We illustrate, using a simple model, that in the usual formulation the time-component of the Klein–Gordon current is not generally positive definite even if one restricts allowed solutions to those with positive frequencies. Since in de Broglie's theory of particle trajectories the particle follows the current this leads to difficulties of interpretation, with the appearance of trajectories which are closed loops in space-time and velocities not limited from above. We show that at least this pathology can be avoided if one (...) adapts in a covariant form the formulation of relativistic point particle dynamics proposed by Gitman and Tyutin. (shrink)

This paper is motivated by the desire to formulate a relativistically covariant hidden-variable particle trajectory interpretation of the quantum theory of the vector field that is formulated in such a way as to allow the inclusion of gravity. We present a methodology for calculating the flows of rest energy and a conserved density for the massive vector field using the time-like eigenvectors and eigenvalues of the stress-energy-momentum tensor. Such flows may be used to define particle trajectories which follow the flow. (...) This work extends our previous work which used a similar procedure for the scalar field. The massive, spin-one, complex vector field is discussed in detail and the flows of energy-momentum are illustrated in a simple example of standing waves in a plane. (shrink)

The desire-satisfaction theory of well-being says, in its simplest form, that a person’s level of welfare is determined by the extent to which their desires are satisfied. A question faced by anyone attracted to such a view is, *Which desires*? This paper proposes a new answer to this question by characterizing a distinction among desires that isn’t much discussed in the well-being literature. This is the distinction between what a person wants in a merely behavioral sense, in that the person (...) is, for some reason or other, disposed to act so as to try to get it, and what a person wants in a more robust sense, the sense of being *genuinely attracted* to the thing. I try to make this distinction more clear, and I argue for its axiological relevance by putting it to work in solving four problem cases for desire satisfactionism. The theory defended holds that only desires in the latter, genuine-attraction sense are relevant to welfare. (shrink)

The past 50 years have seen an accumulation of evidence suggesting that associative learning depends on high-level cognitive processes that give rise to propositional knowledge. Yet, many learning theorists maintain a belief in a learning mechanism in which links between mental representations are formed automatically. We characterize and highlight the differences between the propositional and link approaches, and review the relevant empirical evidence. We conclude that learning is the consequence of propositional reasoning processes that cooperate with the unconscious processes involved (...) in memory retrieval and perception. We argue that this new conceptual framework allows many of the important recent advances in associative learning research to be retained, but recast in a model that provides a firmer foundation for both immediate application and future research. (shrink)

This entry considers the philosophical subject called 'metaphysics'. There have been many conceptions of metaphysics, and metaphysics has faced severe criticism throughout the history of philosophy and continues to do so. Besides discussing some major trends in analytic metaphysics - understood as 'metaphysics done by analytic philosophers' - we consider some of the criticisms and possible responses.

Explains the desire-fulfillment theory of well-being, its history, its development, its varieties, its advantages, and its challenges.

_The Good Life of Teaching_ extends the recent revival of virtue ethics to professional ethics and the philosophy of teaching. It connects long-standing philosophical questions about work and human growth to questions about teacher motivation, identity, and development. Makes a significant contribution to the philosophy of teaching and also offers new insights into virtue theory and professional ethics Offers fresh and detailed readings of major figures in ethics, including Alasdair MacIntyre, Charles Taylor, and Bernard Williams and the practical philosophies of (...) Hannah Arendt, John Dewey and Hans-Georg Gadamer Provides illustrations to assist the reader in visualizing major points, and integrates sources such as film, literature, and teaching memoirs to exemplify arguments in an engaging and accessible way Presents a compelling vision of teaching as a reflective practice showing how this requires us to prepare teachers differently. (shrink)

Subjective theories of well-being claim that how well our lives go for us is a matter of our attitudes towards what we get in life rather than the nature of the things themselves. This article explains in more detail the distinction between subjective and objective theories of well-being; describes, for each approach, some reasons for thinking it is true; outlines the main kinds of subjective theory; and explains their advantages and disadvantages.

Choice architecture is heralded as a policy approach that does not coercively reduce freedom of choice. Still we might worry that this approach fails to respect individual choice because it subversively manipulates individuals, thus contravening their personal autonomy. In this article I address two arguments to this effect. First, I deny that choice architecture is necessarily heteronomous. I explain the reasons we have for avoiding heteronomous policy-making and offer a set of four conditions for non-heteronomy. I then provide examples of (...) nudges that meet these conditions. I argue that these policies are capable of respecting and promoting personal autonomy, and show this claim to be true across contrasting conceptions of autonomy. Second, I deny that choice architecture is disrespectful because it is epistemically paternalistic. This critique appears to loom large even against non-heteronomous nudges. However, I argue that while some of these policies may exhibit epistemically paternalistic tendencies, these tendencies do not necessarily undermine personal autonomy. Thus, if we are to find such policies objectionable, we cannot do so on the grounds of respect for autonomy. (shrink)

This paper responds to a new objection, due to Ben Bramble, against attitudinal theories of sensory pleasure and pain: the objection from unconscious pleasures and pains. According to the objection, attitudinal theories are unable to accommodate the fact that sometimes we experience pleasures and pains of which we are, at the time, unaware. In response, I distinguish two kinds of unawareness and argue that the subjects in the examples that support the objection are unaware of their sensations in only a (...) weak sense, and this weak sort of unawareness of a sensation does not preclude its being an object of one’s attitudes. (shrink)

In recent work, Peter Hanks and Scott Soames argue that propositions are types whose tokens are acts, states, or events. Let’s call this view the type view. Hanks and Soames think that one of the virtues of the type view is that it allows them to explain why propositions have semantic properties. But, in this paper, we argue that their explanations aren’t satisfactory. In Section 2, we present the type view. In Section 3, we present one explanation—due to Hanks (2007, (...) 2011) and Soames (2010)—of why propositions have semantic properties. We criticize this first explanation in Section 4. In Section 5, we present another explanation—due to Soames (2104)—of why propositions have semantic properties. We criticize this second explanation in Section 6. (shrink)

We consider the influence that John Forrester’s work has had on thinking in, with, and from cases in multiple disciplines. Forrester’s essay ‘If p, Then What? Thinking in Cases’ was published in History of the Human Sciences in 1996 and transformed understandings of what a case was, and how case-based thinking worked in numerous human sciences. Forrester’s collection of essays Thinking in Cases was published posthumously, after his untimely death in 2015, and is the inspiration for the special issue we (...) introduce. This comprises new research from authors working in and across the history of science and medicine, gender and sexuality studies, philosophy of science, semiotics, film studies, literary studies and comparative literature, psychoanalytic studies, medical humanities, and sociology. This research addresses what it means to reason in cases in particular temporal, spatial, or genre-focused contexts; introduces new figures into lineages of case-based reasoning; emphasizes the unfinished and unfinishable character of some case reading and autobiographical accounts; and shows the frequency with which certain kinds of reasoning attempted with cases fail. The special issue opens up new directions for thinking and working with cases and case-based reasoning in the humanities and human sciences. (shrink)

A short encyclopedia entry on the issue of whether the value of a whole is equal to the sum of the values of its parts.

This essay discusses monism and pluralism about two related evaluative notions: welfare, or what makes people better off, and value simpliciter, or what makes the world better. These are stipulatively referred to as 'axiological value'. Axiological value property monists hold that one of these notions is reducible to the other (or else eliminable), while axiological value property pluralists deny this. Substantive monists about axiological value hold that there is just one basic kind of thing that makes our lives or the (...) world better, while substantive pluralists hold that there is more than one such thing. A more radical kind of pluralism holds that each of the plurality of good things is good in its own way, thus raising questions concerning value comparability and compensability. The essay elucidates these theories and discusses important arguments for and against them. (shrink)

An important and widely-endorsed argument for moral realism is based on alleged parallels between that doctrine and epistemic realism -- roughly the view that there are genuine epistemic facts, facts such as that it is reasonable to believe that astrology is false. I argue for an important disanalogy between moral and epistemic facts. Epistemic facts, but not moral facts, are plausibly identifiable with mere descriptive facts about the world. This is because, whereas the much-discussed moral open-question argument is compelling, the (...) little-discussed epistemic open-question argument is not. This paper is a critical notice of Terence Cuneo's The Normative Web: An Argument for Moral Realism (Oxford University Press, 2007). (shrink)

An introduction to the philosophical debate over what makes a person's life go well. It attempts to clarify the question of welfare and to explore several of the most important answers, while displaying the main contours of the dialectic.

In this essay, the authors analyze and interpret facsimiles of important original documents—published here for the first time—that are deeply relevant to the education of the young Ayn Rand at the University of Petrograd. This definitive reading of source material provides significant documentation of Rand’s courses, teachers, and textbooks—and what she might have learned from them. Other original source materials are revealed to advance further investigations of this key period in Rand’s life. Recent commentary on Rand’s education in Gary H. (...) Merrill’s book, False Wisdom, is also considered. (shrink)

Ethical cultures, corporate social responsibility (CSR), and sustainability strategies are increasingly being addressed through formal organisational policies and structures. This is evidenced by codes of ethics, conduct, whistle-blowing reporting lines, anti-bribery and corruption policies, and broader stakeholder and environmental engagement strategies. In the United States, corporate ethics managers are responsible for these functions, supported by specific professional and university-level qualifications. However, this is not the case in Australia and Asia where the role appears delegated to human resource personnel in organisations. (...) Human resource management (HRM) is increasingly advanced as a formal profession, yet whether corporate ethics content features as a significant component of the HRM profession is unclear. Expert knowledge is a foundation of a profession along with the duty to act within the limits of that knowledge and expertise. This paper scopes what constitutes professional expert knowledge. It examines corporate ethics expertise and HRM within this context. Major Australian and Asian organisations are examined to verify that HRM Departments, and thus HRM practitioners, are responsible for managing corporate ethics. Given the seniority and strategic importance of this function, the content of selected Masters in HRM and related fields are examined to identify the extent of ethics content. This is considered in the light of the expertise required to manage corporate ethics, and conclusions are drawn whether the HRM discipline is appropriately qualified to manage this function. Finally, recommendations and further research towards advancing the role and function of corporate ethics managers in general are proposed. (shrink)

Chris Daly; Tropes, Proceedings of the Aristotelian Society, Volume 94, Issue 1, 1 June 1994, Pages 253–262, https://doi.org/10.1093/aristotelian/94.1.253.

We address three questions raised by Cummings and Foreman regarding a model of Gitik and Sharon. We first analyze the PCF-theoretic structure of the Gitik–Sharon model, determining the extent of good and bad scales. We then classify the bad points of the bad scales existing in both the Gitik–Sharon model and other models containing bad scales. Finally, we investigate the ideal of subsets of singular cardinals of countable cofinality carrying good scales.

This paper develops and defends a novel version of a relatively neglected category of theory of the nature of happiness: the desire-satisfaction theory. My account is similar in its fundamentals to Wayne Davis’s theory of happiness-as-subjective-desire-satisfaction. After arguing that this is the best general way to proceed for the desire-based approach, I develop an improved version of subjective desire satisfactionism in light of recent arguments in the happiness literature.

Support vector machines are being used increasingly in affective science as a data-driven classification method and feature reduction technique. Whereas traditional statistical methods typically compare group averages on selected variables, SVMs use a predictive algorithm to learn multivariate patterns that optimally discriminate between groups. In this review, we provide a framework for understanding the methods of SVM-based analyses and summarize the findings of seminal studies that use SVMs for classification or data reduction in the behavioral and neural study of emotion (...) and affective disorders. We conclude by discussing promising directions and potential applications of SVMs in future research in affective science. (shrink)

Dale Dorsey’s wide-ranging A Theory of Prudence contains ideas and arguments worthy of our attention on quite a variety of self-interest-related normative topics. In this essay I focus on Dorsey’s theory of prudential rationality, which is designed to deliver a negative answer to this essay’s titular question. Dorsey’s negative answer may be more intuitive, but I believe the positive answer is more defensible. From the perspective of prudence, it is just as reasonable to change your desires to fit the world (...) as it is to change the world to fit your desires. (shrink)

In previous work, I defend the following disparity between moral and epistemic facts: whereas moral facts are irreducibly normative, epistemic facts – facts such as that some subject is epistemically justified in believing something – are reducible to facts from some other domain (such as facts about probabilities). This moral-epistemic disparity is significant because it undercuts an important kind of argument for robust moral realism. My defense of epistemic reductionism and of the moral-epistemic disparity has been criticized by Richard Rowland (...) (2013) and by Terence Cuneo and Christos Kyriacou (forthcoming). This paper aims to rebut these criticisms and, more generally, to clarify and strengthen the case for epistemic reductionism and the moral-epistemic disparity. (shrink)

Much of Stephen Jay Gould’s legacy is dominated by his views on the contingency of evolutionary history expressed in his classic Wonderful Life. However, Gould also campaigned relentlessly for a “nomothetic” paleontology. How do these commitments hang together? I argue that Gould’s conception of science and natural law combined with his commitment to contingency to produce an evolutionary science centered around the formulation of higher-level evolutionary laws.

Metaethical non-naturalists maintain that normative or evaluative properties cannot be reduced to, or otherwise explained in terms of, natural properties. They thus have difficulty explaining what these irreducibly normative properties are supposed to be, other than by saying what they are not. I offer a partial, positive characterization of irreducible normativity in naturalistic terms. At a first pass, it is this: that to attribute a normative property to something is necessarily to commend or condemn that thing, due to the nature (...) of the property attributed. This theory characterizes normativity in terms of the natural phenomenon of performing certain familiar speech acts. The hypothesis does other explanatory work as well: it provides for an account of the "queerness" of normative properties, one superior to other accounts; it explains why metaethical reductionism is bound to fail, in a way friendly to non-naturalism (as opposed to non-cognitivism); and it can help deflect arguments against non-naturalism from the "essential practicality" of normativity. (shrink)

Objective—To identify and describe the current state of clinical ethics support services in the UK.Design—A series of questionnaire surveys of key individuals in National Health Service (NHS) trusts, health authorities, health boards, local research ethics committees and health professional organisations. Interviews with chairmen/women of clinical ethics committees identified in the surveys.Setting—The UK National Health Service.Results—Responses to the questionnaires were received from all but one NHS trust and all but one health authority/board. A variety of models of clinical ethics support were (...) identified including twenty formal clinical ethics committees (CECs). A further twenty NHS trusts expressed an intention to establish a CEC within the next twelve months. Most CECs in the UK have been in existence less than five years and are still defining their role. The chairmen identified education of committee members and contact with other ethics committees as important requirements for committee development. Problems were identified around lack of support for the committee and with raising the profile of the committee within the institution. There has been little evaluation of clinical ethics support services either in the UK or in other countries with longer established services. What evaluation has occurred has focused on process rather than outcome measures.Conclusions—Clinical ethics support services are developing in the UK. A number of issues have been identified that need to be addressed if such support services are to develop effectively. (shrink)

An argument that science is indeed 'socially constructed' but in a way that exposes it to a Darwinian version of variability and selection which ensures its success.

In this article we address the question of how many impossible images Escher produced. To answer requires us first to clarify a range of concepts, including content, ambiguity, illusion, and impossibility. We then consider, and reject, several candidates for impossibility before settling on an answer.

This paper offers an inconsistent model of motion perception. It was prompted by work on inconsistent motion due to Hegel and, following him, Priest. But the paper skirts Hegel's full scale idealism, by proposing that the inconsistency is with the cognitive contents of motion perception. The paper draws on work in the psychology of perception, and in the theory of inconsistency. I begin by noting the prima facie argument that temporal change threatens inconsistency, and canvassing ways in which this might (...) be avoided. The orthodox reply to the prima facie argument is that one and the same thing can have different incompatible properties at different times. This is plausible when applied to motion in the physical world. However, applied to cognition, it can be seen that the phenomenon of phi or beta, combined with the mechanism of a Reichardt detector, lends support to one key step in the prima facie argument, namely re-identification over time. The inconsistency of the model is then seen to follow from application of the Fade Principle. Advantages of the model are stressed: including a simple explanation of the debilitating condition of akinetopsia, that is, motion blindness; and a suggestion as to how to account for the “moving now.”. (shrink)

This Element provides an opinionated introduction to the debate in moral philosophy over identifying the basic elements of well-being and to the related debate over the nature of happiness. The question of the nature of happiness is simply the question of what happiness is, and the central philosophical question about well-being is the question of what things are in themselves of ultimate benefit or harm to a person, or directly make them better or worse off.

As Early Years care and education comes under closer outside scrutiny the number of practitioners moving into managerial roles is constantly increasing, this book focuses on how to make policy work in practice: clarifying the manager’s responsibilities and his or her duty to lead exploring the use of policy and procedures, why we have procedure, how to create procedures and how to put it into practice offering advice on effective planning, how to monitor progress and activity, and tips on feedback (...) and reflection providing links to Ofsted. This is a must-have for students, assessors, nursery nurses with an interest in career development into management and anyone working within a early-years environment in a managerial role. (shrink)

This introduction to the twentieth anniversary volume of The Journal of Ayn Rand Studies celebrates the creating and sustaining of a forum in which writers coming from virtually every discipline, representing a diverse range of critical perspectives, have advanced the scholarly study of Ayn Rand and her times.

Critics have long dismissed paternalistic choice architecture as conceptually muddled at best and oxymoronic at worst. In this article, I argue that this criticism remains true despite recent replies to the contrary. Further, I suggest that a similar conceptual criticism also applies to non-paternalistic choice architecture. This is due to a three-way tension between the effectiveness, avoidability, and distinctiveness of each nudge. To illustrate this tension, I provide a novel explanation of the mechanics of nudging and a taxonomy of these (...) interventions. I then argue that choice architects who defend the distinctiveness of nudging according to how it guides our behaviour via our unreflective intuitive reasoning encounter a trilemma because the distinctiveness of nudging hinges on interventions being both avoidable and effective. Choice architects cannot achieve this aim without harnessing both our automatic and reflective systems of thought in tandem. However, this diminishes the distinctive character of nudging by bringing it closer to other traditional policy interventions. This establishes the choice architect’s trilemma: a nudge is likely to be either ineffective, effective via some morally unacceptable means, or effective in a manner that is conceptually indistinct from other evidence-based policy interventions. (shrink)

Derek Parfit's monumental 1984 book Reasons and Persons contains a little appendix called "What Makes Someone's Life Go Best," a mini-essay on well-being that has taken on a life of its own apart from the body to which it is attached. This paper serves as a critical guide to that appendix. Topics include: the nature of pleasure and pain and its relation to theories of well-being; the unrestricted desire-fulfillment theory and the problem of remote desires; whether a person's actual preferences (...) should determine their counterfactual well-being; summative vs. global desire-fulfillment theories; the single-life repugnant conclusion; and objective vs. subjective vs. hybrid theories of well-being. Opinions being defended include: that Parfit's solution to the problem of remote desires fails; that his view on actual preferences and counterfactual well-being is right; that his arguments for global over summative desire-fulfilment theories fail; and that the single-life repugnant conclusion should be accepted. (shrink)

Action research began as an ambitious epistemological and social intervention. As the concept has become reified, packaged for methodology textbooks and professional development workshops, it has degenerated into a cure that may be worse than the disease. The point is not the trivial one that action research, like any practice, sometimes shows up in cheap or corrupt forms. The very idea that action research already exists as a live option is mystifying, distracting us from the deep challenge that action research (...) ultimately represents. Though Joseph Schwab is sometimes credited as a forerunner of action research, it is likely that he would see the new talk of ‘the teacher as researcher’ as indicative of the very epitomization of which he warned. Dewey’s new conception of knowledge, action, and communication – and the vision of the teacher as learner it entails – requires nothing short of a radical rethinking of teaching and inquiry, schooling and teacher education. This essay recalls the promise of... (shrink)

Building upon his previous books about Marx, Hayek, and Rand, _Total Freedom_ completes what _Lingua Franca_ has called Sciabarra’s "epic scholarly quest" to reclaim dialectics, usually associated with the Marxian left, as a methodology that can revivify libertarian thought. Part One surveys the history of dialectics from the ancient Greeks through the Austrian school of economics. Part Two investigates in detail the work of Murray Rothbard as a leading modern libertarian, in whose thought Sciabarra finds both dialectical and nondialectical elements. (...) Ultimately, Sciabarra aims for a dialectical-libertarian synthesis, highlighting the need to think of the "totality" of interconnections in a dynamic system as the way to ensure human freedom while avoiding "totalitarianism". (shrink)

Some understand Stein’s “Yes, but…” as an entry in the realism—instrumentalism debate (RID) itself, albeit one dissatisfied with then-extant positions. In this paper, however, I argue the opposite: Stein’s conception of science and his approach to its history and philosophy actually preclude the RID. First, I characterize Stein as persistently attending to his own historical and philosophical methods. I then describe his conception of science as both a dialectic and an enterprise, and I draw from this conception several conclusions about (...) the relations between science and its history and philosophy. Finally, I provide a reading of “Yes, but…” that follows from Stein’s conception of science. On this reading, the RID is either irrelevant to or wrong of science and, moreover, distracts from a legitimate inquiry. I conclude by interpreting Stein’s remark that there is ``no difference that makes a difference’’ between a cogent and enlightened realism and a sophisticated instrumentalism. (shrink)

This paper makes two claims. Firstly, it shows that thinking the truth of any particular concept (such as politics) is founded upon an instrumental logic that betrays the truth of a situation. Truth cannot be thought ‘of something’, for this would fall back into a theory of correspondence. Instead, truth is a function of thought. In order to make this move to a functional concept of truth, I outline Dewey’s criticism, and two important repercussions, of dogmatically instrumental philosophy. I then (...) show how Badiou’s philosophy is indeed guilty of instrumentalisation, but emphasise that his prioritisation of truth is nevertheless important to maintain. The second claim this paper makes is that the criticism of Deleuze’s conception of truth as circular is misplaced, as it is founded on the assumption that Deleuze conceptualises the truth of objects. Instead, I show that, for Deleuze, truth is not a property of an object but of its production. To reach this conclusion, I develop what I call Dewey’s account of pragmatic instrumentalisation (as opposed to the dogmatic instrumentalisation he criticises) into Deleuze’s conceptualisation of truth as the process of making sense of our precarious world. I conclude by making some provisional remarks that Deleuze’s pragmatic account of truth paves the way for an ethics that is not founded on truths it cannot explain (i.e. God or mathematics), but as an ongoing, subversive practice. (shrink)

This essay discusses the passing of two figures important to Ayn Rand studies: Allan Gotthelf and Barbara Branden. It also contextualizes some of the essays published in the current issue.

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n × n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski–Mulvey) of the “Bohrification” \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} of A, which is a commutative Rickart C*-algebra in the topos of functors from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}A}$$\end{document} to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns–Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} for A = B(H). (shrink)

Political liberals aim to treat citizens as free and equal participants in a society governed by principles endorsable from a wide range of reasonable conceptions of the good. This popular account of political morality struggles to accommodate child citizens yet to develop the capacities for freedom and equality enjoyed by citizens under political liberalism. It appears political liberals must either accept political liberalism should not apply to all citizens or intrusively constrain parental rights to shape the values of their children (...) in line with anti-perfectionism. I defend a third possibility that justifies perfectionism in parenting and anti-perfectionism in education. (shrink)