 discusses the nature of necessary a posteriori truth, touching on questions in the philosophy of language and mind concerning the notion of de re thought. ;It is argued that essentialism about natural kinds raises problems of its own: some of these are discussed in Chapters 7 and 8. Here the main topic is the connection between semantic theory and natural kind essentialism. Concluding that the essentialism should be regarded as in an important sense independent of semantic theory, the chapters add to, and also criticise, the work of other writers who have reached the same verdict. Scepticism is also expressed about the independent plausibility of natural kind essentialism. ;Recent interest in essentialism owes its genesis chiefly to the work of Saul Kripke and Hilary Putnam: these figures stand in the background throughout the discussion. Among the other writers whose work is discussed are Baruch Brody, Gareth Evans, Graeme Forbes, Colin McGinn, J. L. Mackie, D. H. Mellor, Nathan Salmon, and David Wiggins. (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)

First published in 1991. Routledge is an imprint of Taylor & Francis, an informa company.

This paper reconstructs Steel’s multiverse project in his ‘Gödel’s program’ (Steel [2014]), first by comparing it to those of Hamkins [2012] and Woodin [2011], then by detailed analysis what’s presented in Steel’s brief text. In particular, we reconstruct his notion of a ‘natural’ theory, describe his multiverse axioms and his translation function, and assess the resulting status of the Continuum Hypothesis. In the end, we reconceptualize the defect that Steel thinks CH might suffer from and isolate what it would take (...) to remove it while working within his framework. As our goal is to present as coherent and compelling a philosophical and mathematical story as we can, we allow ourselves to augment Steel’s story in places (e.g., in the treatment of Amalgamation) and to depart from it in others (e.g., the removal of ‘meaning’ from the account). The relevant mathematics is laid out in the appendices. (shrink)

The work of the distinguished philosopher Sarah Kofman has, since her tragic death in 1994, become a focus for many scholars interested in contemporary French philosophy. The first critical collection on her thought to appear in English, Enigmas evaluates Kofman's most important contributions to philosophy, psychoanalytic theory, feminism, and literary theory. These insightful essays range from analyses of Kofman's first book, L'Enfance de l'art, to her last, L'Imposture de la beauté. This unique volume represents the major themes in Kofman's scholarship: (...) literature and aesthetics; philosophy and metaphor; women, feminism, and psychoanalysis; and Jews and German nationalism. Selected essays explore and diagnose Kofman's personal struggles as they are reflected in her writing. (shrink)

This paper presents the real case of a military surgeon who is the only one working at a small hospital in Iraq. The military surgeon can only operate on one wounded soldier due to limited medical resources. The first wounded soldier to arrive is the enemy. The second wounded soldier to arrive shortly after the enemy is a compatriot. Both soldiers will die without lifesaving surgery. The military surgeon is ordered by his superior not to operate on the enemy. Under (...) the Geneva Conventions, physician-soldiers are legally required to give medical attention impartially. The only exception is urgent medical need. Both soldiers, friend and foe, have an urgent medical need. Dual-loyalty dilemmas such as this one can arise for military medical practitioners when loyalty to patients comes into conflict with loyalty to third parties such as the state. In this paper, several solutions to the dual-loyalty dilemma are considered and rejected. Solutions to the dual-loyalty dilemma ultimate fail because they rest on the physician-as-healer model which grounds contemporary medical ethics. The view that the ultimate objective of physicians and medicine is winning battles is defended. Physicians are non-neutral and partial fighters who sometimes must do harm. Medicine is a weapon that physicians use to fight an enemy. The only relevant differences between a soldier and physician are the kind of enemy, location of the enemy, and the type of weapons used against the enemy. The paper concludes that physician-soldiers are doctors with borders. There is no dual-loyalty dilemma on the physician-as-fighter model. The military surgeon should obey his orders and not operate on the enemy. Implications of the physician-as-fighter model for mass casualty triage and physician-soldier participation in non-lethal weapons development are considered. (shrink)

This paper outlines a second-philosophical account of arithmetic that places it on a distinctive ground between those of logic and set theory.

Meditation comprises a series of practices mainly developed in eastern cultures aiming at controlling emotions and enhancing attentional processes. Several authors proposed to divide meditation techniques in focused attention and open monitoring techniques. Previous studies have reported differences in brain networks underlying FA and OM. On the other hand common activations across different meditative practices have been reported. Despite differences between forms of meditation and their underlying cognitive processes, we propose that all meditative techniques could share a central process that (...) would be supported by a core network for meditation since their general common goal is to induce relaxation, regulating attention and developing an attitude of detachment from one’s own thoughts. To test this hypothesis, we conducted a quantitative meta-analysis based on activation likelihood estimation of 10 neuroimaging studies on different meditative techniques to evidence the core cortical network subserving meditation. We showed activation of basal ganglia , limbic system and medial prefrontal cortex . We discuss the functional role of these structures in meditation and we tentatively propose a neurocognitive model of meditation that could guide future research. (shrink)

Does V = L? Is the Axiom of Constructibility true? Most people with an opinion would answer no. But on what grounds? Despite the near unanimity with which V = L is declared false, the literature reveals no clear consensus on what counts as evidence against the hypothesis and no detailed analysis of why the facts of the sort cited constitute evidence one way or another. Unable to produce a well-developed argument one way or the other, some observers despair, retreating (...) to unattractive fall-back positions, e.g., that the decision on whether or not V = L is a matter of personal aesthetics. I would prefer to avoid such conclusions, if possible. If we are to believe that L is not V, as so many would urge, then there ought to be good reasons for this belief, reasons that can be stated clearly and subjected to rational evaluation. Though no complete argument has been presented, the literature does contain a number of varied argument fragments, and it is worth asking whether some of these might be developed into a persuasive case.One particularly simple approach would be to note that the existence of a measurable cardinal implies that V ≠ L,1and to argue that there is a measurable cardinal. The drawback to this approach is that its implying V ≠ L cannot then be counted as evidence in favor of MC, as it often is. Indeed, there seems to have been considerable sentiment against V = L even before the proof of its negation from MC,2and this sentiment must either be accounted for as reasonable or explained away as an aberration of some kind. (shrink)

This article compares translation and commentary practices surrounding the texts associated with French feminism with those of contemporary French women philosophers more generally. Many of the latter, discussing the history of philosophy, ask questions such as “How do texts play against the means they supply themselves?” and “How are philosophical forces, and the institutions of commentary, countered, destabilized, deregulated?” Deutscher asks what institutional means are available to understand this work as innovative philosophy, and to what extent these projects can usefully (...) be analyzed as the gestures of women in philosophy. (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.

What is the modal significance of sortal concepts? It is generally accepted that sortal concepts provide persistence conditions with modal implications that are de re, and not merely de dicto. I do not think that this important assumption has received the scrutiny that it deserves. In this paper, I examine the contrast between a ‘pure de dicto’ theory of the persistence conditions associated with sortal concepts and a variety of de re theories, both essentialist and non-essentialist. I conclude that although (...) there is a defensible argument against the pure de dicto theory, it has two interesting implications. First, the argument lends no support to an essentialist version of the de re theory. Secondly, it appears to support the rejection of the pure de dicto theory only by a theorist who is also a pluralist about coincidence. Hence it appears to provide no justification for the rejection of the pure de dicto theory on the part of a contingent identity theorist. (shrink)

What is the modal significance of sortal concepts? It is generally accepted that sortal concepts provide persistence conditions with modal implications that are de re, and not merely de dicto. I do not think that this important assumption has received the scrutiny that it deserves. In this paper, I examine the contrast between a ‘pure de dicto’ theory of the persistence conditions associated with sortal concepts and a variety of de re theories, both essentialist and non-essentialist. I conclude that although (...) there is a defensible argument against the pure de dicto theory, it has two interesting implications. First, the argument lends no support to an essentialist version of the de re theory. Secondly, it appears to support the rejection of the pure de dicto theory only by a theorist who is also a pluralist about coincidence. Hence it appears to provide no justification for the rejection of the pure de dicto theory on the part of a contingent identity theorist. (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)

My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in (...) social arrangements, governments, power structures, or some such thing, but I resist the full force of this way of thinking, clinging to the old school notion that we have gradually learned more about the world over time, that our opinions on these matters have improved, and that seeing how we reached the point we now occupy may help us avoid falling back into old philosophies that are now no longer viable. In that spirit, it seems to me that once we focus on the general question of how mathematics relates to science, one observation is immediate: the march of the centuries has produced an amusing reversal of philosophical fortunes. Let me begin there. In the beginning, that is, in Plato, mathematical knowledge was sharply distinguished from ordinary perceptual belief about the world. According to Plato’s metaphysics, mathematics is the study of eternal and unchanging abstract Forms,1 while science is uncertain and changeable opinion about the world of mere becoming. Indeed, in Plato’s lights, of the two, only mathematics deserves to be called ‘knowledge’ at all! Of course if sense perception cannot give us knowledge, if mathematics is not about perceivable things, then Plato owes us an account of how we ordinary humans achieve this wonderful insight into the properties of the abstract world of Forms. Plato’s answer is that we do not actually acquire mathematical knowledge at all; rather, we recollect it from a time before birth, when our souls, unencumbered by physical bodies, were free to commune with the Forms, and not just the mathematical ones, either – also Truth, Beauty, Justice, the Good, and so on.2 Whatever appeal this position may have held for the ancient Greeks, it will not begin to satisfy a contemporary, scientifically minded philosopher.. (shrink)

Story is central to everyday theology, translating concepts into images which reach into our deepest psyche. This is graphically illustrated in the story of the Magi which conveys in dramatic form essences of belief and understanding. St. Francis appreciated the power of drama and imagery and the Franciscans, nurtured in this tradition, carried it with them to Mexico. Of all these stories introduced after 1524, one of the most enthusiastically received by the Aztecs was the story of the feast of (...) the Epiphany. It is a testament to its popularity that we have inherited two almost contemporaneous autos, La Adoración de los Reyes and La Comedia de los Reyes. Horcasitas comments on this phenomenon: “The Feast of the... (shrink)

My aim in this paper is to propose what seems to me a distinctive approach to set theoretic methodology. By ‘methodology’ I mean the study of the actual methods used by practitioners, the study of how these methods might be justified or reformed or extended. So, for example, when the intuitionist's philosophical analysis recommends a wholesale revision of the methods of proof used in classical mathematics, this is a piece of reformist methodology. In contrast with the intuitionist, I will focus (...) more narrowly on the methods of contemporary set theory, and, more importantly, I will certainly recommend no sweeping reforms. Rather, I begin from the assumption that the methodologist's job is to account for set theory as it is practiced, not as some philosophy would have it be. This credo lies at the very heart of the so-called ‘naturalism’ to be described here.A philosopher looking at set theoretic practice from the outside, so to speak, might notice any number of interesting methodological questions, beginning with the intuitionist's ‘why use classical logic?’, but this sort of question is not a live issue for most practicing set theorists. One central question on which the philosopher's and the practitioner's interests converge is this: what is the status of independent statements like the continuum hypothesis (CH)? A number of large questions arise in its wake: what criteria should guide the search for new axioms? For that matter, what reasons support our adoption of the old axioms? (shrink)

The mature Wittgenstein's groundbreaking analyses of sense and the logical must—and the powerful new method that made them possible—were the result of a multi‐year process of writing, re‐arranging, re‐writing and one large‐scale revision that eventually produced the Philosophical Investigations and RFM I. In contrast, his struggles during the same period with questions of arithmetic and higher mathematics remained largely in first‐draft form, and he drops the topic entirely after 1945. In this paper, I argue that Wittgenstein's new method can be (...) applied to the cases of arithmetic and set theory and that the result is innovative, recognizably Wittgensteinian, and independently appealing. I conclude by acknowledging the reasons Wittgenstein himself might have had to resist applying his own proven method to the case of mathematics—particularly to set theory—and by indicating why I think those reasons are ultimately unsound. (shrink)