End-of-life decision making is fraught with ethical challenges. Withholding or withdrawing life support therapy is widely considered ethical in patients with high treatment burden, poor premorbid status, or significant projected disability even when such treatment is not “futile.” Whether such withdrawal of therapy in the aftermath of attempted suicide is ethical is not well established in the literature. We provide a clinical vignette and propose criteria under which such withdrawal would be ethical. We suggest that it is appropriate to withdraw (...) life support, regardless of the cause of the critical illness or disability, when the following criteria are met: (1) Surrogates request withdrawal of care and the adequacy of surrogates is confirmed, (2) an external reasonability standard is met, (3) passage of time, perhaps 72 hours, to allow certainty regarding the patient's wishes, and (4) psychiatric morbidity should be considered as grounds for withdrawal only in truly treatment-refractory cases. Fundamentally, we believe the question to ask is, “If this were not an attempted suicide, would a request to withdraw care be reasonable?” We believe that under these circumstances, such withdrawal of life support, even in an individual who has attempted suicide, does not constitute physician assistance with suicide and is distinct from physician aid-in-dying in several important respects. (shrink)

End-of-life decision making is fraught with ethical challenges. Withholding or withdrawing life support therapy is widely considered ethical in patients with high treatment burden, poor premorbid status, or significant projected disability even when such treatment is not ?futile.? Whether such withdrawal of therapy in the aftermath of attempted suicide is ethical is not well established in the literature. We provide a clinical vignette and propose criteria under which such withdrawal would be ethical. We suggest that it is appropriate to withdraw (...) life support, regardless of the cause of the critical illness or disability, when the following criteria are met: (1) Surrogates request withdrawal of care and the adequacy of surrogates is confirmed, (2) an external reasonability standard is met, (3) passage of time, perhaps 72 hours, to allow certainty regarding the patient's wishes, and (4) psychiatric morbidity should be considered as grounds for withdrawal only in truly treatment-refractory cases. Fundamentally, we believe the question to ask is, ?If this were not an attempted suicide, would a request to withdraw care be reasonable?? We believe that under these circumstances, such withdrawal of life support, even in an individual who has attempted suicide, does not constitute physician assistance with suicide and is distinct from physician aid-in-dying in several important respects. (shrink)

We are grateful for the careful reading and insightful responses of the several peer commentaries to our proposed approach to requests to withhold or withdraw life support therapies among patients...

We are grateful for the careful reading and insightful responses of the several peer commentaries to our proposed approach to requests to withhold or withdraw life support therapies among patients...

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then (...) make the case for intuitionism as a suitable candidate to fill this void. (shrink)

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then (...) make the case for intuitionism as a suitable candidate to fill this void. (shrink)

Epistemic democratic theory often focuses on defending democracy from various forms of elitism, such as epistocracy. However, democracy’s informational properties may also be compared with those of the market, and not other forms of political decision-making. While Kevin Elliott’s critique of the market’s epistemic properties is a welcome contribution that broadens the range of comparisons epistemic democratic theory engages with, Elliott mischaracterizes arguments made by market theorists, overlooks their justifications for employing unrealistic assumptions, and ignores instances where they (...) agree with his critiques and arguments. This paper examines arguments regarding the epistemology of democracy and the market, and discusses the comparative knowledge requirements each competitive system requires of its participants within the wider context of epistemic democratic theory. (shrink)

What thesis is Hume trying to establish in his essay “On Miracles” and does he succeed? John Earman’s answer to the latter question is clearly conveyed by the title of his new book. Earman uses a Bayesian representation of the problem to make his case. For Earman, this mode of analysis is both perspicuous and nonanachronistic, in that probability reasoning was central to the 18th century debate about miracles in particular and testimony in general. Indeed, one of Hume’s most interesting (...) antagonists, Richard Price, was the person to whom Thomas Bayes entrusted his now-famous essay for posthumous publication. For Earman, Price is the proper Bayesian, while Hume’s essay provides only “rhetoric and schein geld”. Earman’s tone is consistently prosecutorial and sometimes snide; he says that his animus is not so much against Hume himself as against those who smugly invoke Hume’s essay as definitively settling the matter. This tone should not deter potential readers who are convinced that Hume’s essay contains something of value. Earman’s book is interesting and provocative in multiple ways—it places Hume’s essay in its historical setting, it offers an insightful close reading of the text, and it shows how the resources of Bayesianism can be powerfully put to work. Besides Earman’s own essay, the volume also contains Hume’s essay and relevant work by others, including Locke, Spinoza, Samuel Clarke, Price, Laplace, and Babbage. The book would be an excellent choice for an advanced undergraduate or graduate seminar. (shrink)

Loyalty is considered central to people’s moral life, yet little is known about how people think about what it means to be loyal. We used a prototype approach to understand how loyalty is represented in Colombia and the United States and how these representations mediate attributions of loyalty and moral judgments of loyalty violations. Across 7 studies (N = 1,984), we found cross-cultural similarities in the associative meaning of loyalty (Study 1) but found differences in the centrality of features associated (...) with loyalty (Study 2) and the latent structure of loyalty representations (Study 3). Colombians represent loyalty in terms of more general moral characteristics, while US participants represent loyalty in terms of interpersonal commitment, both in contrast with current approaches to loyalty. By comparing representations of loyalty and honesty, we establish that difference in loyalty conceptualizations reflect a different way of thinking about loyalty rather than morality more generally (Study 4). Further, Colombians attributed greater loyalty to individuals with general moral characteristics compared to participants from the United States sample (Study 5) and were more likely to classify non-loyal values as loyalty-related (Study 6). While the centrality of prototypical features predicts categorizing norm violations as loyalty-related, differences in prototypical structure account for differences in the severity of moral judgment for such violations (Study 7), which suggests that loyalty representations have similar functions even though these representations differ in structural characteristics. (shrink)

Knowledge of mechanisms is critical for causal reasoning. We contrasted two possible organizations of causal knowledge—an interconnected causal network, where events are causally connected without any boundaries delineating discrete mechanisms; or a set of disparate mechanisms—causal islands—such that events in different mechanisms are not thought to be related even when they belong to the same causal chain. To distinguish these possibilities, we tested whether people make transitive judgments about causal chains by inferring, given A causes B and B causes C, (...) that A causes C. Specifically, causal chains schematized as one chunk or mechanism in semantic memory led to transitive causal judgments. On the other hand, chains schematized as multiple chunks led to intransitive judgments despite strong intermediate links. Normative accounts of causal intransitivity could not explain these intransitive judgments. (shrink)

In this article, I explicate Kant’s position on the wide right to abortion. That is, I explore the extent to which, according to Kant’s practical philosophy, abortion is punishable, even if it involves an unjust infringement of the right to life. By focusing on the state’s right to punish, rather than the right to life or the onset of personhood, I use Kant to expose a novel range of issues and questions about the legal status of abortion (and criminal punishment (...) more generally). The article is divided into four sections. In the first, I lay the groundwork for Kant’s theory of rights and briefly canvass some of the literature on Kantian approaches to abortion. In the second, I look at Kant’s discussion of equivocal rights. In the third, I turn to Kant’s discussions of capital punishment and suicide. In the fourth, I examine Kant on honor killings, and I use his position on infanticide in order to extrapolate and explain his ideas about the right to punish in the context of abortion. (shrink)

Adaptationism is a doctrine that has meant different things to different people. In this essay, I want to isolate and discuss a reading of adaptationism that makes it a non-trivial empirical thesis about the history of life. I'll take adaptationism to be the following claim: natural selection has been the only important cause of most of the phenotypic traits found in most species. I won't try to determine whether adaptationism, so defined, is true. Rather, my task will be one of (...) clarification. What does this statement mean, and how is it related to various remarks that biologists have made about adaptationism, pro and con? (shrink)

In ‘Two Dogmas of Empiricism’, Quine attacks the analytic/synthetic distinction and defends a doctrine that I call epistemological holism. Now, almost fifty years after the article’s appearance, what are we to make of these ideas? I suggest that the philosophical naturalism that Quine did so much to promote should lead us to reject Quine’s brief against the analytic/synthetic distinction; I also argue that Quine misunderstood Carnap's views on analyticity. As for epistemological holism, I claim that this thesis does not follow (...) from the logical point that Duhem and Quine made about the role of auxiliary assumptions in hypothesis testing, and that the thesis should be rejected. (shrink)

The story of God -- The story of the church -- The story of ethics -- The story of Christian ethics -- Universal ethics -- Subversive ethics -- Ecclesial ethics -- Good order -- Good life -- Good relationships -- Good beginnings and endings -- Good earth.

First published in 1987, Althusser, The Detour of Theory was widely received as the fullest account of its subject to date. Drawing on a wide range of hitherto untranslated material, it examined the political and intellectual contexts of Althusser's `return to Marx' in the mid-1960s and proclamaed of a `crisis of Marxism'. It concluded with a balance-sheet of Althusser's contribution to historical materialism. In this second edition, Gregory Elliott has added a substantial postscript in which he surveys the posthumous (...) edition of the French philosopher's work. (shrink)

In Improvisation, Samuel Wells defines improvisation in the theater as "a practice through which actors seek to develop trust in themselves and one another in order that they may conduct unscripted dramas without fear." Sounds a lot like life, doesn't it? Building trust, overcoming fear, conducting relationships, and making choices--all without a script. Wells establishes theatrical improvisation as a model for Christian ethics, a matter of "faithfully improvising on the Christian tradition." He views the Bible not as a "script" (...) but as a "training school" that shapes the habits and practices of the Christian community. Drawing on scriptural narratives and church history, Wells explains six practices that characterize both improvisation and Christian ethics. His model of improvisation reinforces the goal of Christian ethics--to teach Christians to "embody their faith in the practices of discipleship all the time."--Publisher description. (shrink)

Attempts to show that the simplicity of a hypothesis can be measured by attending to how well it answers certain kinds of questions.

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in ...

Person-affecting views in population ethics state that (in cases where all else is equal) we’re permitted but not required to create people who would enjoy good lives. In this paper, I present an argument against every possible variety of person-affecting view. The argument takes the form of a dilemma. Narrow person-affecting views must embrace at least one of three implausible verdicts in a case that I call ‘Expanded Non-Identity.’ Wide person-affecting views run into trouble in a case that I call (...) ‘Two-Shot Non-Identity.’ One plausible practical upshot of my argument is as follows: we individuals and our governments should be doing more to reduce the risk of human extinction this century. (shrink)

I explain and motivate the shutdown problem: the problem of creating artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I then propose a solution: train agents to have incomplete preferences. Specifically, I propose that we train agents to lack a preference between every pair of different-length trajectories. I suggest a way to train such agents using reinforcement learning: (...) we give the agent lower reward for repeatedly choosing same-length trajectories. (shrink)

Critical-set views avoid the Repugnant Conclusion by subtracting some constant from the welfare score of each life in a population. These views are thus sensitive to facts about biographical identity: identity between lives. In this paper, I argue that questions of biographical identity give us reason to reject critical-set views and embrace the total view. I end with a practical implication. If we shift our credences towards the total view, we should also shift our efforts towards ensuring that humanity survives (...) for the long term. (shrink)

I am writing on moral knowledge in Locke's Essay Concerning Human Understanding. There are two basic parts. In the first part, I articulate and attack a predominant interpretation of the Essay . This interpretation attributes to Locke the view that he did not write in the Essay anything that would be inconsistent with his early views in the Questions Concerning the Laws of Nature that there exists a single, ultimate, moral standard, i.e., the Law of Nature. For example, John Colman, (...) in his book John Locke's Moral Philosophy , argues that even though Locke explains in the Essay that we arbitrarily create our moral notions, they are still objective since they are bound together with the Law of Nature. Colman explains that the features of human nature relevant to the derivation of the Law of Nature are universally shared needs and concerns . I argue that this presupposes a view of Locke which assumes that there are essences of species independent of our beliefs about them. However, I attempt to show from the text of the Essay that this view cannot be supported. ;In the second part, I argue that the text of the Essay supports two alternative theses. The first is that given the kind of metaphysical world-view presupposed by the corpuscular method of science employed within the Essay, coupled with Locke's commitment to the possibility of moral knowledge, he was left with only one option with reference to ethics, viz., to make moral goodness or evil a mind-dependent relation between a rule and an action, instead of a property of an action or person which exists independently of our moral beliefs. This view is logically inconsistent with the existence of the Law of Nature. The second is that Locke has a semantical view of moral claims which is consistent with his relational view of moral goodness, viz., the primary function of moral judgments is to recommend behavior for ourselves and others. I described. However, Locke explains in the Essay that the opposite takes place with respect to our moral notions: events and persons must conform to the moral notion. ;On the account that I offer, Locke's views on moral epistemology are much closer to David Hume's than many have supposed, and correspondingly, anticipate the more skeptical views of moral epistemology in the twentieth century. (shrink)

Many philosophers are attracted to a complaints-based theory of the procreation asymmetry, according to which creating a person with a bad life is wrong (all else equal) because that person can complain about your act, whereas declining to create a person who would have a good life is not wrong (all else equal) because that person never exists and so cannot complain about your act. In this paper, I present two problems for such theories: the problem of impairable-life acceptance and (...) an especially acute version of the problem of improvable-life avoidance. I explain how these problems afflict two recent complaints-based theories of the procreation asymmetry, from Joe Horton and Abelard Podgorski. (shrink)

[Elliott Sober] In 'Two Dogmas of Empiricism', Quine attacks the analytic/synthetic distinction and defends a doctrine that I call epistemological holism. Now, almost fifty years after the article's appearance, what are we to make of these ideas? I suggest that the philosophical naturalism that Quine did so much to promote should lead us to reject Quine's brief against the analytic/synthetic distinction; I also argue that Quine misunderstood Carnap's views on analyticity. As for epistemological holism, I claim that this thesis (...) does not follow from the logical point that Duhem and Quine made about the role of auxiliary assumptions in hypothesis testing, and that the thesis should be rejected. \\\ [Peter Hylton] Section I of this essay discusses Quine's views about reference, contrasting them with those of Russell. For the latter, our language and thought succeed in being about the world because of our acquaintance with objects; the relation of reference-roughly, the relation between a name and its bearer-is thus fundamental. For Quine, by contrast, the fundamental relation by which our language comes to be about the world, and to have empirical content, is that between a sentence and stimulations of our sensory surfaces; reference, while important, is a derivative notion. Section II shows how this view of reference as derivative makes possible the notorious Quinean doctrine of ontological relativity. Section III raises the issue of realism. It argues that somewhat different notions of realism are in play for Quine and for Russell-for Russell, objects, and our knowledge of objects, play the fundamental role, while for quine objectivity and truth are fundamental, with ontology being derivative. (shrink)

I explain the shutdown problem: the problem of designing artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I prove three theorems that make the difficulty precise. These theorems show that agents satisfying some innocuous-seeming conditions will often try to prevent or cause the pressing of the shutdown button, even in cases where it’s costly to do so. And (...) patience trades off against shutdownability: the more patient an agent, the greater the costs that agent is willing to incur to manipulate the shutdown button. I end by noting that these theorems can guide our search for solutions. (shrink)

According to Critical-Level Views in population axiology, an extra life improves a population only if that life’s welfare exceeds some fixed ‘critical level.’ An extra life at the critical level leaves the new population equally good as the original. According to Critical-Range Views, an extra life improves a population only if that life’s welfare exceeds some fixed ‘critical range.’ An extra life within the critical range leaves the new population incommensurable with the original. -/- In this paper, I sharpen some (...) old objections to these views and offer some new ones. Critical-Level Views cannot avoid certain Repugnant and Sadistic Conclusions. Critical-Range Views imply that lives featuring no good or bad components whatsoever can nevertheless swallow up and neutralise goodness or badness. Both classes of view entail that certain small changes in welfare correspond to worryingly large differences in contributive value. -/- I then offer a view that retains much of the appeal of Critical-Level and Critical-Range Views while avoiding the above pitfalls. On the Imprecise Exchange Rates View, the quantity of some good required to outweigh a given unit of some bad is imprecise. This imprecision is the source of incommensurability between lives and populations. (shrink)

In 'Two Dogmas of Empiricism', Quine attacks the analytic/synthetic distinction and defends a doctrine that I call epistemological holism. Now, almost fifty years after the article's appearance, what are we to make of these ideas? I suggest that the philosophical naturalism that Quine did so much to promote should lead us to reject Quine's brief against the analytic/synthetic distinction; I also argue that Quine misunderstood Carnap's views on analyticity. As for epistemological holism, I claim that this thesis does not follow (...) from the logical point that Duhem and Quine made about the role of auxiliary assumptions in hypothesis testing, and that the thesis should be rejected. \\\ [Peter Hylton] Section I of this essay discusses Quine's views about reference, contrasting them with those of Russell. For the latter, our language and thought succeed in being about the world because of our acquaintance with objects; the relation of reference-roughly, the relation between a name and its bearer-is thus fundamental. For Quine, by contrast, the fundamental relation by which our language comes to be about the world, and to have empirical content, is that between a sentence and stimulations of our sensory surfaces; reference, while important, is a derivative notion. Section II shows how this view of reference as derivative makes possible the notorious Quinean doctrine of ontological relativity. Section III raises the issue of realism. It argues that somewhat different notions of realism are in play for Quine and for Russell-for Russell, objects, and our knowledge of objects, play the fundamental role, while for quine objectivity and truth are fundamental, with ontology being derivative. (shrink)

Lexical views in population axiology can avoid the Repugnant Conclusion without violating Transitivity or Separability. However, they imply a dilemma: either some good life is better than any number of slightly worse lives, or else the ‘at least as good as’ relation on populations is radically incomplete. In this paper, I argue that Archimedean views face an analogous dilemma. I thus conclude that the lexical dilemma gives us little reason to prefer Archimedean views. Even if we give up on lexicality, (...) problems of the same kind remain. (shrink)

Common wisdom holds that communication is impossible when messages are costless and communicators have totally opposed interests. This article demonstrates that such wisdom is false. Non-convergent dynamics can sustain partial information transfer even in a zero-sum signalling game. In particular, I investigate a signalling game in which messages are free, the state-act payoffs resemble rock–paper–scissors, and senders and receivers adjust their strategies according to the replicator dynamic. This system exhibits Hamiltonian chaos and trajectories do not converge to equilibria. This persistent (...) out-of-equilibrium behaviour results in messages that do not perfectly reveal the sender's private information, but do transfer information as quantified by the Kullback–Leibler divergence. This finding shows that adaptive dynamics can enable information transmission even though messages at equilibria are meaningless. This suggests a new explanation for the evolution or spontaneous emergence of meaning: non-convergent adaptive dynamics. (shrink)

How should the concept of evidence be understood? And how does the concept of evidence apply to the controversy about creationism as well as to work in evolutionary biology about natural selection and common ancestry? In this rich and wide-ranging book, Elliott Sober investigates general questions about probability and evidence and shows how the answers he develops to those questions apply to the specifics of evolutionary biology. Drawing on a set of fascinating examples, he analyzes whether claims about intelligent (...) design are untestable; whether they are discredited by the fact that many adaptations are imperfect; how evidence bears on whether present species trace back to common ancestors; how hypotheses about natural selection can be tested, and many other issues. His book will interest all readers who want to understand philosophical questions about evidence and evolution, as they arise both in Darwin's work and in contemporary biological research. (shrink)

Arrhenius’s impossibility theorems purport to demonstrate that no population axiology can satisfy each of a small number of intuitively compelling adequacy conditions. However, it has recently been pointed out that each theorem depends on a dubious assumption: Finite Fine-Grainedness. This assumption states that there exists a finite sequence of slight welfare differences between any two welfare levels. Denying Finite Fine-Grainedness makes room for a lexical population axiology which satisfies all of the compelling adequacy conditions in each theorem. Therefore, Arrhenius’s theorems (...) fail to prove that there is no satisfactory population axiology. In this paper, I argue that Arrhenius’s theorems can be repurposed. Since all of our population-affecting actions have a non-zero probability of bringing about more than one distinct population, it is population prospect axiologies that are of practical relevance, and amended versions of Arrhenius’s theorems demonstrate that there is no satisfactory population prospect axiology. These impossibility theorems do not depend on Finite Fine-Grainedness, so lexical views do not escape them. (shrink)

This book is a benchmark critique of Freudian theory in which a dialogue between the Frankfurt School, the Lacanian tradition and post-Lacanian developments in critical and feminist theory is developed. Considering afresh the relations between self and society, Elliot argues for the importance of imagination and the unconscious in understanding issues about the self and self-identity, ideology and power, sexual difference and gender. The second edition surveys the recent changes that have taken place in psychoanalytic social theory.

_Current Controversies in Values and Science_ asks ten philosophers to debate five questions that are driving contemporary work in this important area of philosophy of science. The book is perfect for the advanced student, building up her knowledge of the foundations of the field while also engaging its most cutting-edge questions. Introductions and annotated bibliographies for each debate, preliminary descriptions of each chapter, study questions, and a supplemental guide to further controversies involving values in science help provide clearer and richer (...) snapshots of active controversies for all readers._ _. (shrink)

This Element analyzes the various forms that design arguments for the existence of God can take, but the main focus is on two such arguments. The first concerns the complex adaptive features that organisms have. Creationists who advance this argument contend that evolution by natural selection cannot be the right explanation. The second design argument - the argument from fine-tuning - begins with the fact that life could not exist in our universe if the constants found in the laws of (...) physics had values that differed more than a little from their actual values. Since probability is the main analytical tool used, the book provides a primer on probability theory. (shrink)

Reconstructing the Past seeks to clarify and help resolve the vexing methodological issues that arise when biologists try to answer such questions as whether human beings are more closely related to chimps than they are to gorillas. It explores the case for considering the philosophical idea of simplicity/parsimony as a useful principle for evaluating taxonomic theories of evolutionary relationships. For the past two decades, evolutionists have been vigorously debating the appropriate methods that should be used in systematics, the field that (...) aims at reconstructing phylogenetic relationships among species. This debate over phylogenetic inference, Elliott Sober observes, raises broader questions of hypothesis testing and theory evaluation that run head on into long standing issues concerning simplicity/parsimony in the philosophy of science. Sober treats the problem of phylogenetic inference as a detailed case study in which the philosophical idea of simplicity/parsimony can be tested as a principle of theory evaluation. Bringing together philosophy and biology, as well as statistics, Sober builds a general framework for understanding the circumstances in which parsimony makes sense as a tool of phylogenetic inference. Along the way he provides a detailed critique of parsimony in the biological literature, exploring the strengths and limitations of both statistical and nonstatistical cladistic arguments. (shrink)

Akaike's framework for thinking about model selection in terms of the goal of predictive accuracy and his criterion for model selection have important philosophical implications. Scientists often test models whose truth values they already know, and they often decline to reject models that they know full well are false. Instrumentalism helps explain this pervasive feature of scientific practice, and Akaike's framework helps provide instrumentalism with the epistemology it needs. Akaike's criterion for model selection also throws light on the role of (...) parsimony considerations in hypothesis evaluation. I explain the basic ideas behind Akaike's framework and criterion; several biological examples, including the use of maximum likelihood methods in phylogenetic inference, are considered. (shrink)

Ockham's razor, the principle of parsimony, states that simpler theories are better than theories that are more complex. It has a history dating back to Aristotle and it plays an important role in current physics, biology, and psychology. The razor also gets used outside of science - in everyday life and in philosophy. This book evaluates the principle and discusses its many applications. Fascinating examples from different domains provide a rich basis for contemplating the principle's promises and perils. It is (...) obvious that simpler theories are beautiful and easy to understand; the hard problem is to figure out why the simplicity of a theory should be relevant to saying what the world is like. In this book, the ABCs of probability theory are succinctly developed and put to work to describe two 'parsimony paradigms' within which this problem can be solved. (shrink)