I compare deterministic and stochastic hidden variable models of the Bell experiment, exphasising philosophical distinctions between the various ways of combining conditionals and probabilities. I make four main claims. (1) Under natural assumptions, locality as it occurs in these models is equivalent to causal independence, as analysed (in the spirit of Lewis) in terms of probabilities and conditionals. (2) Stochastic models are indeed more general than deterministic ones. (3) For factorizable stochastic models, relativity's lack of superluminal causation does not favour (...) locality over completeness. (4) If we prohibit all superluminal causation, then the violation of the Bell inequality teaches us a lesson, besides quantum mechanics' familiar ones that quantities can lack precise values and that pairs of quantities can lack joint probabilities: namely, some pairs of events are not screened off by their common past. (shrink)

We use model-theoretic methods described in [3] to obtain ordinal analyses of a number of theories of first- and second-order arithmetic, whose proof-theoretic ordinals are less than or equal to Γ0.

In this paper we present a schema for describing dualities between physical theories, and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory. The schema develops proposals in De Haro : these proposals include construals of notions related to duality, like representation, model, symmetry and interpretation. The aim of the schema is to give a more precise criterion for duality than has so far been considered. The bosonization example, or boson-fermion duality, has (...) the feature of being simple, yet rich enough, to illustrate the most relevant aspects of our schema, which also apply to more sophisticated dualities. The richness of the example consists, mainly, in its concern with two non-trivial quantum field theories: including massive Thirring-sine-Gordon duality, and non-abelian bosonization. This prompts two comparisons with the recent philosophical literature on dualities:--- Unlike the standard cases of duality in quantum field theory and string theory, where only specific simplifying limits of the theories are explicitly known, the boson-fermion duality is known to hold {\it exactly}. This exactness can be exhibited explicitly. The bosonization example illustrates both the cases of isomorphic and {\it non-isomorphic} models: which we believe the literature on dualities has not so far discussed. (shrink)

Hypnosis is considered a unique tool capable of modulating cognitive processes. The extent to which hypnotic suggestions intervenes is still under debate. This study was designed to provide a new insight into this issue, by focusing on an unintentional emotional process: attentional bias. In Experiment 1, highly suggestible participants performed three sessions of an emotional Stroop task where hypnotic suggestions aiming to increase and decrease emotional reactivity towards emotional stimuli were administered within an intra-individual design. Compared to a baseline condition (...) (without hypnotic suggestion), a significant increase in attentional bias was found when a hypnotic suggestion to increase emotional reactivity was administered. In contrast, the bias was eliminated when a suggestion to decrease emotional reactivity was administered. Experiment 2 investigated the effect of session repetition on attentional bias across three successive experimental sessions without hypnosis, and showed that the emotional Stroop effect did not vary across sessions. Hence, session repetition could not account for part of the modulation of attentional bias in Experiment 1. Taken together, the results suggest that specific hypnotic suggestions can influence elicitation of unintentional emotional processing. The implications are discussed regarding the locus of intervention of hypnotic suggestion in cognitive and emotional processes. (shrink)

We report a series of experiments carried out with Palestinian and Israeli participants showing that violent opposition to compromise over issues considered sacred is increased by offering material incentives to compromise but decreased when the adversary makes symbolic compromises over their own sacred values. These results demonstrate some of the unique properties of reasoning and decision-making over sacred values. We show that the use of material incentives to promote the peaceful resolution of political and cultural conflicts may backfire when adversaries (...) treat contested issues as sacred values. (shrink)

Henri Poincaré was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to (...) society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world. (shrink)

I discuss the idea of relativistic causality, i.e., the requirement that causal processes or signals can propagate only within the light-cone. After briefly locating this requirement in the philosophy of causation, my main aim is to draw philosophers' attention to the fact that it is subtle, indeed problematic, in relativistic quantum physics: there are scenarios in which it seems to fail. I set aside two such scenarios, which are familiar to philosophers of physics: the pilot-wave approach, and the Newton-Wigner representation. (...) I instead stress two unfamiliar scenarios: the Drummond-Hathrell and Scharnhorst effects. These effects also illustrate a general moral in the philosophy of geometry: that the mathematical structures, especially the metric tensor, that represent geometry get their geometric significance by dint of detailed physical arguments. (shrink)

On September 6, 2004, using the Isabelle proof assistant, I verified the following statement: (%x. pi x * ln (real x) / (real x)) ----> 1 The system thereby confirmed that the prime number theorem is a consequence of the axioms of higher-order logic together with an axiom asserting the existence of an infinite set. All told, our number theory session, including the proof of the prime number theorem and supporting libraries, constitutes 673 pages of proof scripts, or roughly 30,000 (...) lines. This count includes about 65 pages of elementary number theory that we had at the outset, developed by Larry Paulson and others; also about 50 pages devoted to a proof of the law of quadratic reciprocity and properties of Euler’s ϕ function, neither of which are used in the proof of the prime number theorem. The page count does not include the basic HOL library, or properties of the real numbers that we obtained from the HOL-Complex library. (shrink)

Hilbert’s program: • Formalize abstract, infinitary, nonconstructive mathematics. • Prove consistency using only finitary methods.

The rotating discs argument against perdurantism has been mostly discussed by metaphysicians, though the argument of course appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. I argue for three main conclusions. The first conclusion is that the RDA can be formulated more strongly than is usually recognized: it is not necessary to ‘imagine away’ the dynamical effects of rotation. The second is that in general relativity, (...) the RDA fails because of frame-dragging. The third conclusion is that even setting aside general relativity, the strong formulation of the RDA can after all be defeated, namely, by the perdurantist taking objects in classical mechanics to have only temporally extended temporal parts, which immediately blocks the RDA. Admittedly, this version of perdurantism defines persistence in a weaker sense of ‘definition’ than pointilliste versions that aim to define persistence assuming only instantaneous temporal parts. But I argue that temporally extended temporal parts can do the jobs within the endurantism– perdurantism debate that the perdurantist wants temporal parts to do and are supported by both classical and quantum mechanics. Introduction The story so far 2.1 The RDA 2.2 Intrinsic properties and the idea of velocity 2.2.1 The intrinsic–extrinsic distinction 2.2.2 Velocity to the rescue? 2.3 ‘Naturalism’ 2.4 The accompaniments of rotation 2.5 Two kinds of reply: against the consensus Describing rotation 3.1 Rotation is kinematic 3.2 Beware of rigidity 3.3 An improved RDA: allowing the actual accompaniments 3.4 The RDA fails in general relativity Perdurantism without tears: the classical case 4.1 Rejecting instantaneous temporal parts 4.2 Replying to the RDA 4.2.1 ‘Kinematics’ 4.2.2 ‘Dynamics’ 4.2.3 An ‘anti-pointilliste’ objection and reply 4.3 Intrinsic properties of non-instantaneous temporal parts 4.3.1 Can the perdurantist appeal to them? 4.3.2 Temporal intrinsicality at an instant is rare 4.3.3 A better reason for temporal intrinsicality 4.4 Non-instantaneous parts can do the jobs 4.4.1 Humean supervenience revisited 4.4.2 The problem of change 4.4.3 Puzzles of coincidence 4.5 Instantaneous velocity is hardly extrinsic Support from decoherence in quantum theory 5.1 Classical and quantum: relativizing the intrinsic–extrinsic distinction 5.1.1 Unitarity: momentum as temporally intrinsic 5.2 Position and existence as nomically extrinsic. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Relationism claims that our physical theory does not commit us to spacetime points. I consider how a relationist might rewrite physical theories without referring to spacetime points, by appealing to possible objects and possible configurations of objects. I argue that a number of difficulties confront this project. I also argue that a relationist need not be Machian in the sense of claiming that objects' spatiotemporal relations determine whether any object is accelerating.

It is often suggested that, since the state of affairs in which God creates a good universe is better than the state of affairs in which He creates nothing, a perfectly good God would have to create that good universe. Making use of recent work by Christine Korgaard on the relational nature of the good, I argue that the state of affairs in which God creates is actually not better, due to the fact that it is not better for anyone (...) or anything in particular. Hence, even a perfectly good God would not be compelled to create a good universe. (shrink)

Jeremy Waldron’s essay centres around Martha Nussbaum’s ideas on cosmopolitan education: Nussbaum argues that we should make ‘world citizenship, rather than democratic or national citizenship, the focus for civic education’. The essay provides just a few examples to illustrate the concrete particularity of the world community for which we are urged by Nussbaum to take responsibility, with the aim of refuting the view of those who condemn cosmopolitanism as an abstraction. The arguments for and against Nussbaum’s idea are presented, (...) and one of the opposing views highlighted: that cosmopolitan moral education is not just an education in moral ideas; it is an education in the particular ways in which people have inhabited the world. The different sections of the chapter look at how a society becomes multicultural, the infrastructure of cultural interaction, the identification of citizenship, the language of citizenship, and its concrete reality and its cosmopolitan dimensions. (shrink)

I survey some of the connections between the metaphysics of the relation between mind and matter, and quantum theory’s measurement problem. After discussing the metaphysics, especially the correct formulation of physicalism, I argue that two state-reduction approaches to quantum theory’s measurement problem hold some surprises for philosophers’ discussions of physicalism. Though both approaches are compatible with physicalism, they involve a very different conception of the physical, and of how the physical underpins the mental, from what most philosophers expect. And one (...) approach exemplifies a a problem in the definition of physicalism which the metaphysical literature has discussed only in the abstract. A version of the paper has appeared in Consciousness and Human Identity, ed. John Cornwell, OUP 1998. (shrink)

Many nations in the developing world invest scarce funding into training health workers. When these workers migrate to richer countries, particularly when this migration occurs before the source community can recoup the costs of training, the destination community realizes a net gain in resources by obtaining the workers' skills without having to pay for their training. This effect of health worker migration has frequently been condemned as 'poaching' or a case of theft. I assess the charge that the rich nations (...) of the world poach the resources of the developing world through the active recruitment of migrants. I argue that the charge of poaching is misguided in these cases. The misuse of the term poaching is particularly troubling as it distracts attention away from the many actual moral wrongs taking place through the process of health worker migration and objectifies health workers. (shrink)

Empirical research in bioethics can be defined as the application of research methods in the social sciences to the direct examination of issues in [bioethics]. As such, empirical work is a form of descriptive ethics, focused on describing a particular state of affairs that has some moral or ethical relevance. For example, empirical research can help to describe cultural beliefs about the appropriateness of providing health-related information, such as the diagnosis of a life-threatening illness, which informs deliberations about the extent (...) to which it is morally important for clinicians to provide comprehensive information to patients in different cultural contexts. Similarly, empirical research can delineate popular attitudes and experiences related to contentious issues such as abortion, cloning, stem-cell research, and physician-assisted suicide to enlighten discussions and policy formulations regarding them. (shrink)

For all the talk there has been lately about privilege, few have commented on the moral obligations that are associated with having privilege. Those who have commented haven't gone much beyond the idea that the privileged should be conscious of their privilege, should listen to those who don't have it. Here we want to go further, and build an account of the moral obligations of those with a particular kind of privilege: race privilege. In this paper we articulate an understanding (...) of race privilege, say how a person can know when she has it, and argue that a race-privileged person has obligations to offset her privilege. We make concrete suggestions for how she can, at least approximately, do this. We use particular racial group disparities in the United States as our running example throughout the paper, although our conclusions generalize. (shrink)

ABSTRACTAlthough item-memory for emotional information is enhanced, memory for associations between items is often impaired for negative, emotionally arousing compared to neutral information. We te...

We often hear stories of people in terrible and seemingly intractable situations that are preyed upon by individuals offering empty promises of help. Frequently these cases are condemned as "exploiting the hope" of another. These accusations are made in a range of contexts, including human smuggling, the beauty industry, and unproven medical interventions. This concept is meant to do heavy lifting in public discourse, identifying a specific form of unethical conduct. However, it is poorly understood what is intended to be (...) wrong by exploiting hope, the range of activities that can accurately be captured under this concept, and what should be done about it. Thus, it is an ethical concept that is ripe for extended analysis and discussion. (shrink)

Frankfurt-type examples seem to show that agents can be morally responsible for their actions and omissions even if they could not have done otherwise. Fischer and Ravizza's influential account of moral responsibility is largely based on such examples. I examine a problem with their account of responsibility in cases where we fail to act. The solution to this problem has a surprising and far reaching implication concerning the construction of successful Frankfurt-type examples. I argue that the role of the counterfactual (...) intervener in such examples can only be filled by a rational agent. (shrink)

Scholarship aiming to describe the wrongness of exploitation, especially when it is voluntary and mutually beneficial, has increased greatly in recent years. In this paper, I expand the scope of this discussion by highlighting a set of additional ethical concerns associated with many cases of mutually voluntary and beneficial exploitation. Specifically, I argue that the phenomenon of persons desperately seeking out and gratefully accepting exploitative interactions raises special moral concerns. The element of voluntariness is key to understanding how and why (...) some exploitative interactions are degrading to exploitees. When an exploitative offer does not allow the exploitee sufficient progress toward a decent minimum of human functioning, these offers can create what I call a 'demeaning choice', where the exploitee may either accept the status quo or accept an offer that improves the exploitee's insufficiently. In these cases, the exploitee's participation in the interaction contributes to its demeaning quality, creating a form of `surface endorsement' of the treatment that she receives. (shrink)

In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed valuations (...) could arise much more generally than just in quantum physics; in particular, they arise as naturally in classical physics. Second, we give another motivation for such valuations (that applies equally to classical and quantum physics). This arises from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. (shrink)

Introduction, by C.K. Ogden.--The theory of fictions, by Jeremy Bentham.

There is a massive and so far quite mysterious difference between thinking of cosmopolitan norms as law and thinking in legal terms about the norms of an ordinary municipal system. Until one has something more to say about the former, the idea of a cosmopolitan order remains unanalyzed. This book's notion of “democratic iteration” contributes a substantial amount of what is needed here, to resolve this obscurity. However, this chapter pursues that idea in a slightly different way from the way (...) in which the book pursues it. The outset of the author's lectures indicates that she has a particular interest in norms defining “crimes against humanity” and by extension human rights norms and what she calls “cosmopolitan norms of justice.” What distinguishes these from the more familiar rules of international law is that cosmopolitan norms offer rights and protections to, and impose obligations on, human individuals as such, not just states. (shrink)

The widespread association of business with maximising profit has tended to obscure its social dimension. Indeed some writers doubt whether business can ever be socially engaged and others claim that it should not. This paper seeks to show that besides seeking profit businesses can properly practise social responsibility, defined as involving themselves in their communities and engaging in non-profit activities. It explores the ways in which business social responsibility can contribute to social capital, the resources created by social bonds which (...) members of a society can draw upon and which make it possible to achieve otherwise unattainable ends.2. (shrink)

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping (...) us understand the general principles by which it serves its purposes well. (shrink)

In standard models of decision making, participation in violent political action is understood as the product of instrumentally rational reasoning. According to this line of thinking, instrumentally rational individuals will participate in violent political action only if there are selective incentives that are limited to participants. We argue in favor of an alternate model of political violence where participants are motivated by moral commitments to collective sacred values. Correlative and experimental empirical evidence in the context of the Israeli–Palestinian conflict strongly (...) supports this alternate view. (shrink)

We investigate the entrepreneurial opportunities and ethical dilemmas presented by technological turbulence. More specifically we investigate the line between Baumol’s [J. Polit. Econ. 98 (1990) 893] productive (e.g. innovation), unproductive (e.g. rent seeking) and destructive (e.g. criminal) entrepreneurship through three examples of Internet innovation – spam (destructive), music file sharing (unproductive), and Internet pharmacies (potentially productive). The emergence of accessible Internet technologies, under present norms, has created the potential for all three entrepreneurial activities. Because of the propensity for self-serving biases (...) and for bending the rules, the need for creativity in overcoming obstacles and overall liabilities of newness, entrepreneurs are likely to challenge established industrial morals and laws. Unlike new entrants, incumbents must abide by the currently accepted norms, and thus suffer from “liabilities of oldness”. The challenge for new entrants is to change sociopolitical legitimacy, whereas incumbents need to defend the established norms. We discuss competitive and other issues that result from technological turbulence and innovation. (shrink)

Civilizational analysis has not concerned itself too greatly with the historical experiences of the American New World. There are good reasons to correct this position and Shmuel Eisenstadt’s principal work on America’s distinct modernities goes some way to establishing the colonization of the Atlantic world as an opening phase of modernity. Nonetheless, a more far-reaching analysis of the distinctiveness of diverse American societies can be developed that goes beyond the image of a Protestant North America contrasted with southern Latin cultures. (...) This article outlines the basis for a more nuanced approach in three steps: a focus on intercivilizational engagement, examination of civilizational factors neglected by Eisenstadt and reconsideration of the conceptual range of the notion of ‘civilization’ itself. The archetype of two Americas is replaced by a model of four with some consideration given to indigenous civilizations as a fifth America. (shrink)

Steven M. Cahn presented a fascinating and recalcitrant puzzle. Imagine that you own stock in a company that has undertaken an immoral course of action. Most people believe that selling the stock is the right thing to do. But if you sell the stock, you thereby abet the buyer in an immoral course of action, namely the buyer’s coming to own tainted stock. Is principled divestiture possible? If so, what are the moral grounds on which principled divestiture stands? These questions (...) have proven difficult. Cahn answered many attempted replies to his puzzle. In this journal, Saul Smilansky also attempted to answer the divestiture puzzle. Smilansky concluded, “Attempting to divest by offering the stock for sale is, however, morally problematic. It is problematic because it involves the bad faith of putting something forward as morally acceptable while claiming it to be morally tainted.” Smilansky continued, “One needs to get rid of the stock and take it off the market at the same time, i.e., make it impossible for others to purchase the stock.” Smilansky thereby implies that one should destroy the stock. However, Cahn had already replied to this move, noting that destroying one’s stock would increase the moral culpability of other owners. (shrink)

The material in this volume constitutes a philosophical commonplace book, compiled by Bentham in the mid-1770s, in which he worked out the foundational ideas for his new science of legislation. One of Bentham's central concerns was the development of an adequate ontological and epistemological basis for legal terminology, and the replacement of the traditional terminology of English law with that of universal jurisprudence. Preparatory Principles constitutes a remarkable record of the evolving ideas of a major legal philosopher at a formative (...) stage of his career. (shrink)

Medical tourism is the practice of traveling across international borders with the intention of accessing medical care, paid for out-of-pocket. This practice has implications for preferential access to medical care for Canadians both through inbound and outbound medical tourism. In this paper, we identify four patterns of medical tourism with implications for preferential access to care by Canadians: Inbound medical tourism to Canada’s public hospitals; Inbound medical tourism to a First Nations reserve; Canadian patients opting to go abroad for medical (...) tourism; and Canadian patients traveling abroad with a Canadian surgeon. These patterns of medical tourism affect preferential access to health care by Canadians by circumventing domestic regulation of care, creating jurisdictional tensions over the provision of health care, and undermining solidarity with the Canadian health system. (shrink)

Complementary and alternative medicine is used by many in hopes of achieving important health-related goals. Survey data indicate that 42 percent of the U.S. population uses CAM, accounting for 629 million “office” visits a year and expenditures of 27 billion dollars. This high prevalence of use calls for a careful evaluation of CAM so as to ensure the well-being of those using its modalities. Such an evaluation would obviously include assessments of the safety and efficacy of particular approaches, the training (...) and integrity of practitioners, and the appropriateness of modalities for different conditions or uses. Given the lack of published data concerning many of these aspects of CAM, the likely unfamiliarity of its practitioners to the approaches available to clinicians practicing modern scientific medcine, and the need to respect the unique preferences of persons seeking assistance with achieving health-related goals, it is also important to assess the potential roles of informed consent for the use of CAM. Examining such roles is the central task of this paper. (shrink)

Why are people attracted to conspiracy theories? This essay conceives of conspiratorial motivation as an aesthetic phenomenon. To defend this account, I offer a coarse-grained taxonomy of contemporary motivational hypotheses that have been proposed to answer this question, describing their strengths and weaknesses. Next, I offer an aesthetic account of conspiratorial consumption; I argue that people’s preference for conspiratorial narratives is the product of a taste for a particular kind of story. To clarify the approach, I show how aesthetic appreciation (...) is often confused with epistemic evaluation, leading the conspiracy theorist to believe she is involved in epistemic practice instead of aesthetic practice. I then describe the genre of conspiracy theorizing, explaining how my proposed genre account makes sense of several puzzles about conspiratorial consumption. The essay concludes by suggesting that the genre account offers a unique mode of engagement with conspiracy theorists that might be employed in order to profitably dialogue with those who hold these fringe and often dangerous beliefs. (shrink)

This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum theory (or classical physics), not a real number, but a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; in part mathematical---the valuations arise naturally in the theory of presheaves; and in part (...) conceptual---the valuations arise from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. In this paper, I give another conceptual motivation for the proposal. I develop (in Sections 2 and 3) the notion of a topos (of which presheaves give just one kind of example); and explain how this notion gives a satisfactory general framework for making sense of the idea of partial truth. Then I review (in Section 4) how our proposal applies this framework to the case of physical theories. (shrink)

In this essay, the author shows how Foucault's discussions of pastoral power relate to a wider “analytics” of religious power set down in 1975 and 1976 before he deploys the language of the “pastoral”. In shifting the discussion of pastoral power to a wider trajectory, the author considers the question of whether pastoral power persists after the historical shift to governmentality. The chapter maps the specific features of Foucault's idea of pastoral power in the 1977–78 College de France course and, (...) aided by the “dry and schematic character” of the lectures. It examines one of the most neglected aspects of pastoral power, the theological relation of pastoral power, something brought to light in the 1977–78 course. The priority Foucault gave to pastoral power is significant not only for its “decisive” historical importance, but also in showing something of how “religion is a political force”. (shrink)