Purpose: The purpose of this article is to examine the unique challenges faced by choir directors in Ghana and provide recommendations for managing and thriving in this context. It aims to highlight the importance of resilience, resourcefulness, and cultural sensitivity in navigating the funding constraints, limited resources, intense competition, and cultural expectations that characterize the Ghanaian choir environment. Methodology: The methodology used in this article is not explicitly stated. However, the recommendations and insights provided are based on a combination of (...) scholarly research, professional experiences, and observations related to choir management in Ghana. The authors gathered data through a literature review, interviews, and observations to understand the challenges faced by choir directors and identify effective strategies for managing them. Findings: The findings of this study suggest that choir directors in Ghana can overcome challenges and contribute to the country's musical heritage by implementing specific strategies. These include seeking diverse funding sources, engaging with local businesses, cultural organizations, and government agencies for financial support, promoting the unique qualities of their choirs, and emphasizing cultural authenticity, repertoire diversity, and innovative performances to attract audiences and sponsors. Recommendations: The theoretical ideas that informed this article's recommendations and the actual experiences that took place in the Ghanaian choir context validated them. The authors likely drew upon their expertise, scholarly research, and consultation with practitioners to develop and validate these recommendations. They should seek diverse funding sources, engage with local businesses and organizations, and promote the unique qualities of their choirs to attract audiences and sponsors. Policymakers are encouraged to support the development and sustainability of choirs in Ghana by recognizing their cultural significance and providing financial and logistical support. Policies that promote the arts, cultural preservation, and community engagement can contribute to the growth and success of choirs. Additionally, policies addressing funding constraints and resource limitations can alleviate some of the challenges faced by choir directors, enabling them to thrive and contribute to Ghana's musical landscape. The article aims to inspire and guide directors in managing choirs in Ghana, highlighting the potential for cultural enrichment and artistic excellence within this unique context. (shrink)

In the paper Randomizations of Scattered Sentences, Keisler showed that if Martin’s axiom for aleph one holds, then every scattered sentence has few separable randomizations, and asked whether the conclusion could be proved in ZFC alone. We show here that the answer is “yes”. It follows that the absolute Vaught conjecture holds if and only if every \-sentence with few separable randomizations has countably many countable models.

First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.

People increasingly form beliefs based on information gained from automatically filtered Internet ‎sources such as search engines. However, the workings of such sources are often opaque, preventing ‎subjects from knowing whether the information provided is biased or incomplete. Users’ reliance on ‎Internet technologies whose modes of operation are concealed from them raises serious concerns about ‎the justificatory status of the beliefs they end up forming. Yet it is unclear how to address these concerns ‎within standard theories of knowledge and justification. (...) To shed light on the problem, we introduce a ‎novel conceptual framework that clarifies the relations between justified belief, epistemic responsibility, ‎action, and the technological resources available to a subject. We argue that justified belief is subject to ‎certain epistemic responsibilities that accompany the subject’s particular decision-taking circumstances, ‎and that one typical responsibility is to ascertain, so far as one can, whether the information upon which ‎the judgment will rest is biased or incomplete. What this responsibility comprises is partly determined by ‎the inquiry-enabling technologies available to the subject. We argue that a subject’s beliefs that are ‎formed based on Internet-filtered information are less justified than they would be if she either knew how ‎filtering worked or relied on additional sources, and that the subject may have the epistemic ‎responsibility to take measures to enhance the justificatory status of such beliefs.‎. (shrink)

In the age of the `return to the empirical' in which the theoretical disputes of an earlier era seem to have fallen silent, we seek to excavate the intellectual conditions for reviving theoretical debate, for it is upon this recovery that deeper understanding of the nature and purpose of empirical social science depends. We argue against the all too frequent turn to ontology, whereby critical realists have sought an epistemological guarantor of sociological validity. We seek, to the contrary, to crystallize (...) a culturally-based, hermeneutic account of a rational social science. Derived from disputes within the sociology of culture, on the one hand, and the long-standing concerns of interpretive philosophy, on the other, we offer a cultural-sociological approach to epistemology. We view the production of truth in social science as a reading of a meaningful social world, and as a performance of truth-claims that is constrained by evidence, but whose success depends on other contextual factors. We conclude that the rationality of social science can be achieved only by forgoing ontology. Theories are abstractions of investigators' meanings that allow the interpretation of social meanings in turn, whether those are actions, relations, or structures. Successful explanations are those that intertwine these meaning structures of investigators and actors in an effective way. (shrink)

Information providing and gathering increasingly involve technologies like search ‎engines, which actively shape their epistemic surroundings. Yet, a satisfying account ‎of the epistemic responsibilities associated with them does not exist. We analyze ‎automatically generated search suggestions from the perspective of social ‎epistemology to illustrate how epistemic responsibilities associated with a ‎technology can be derived and assigned. Drawing on our previously developed ‎theoretical framework that connects responsible epistemic behavior to ‎practicability, we address two questions: first, given the different technological ‎possibilities available (...) to searchers, the search technology, and search providers, ‎who should bear which responsibilities? Second, given the technology’s ‎epistemically relevant features and potential harms, how should search terms be ‎autocompleted? Our analysis reveals that epistemic responsibility lies mostly with ‎search providers, which should eliminate three categories of autosuggestions: those ‎that result from organized attacks, those that perpetuate damaging stereotypes, and ‎those that associate negative characteristics with specific individuals.‎. (shrink)

Ectogenesis, or “artificial womb technology,” has been heralded by some, such as prominent feminist Shulamith Firestone, as a way to liberate women. In this chapter, we challenge this view by offering an alternative analysis of the technology as relying upon and perpetuating a problematic model of pregnancy which, rather than liberating women, serves to devalue them. We look to metaphysics as the abstract study of reality to elucidate how the entities in a pregnancy are related to one another. We consider (...) two models of the metaphysics of pregnancy: (1) the Parthood Model, whereby the fetus is a part of what/who gestates it; and (2) and the Fetal Container Model, whereby the gestator is a container for the fetus. We suggest that under the assumption of the Fetal Container Model, we are more likely to think that any container will suffice for gestation, even an artificial one. In contrast, under the assumption of the Parthood Model, we are less likely to treat the gestator as interchangeable or replaceable, given the parthood relationship between gestator and fetus. This chapter argues that ectogenesis is conceptually linked to the Fetal Container Model and advocates a more cautious approach in promoting ectogenesis as a tool for women’s liberation. (shrink)

Mill defines utilitarianism as the combination of a “theory of life” and a moral claim: only pleasure and freedom from pain are desirable as ends, and the promotion of happiness is the sole goal of moral action. So defined, utilitarianism is open to ad hominem pessimistic objection: a “theory of life” which entails the impossibility of happiness fits poorly with a morality centered on its promotion. The first two challenges Mill confronts in Utilitarianism share this pessimistic structure. Interestingly, however, these (...) challenges paint inverted pictures of the best utilitarian life: one suggests this life is satisfying but ignoble, the other that it is noble but unsatisfying. I explain Mill's treatment of both challenges as genuinely pessimistic interpretations of utilitarianism's “theory of life.” Read through the lens of Mill's engagement with pessimism, these challenges point to distinctive conceptions of dignity and satisfaction that play a significant role in Mill's ethics. (shrink)

Conceptual engineering is commonly characterized as the method for assessing and improving our representational devices. Little has been said, however, on how best to construe these representational devices—in other words, on what conceptual engineering should be all about. This paper tackles this problem with a basic strategy: First, by presenting a taxonomy of the different possible subject matters for conceptual engineering; then, by comparatively assessing them and selecting the most conducive one with a view to making conceptual engineering an actionable (...) method, that is, a method that can be applied effectively and consistently to specific case studies. The outcome is that conceptual engineering should be all about concepts on pain of pragmatic inconsistencies otherwise. (shrink)

This article will argue that the church is the mystic body of Christ that believers must guard from purveyors bend on twisting the truth. There is no doubt that the Catholic social teaching on medical and moral matters has proven to be pertinent and applicable to the ever-changing circumstances of health care and its delivery. In response to today’s challenges, these same moral principles of Catholic teaching provide the rationale and direction for the community of faith. In times of coronavirus (...) characterized by falsehoods, the truth is a virtue the church must strive for: “… If you abide in My word, you are My disciples indeed. And you shall know the truth, and the truth shall make you free.”(John 8: 31-32). The truth is Christ; it is Christological. Christians must understand the clash of worldviews that is changing the face of Zimbabwean society. A worldview is simply the sum total of our beliefs about the world; Christianity is a worldview that directs our daily decisions and actions. Worldviews affect the way we think. A worldview is a well-reasoned framework of beliefs and convictions that gives a true and unified perspective on the meaning of human existence. To paraphrase from the book of First Samuel (16: 7) – to see as God sees and not how the world sees. Beliefs are not simple propositions held inside us which drive our outward behaviour in predictable ways, they are more of acts of commitment than anything else. There is no doubt that the future of Catholicism lies in the hands of the church’s leadership and the believing Christians. Catholics look to their faith leaders for guidance on big decisions as regards COVID-19 issues. Conspiracy theories around COVID-19 deny that the COVID-19 pandemic is a biological virus. Catholics require direction from the Pope down to the episcopal leadership to chart the way forward. A worldview not only impacts how one understands and makes sense of the world but also influences how one expresses oneself in the world. The constellation of personal values, beliefs, assumptions, attitudes, and ideas that make up our worldview have an effect on our understanding of reality. Coronavirus has caused uncertainty among believers and confusion as to how to cope with the complex problems that arise in COVID-19 related issues. This article will aver that the nature of drawing the contours of catholicity regarding the biblical foundations of the health falls in the hands of orthodox Catholic teachings. (shrink)

Schopenhauer repeatedly claims that all pleasure is negative, and this view seems to play key roles throughout his work. Nonetheless, many scholars have argued that Schopenhauer actually acknowledges certain positive pleasures. Two major arguments have been offered for this reading, one focused on the link between Schopenhauer's view of pleasure and Plato's, and one focused on Schopenhauer's distinction between two components of aesthetic pleasure. I argue that neither way of motivating the positive pleasure reading succeeds. Both overlook a key aspect (...) of Schopenhauer's account: namely, his suggestion that there are two distinct kinds of negative pleasure, pleasures of satisfaction and pleasures of distraction. When Schopenhauer claims that all pleasure is negative, he means it. (shrink)

For a locally compact group G, we show that it is possible to present the class of continuous unitary representations of G as an elementary class of metric structures, in the sense of continuous logic. More precisely, we show how nondegenerate ∗-representations of a general ∗-algebra A (with some mild assumptions) can be viewed as an elementary class, in a many-sorted language, and use the correspondence between continuous unitary representations of G and nondegenerate ∗-representations of L1(G). We relate the notion (...) of ultraproduct of logical structures, under this presentation, with other notions of ultraproduct of representations appearing in the literature, and we characterize property (T) for G in terms of the definability of the sets of fixed points of L1 functions on G. (shrink)

We study ultraproducts of finite residue rings \ where \ is a non-principal ultrafilter. We find sufficient conditions of the ultrafilter \ to determine if the resulting ultraproduct \ has simple, NIP, \ but not simple nor NIP, or \ theory, noting that all these four cases occur.

In this paper I offer an analysis of Plotinus’ argument for the existence of a quasi-psychic entity, the so-called ‘trace of soul’, that functions as an immanent cause of life for an organism’s body. I argue that Plotinus posits this entity primarily in order to account for the body’s possession of certain quasi-psychic states that are instrumental in his account of soul-body interaction. Since these quasi-psychic states imply that an organism’s body has vitality of its own , and Platonic souls (...) are no part or aspect of any body, Plotinus draws the conclusion that the soul must be a cause of the body’s life by imparting a quasi-psychic qualification to it. In so doing, Plotinus introduces elements of hylomorphism into Platonist psychology, and addresses a problem for the animation of the body that Platonic soul-body dualism may plausibly be thought to face. (shrink)

On the dominant interpretation, Schopenhauer possesses a will to will view of boredom: boredom consists in the dissatisfaction of a second-order desire to pursue objects of first-order desire. I ch...

How to accept a conditional? F. P. Ramsey proposed the following test in (Ramsey 1990).(RT) If A, then B must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B.

A foundational idea of evo‐devo is that morphological variation is not isotropic, that is, it does not occur in all directions. Instead, some directions of morphological variation are more likely than others from DNA‐level variation and these largely depend on development. We argue that this evo‐devo perspective should apply not only to morphology but to evolution at all phenotypic levels. At other phenotypic levels there is no development, but there are processes that can be seen, in analogy to development, as (...) constructing the phenotype (e.g., protein folding, learning for behavior, etc.). We argue that to explain the direction of evolution two types of arguments need to be combined: generative arguments about which phenotypic variation arises in each generation and selective arguments about which of it passes to the next generation. We explain how a full consideration of the two types of arguments improves the explanatory power of evolutionary theory. Also see the video abstract here: https://youtu.be/Egbvma_uaKc. (shrink)

We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. In the process, we show that a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary imaginaries, a fact which is new even for discrete first-order real rosy theories.

While the evidential problem of evil has been enormously influential within the contemporary philosophical literature—William Rowe’s 1979 formulation in “The Problem of Evil and Some Varieties of Atheism” being the most seminal—no academic research has explored what cognitive mechanisms might underwrite the appearance of pointlessness in target examples of suffering. In this exploratory paper, we show that the perception of pointlessness in the target examples of suffering that underwrite Rowe’s seminal formulation of the problem of evil is contingent on the (...) absence of broader context. In other words, we show that when such suffering is presented alongside broader contextual information, the appearance of pointlessness, on average, significantly diminishes. In §1 we briefly elucidate Rowe’s formulation of the problem of evil and the thought experiment that motivates a key premise. In §2 and §3 respectively, we briefly explain our hypothesis regarding Rowe’s case and our methods for testing these hypotheses. In §4, we elucidate our results, and in §5 we explore some of the philosophical implications of our findings and gesture towards some areas for future research. Finally, in §6, we briefly connect our research to some of the established philosophical literature on suffering and narrative before concluding. (shrink)

Mechanism realists assert the existence of mechanisms as objective structures in the world, but their exact metaphysical commitments are unclear. We introduce Local Hierarchy Realism (LHR) as a substantive and plausible form of mechanism realism. The limits of LHR reveal a deep tension between two aspects of mechanists’ explanatory strategy. Functional decomposition identifies locally relevant entities and activities, while these same entities and activities are also embedded in a nested hierarchy of levels. In principle, a functional decomposition may identify entities (...) engaging in causal interactions that crosscut the hierarchical structure of composition relations, violating the mechanist’s injunction against interlevel causation. We argue that this possibility is realized in the example of ephaptic coupling, a subsidiary process of neural computation that crosscuts the hierarchy derived from synaptic transmission. These considerations undermine the plausibility of LHR as a general view, yet LHR has the advantages that (i) its metaphysical implications are precisely stateable; (ii) the structure it identifies is not reducible to mere aggregate causation; and (iii) it clearly satisfies intuitive and informal definitions of mechanism. We conclude by assessing the prospects for a form of mechanism realism weaker than LHR that nevertheless satisfies all three of these requirements. (shrink)

Traces the decentered formulation of self at the heart of Paul Ricoeur's philosophy from his earliest works to his most recent.

In this paper, I investigate the foundations of Plotinus’ innovative theory that prime matter is unaffectable. I begin by showing that Plotinus’ main arguments for this thesis (in Ennead 3.6) all rely upon the controversial assumption that the properties prime matter underlies are not properties of prime matter itself. It is then argued that prime matter’s privation of sensible qualities has its conceptual basis in an idiosyncratic understanding of form-matter composition generally, and its primary doctrinal basis in Aristotle’s critical reports (...) on the Platonists’ substratum in Physics 1.9. While Plotinus finds Platonic authority for unaffectible matter in the Receptacle passage of the Timaeus, it is Aristotle’s testimony that provides the crucial impetus for reading that text in this way. On this basis, Plotinus develops a Platonist conception of form’s inherence in matter with distinctively non-Aristotelian features. (shrink)

We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic intuitions in (...) the works of, among others, Quine and Ullian (1978), Levi (1980, 1991), Harman (1988) and Gärdenfors (1988), formal accounts of belief change (AGM, KM – see Gärdenfors (1988); Katsuno and Mendelzon (1991)) have abandoned both principles (see Rott (2000)). We argue for the principles and we show how to construct a contraction operation, which obeys both. An axiom system is proposed. We also prove that the decision-theoretic notion of contraction can be completely characterized in terms of the given axioms. Proving this type of completeness result is a well-known open problem in the field, whose solution requires employing both decision-theoretical techniques and logical methods recently used in belief change. (shrink)

Dominant normative theories of armed conflict orientate themselves around the ultimate goal of peace. Yet the deployment of these theories in the international sphere appears to have failed in advancing toward this goal. In this paper, we argue that one major reason for this failure is these theories’ use of essentially contested concepts—that is, concepts whose internally complex character results in no principled way of adjudicating between rival interpretations of them. This renders the theories susceptible to manipulation by international actors (...) who are able to pursue bellicose policies under the cover of nominally pacific frameworks, and we show how this happened historically in a case study of the Korean War of 1950–1953. In order to better serve the goals of peace, we suggest, the rules of war should be reframed to simpler, but more restrictive, normative principles. (shrink)

Una respuesta al debate metafilosófico sobre si hay o no unos criterios regulativos en filosofía cómo área de investigación lo ofrece la denominada filosofía sintética. Dentro de esta posición se propone una forma de abordar toda la filosofía y teorizar en base a diferentes criterios propuestos, que suelen ser generalmente: la claridad semántica, la coherencia interna, la coherencia externa con las ciencias y la fecundidad teórica con otros campos de estudio. Estos criterios de corte naturalista a su vez se ofrecen (...) como debatibles y ampliables a otros criterios. Se razonará la necesidad de demarcar la filosofía, y, poniendo el foco en su metodología, se argumentarán los previos criterios con tal de fomentar la filosofía sintética como marco general de trabajo filosófico riguroso. Esto excluye de la disciplina tanto aquello que no sea filosófico como aquello que intente emular la filosofía sin serlo en verdad, la pseudofilosofía. (shrink)

We conducted a scoping review to ascertain the landscape of ethics regulations for AD/ADRD research in Africa using Arksey and O'Malley's framework. We sourced regulations from the International Compilation of Human Research Standards. We included regulations from 14 countries published between 1997 and 2020. Provisions in the regulations applicable to research in AD/ADRD were part of broader sub-provisions for research such as with persons under legal disability. Regulations mostly required the appointment of Legally Authorised Representatives, as a major protection for (...) persons with AD/ADRD. Provisions supporting capacity assessment and advance directives were only provided in regulations from five and two countries respectively. No regulation cited the Convention on the Rights of Persons with Disabilities as a foundational instrument for its provisions. In conclusion, regulations specifically applicable to research among AD/ADRD or other cognitively impaired persons in Africa are scarce and provisions in existing regulations mostly lack specificity for practical implementation. (shrink)

There is an important class of conditionals whose assertibility conditions are not given by the Ramsey test but by an inductive extension of that test. Such inductive Ramsey conditionals fail to satisfy some of the core properties of plain conditionals. Associated principles of nonmonotonic inference should not be assumed to hold generally if interpretations in terms of induction or appeals to total evidence are not to be ruled out.

Plotinus maintains that there is a single first principle, the One (or the Good), from which all other things derive. He is usually thought to hold this view on the grounds that any other thing’s existence depends on its participation in a paradigm of unity. This paper argues that Plotinus has a further, independent argument for adopting a single first principle, according to which principle pluralism is committed (unacceptably) to attributing good cosmic states of affairs to chance. This argument exhibits (...) similarities to ancient design arguments, but is used to draw the more radical conclusion that there is only one non-derivative existent. (shrink)

In developing his theory of aether in De Caelo 1, Aristotle argues, in DC 1.4, that one circular motion cannot be contrary to another. In this paper, I discuss how Aristotle can maintain this position and accept the existence of celestial spheres that rotate in contrary directions, as he does in his revision of the Eudoxan theory in Metaphysics 12.8.

Mechanistic explanation involves the attribution of functions to both mechanisms and their component parts, and function attribution plays a central role in the individuation of mechanisms. Our aim in this paper is to investigate the impact of a perspectival view of function attribution for the broader mechanist project, and specifically for realism about mechanistic hierarchies. We argue that, contrary to the claims of function perspectivalists such as Craver, one cannot endorse both function perspectivalism and mechanistic hierarchy realism: if functions are (...) perspectival, then so are the levels of a mechanistic hierarchy. We illustrate this argument with an example from recent neuroscience, where the mechanism responsible for the phenomenon of ephaptic coupling cross-cuts the more familiar mechanism for synaptic firing. Finally, we consider what kind of structure there is left to be realist about for the function perspectivalist. (shrink)

The paper includes a series of letters exchanged between the author and the late Professor Feyerabend, concerning the best "method" for military intelligence, as a test case for the role of conceptual frameworks in philosophy of science. The letters deal with issues like: Is it possible to make an intelligence estimate without a conceptual framework? Does such a framework have any 'positive' role? If so, how should a conceptual framework in intelligence be built? What risks lurk within it? Is it (...) possible to indicate methods for intelligence estimates which are 'better' and more 'successful' than others? (shrink)

We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric structure. As the truth value of a sentence of continuous logic may be any real in [0, 1], we introduce two kinds of diagrams at each level: the closed diagram, which encapsulates weak inequalities of the form $$\phi ^\mathcal {M}\le r$$, and the open diagram, which encapsulates strict inequalities of the form $$\phi ^\mathcal {M}< r$$. We show (...) that the closed and open $$\Sigma _N$$ diagrams are $$\Pi ^0_{N+1}$$ and $$\Sigma ^0_N$$ respectively, and that the closed and open $$\Pi _N$$ diagrams are $$\Pi ^0_N$$ and $$\Sigma ^0_{N + 1}$$ respectively. We then introduce effective infinitary formulas of continuous logic and extend our results to the hyperarithmetical hierarchy. Finally, we demonstrate that our results are optimal. (shrink)

A replicator is simply something that makes copies of itself. There are hypothetical replicators (e.g., self-catalyzing chemical cycles) that are suspected to be unable to exhibit heritable variation. Variation in any of their constituent molecules would not lead them to produce offspring with those new variant molecules. Copying, such as in DNA replication or in xerox machines, allows any sequence to be remade and then sequence variations to be inherited. This distinction has been used against non-RNA-world hypotheses: without RNA replication (...) systems have no capacity to exhibit heritable variation. However, is copying the only way to have heritable variation? This article suggests that evolution can happen without anything being copied and that, in fact, RNA copying is too complex to arise spontaneously as the first pre-biotic system. There would then be a historical gradation of systems from non-alive to alive in which the capacity to have heritable changes would progressively increase and in which copying, as in template-based RNA-replication, would be a crucial but relatively late event. In addition, this article proposes a way by which RNA replication could have arisen, after systems able to evolve arose, as a crucial innovation and how that innovation spread over existing evolutionary systems and became a major driver of subsequent evolution. (shrink)

Científicos del sistema Tierra han demostrado que el planeta es un sistema adaptativo-complejo y que algunos procesos naturales ya no operan en condiciones seguras para preservar la vida. Destaca que poco se ha hecho por explorar las implicaciones en la arena jurídica para responder ante los retos que estas condiciones presuponen para la vida humana y para nuestra supervivencia como especie. Aquí se sostiene que, para mantener el buen funcionamiento planetario, se requiere de una articulación efectiva entre el razonamiento jurídico, (...) su argumentación y la ciencia del sistema Tierra. Al hacer una exploración de la literatura jurídica y del sistema Tierra, este artículo tiene como objetivo exponer el primer esfuerzo sobre cómo debería adaptarse el razonamiento jurídico y su argumentación a un enfoque del sistema Tierra, utilizando para ello diferentes casos de estudio, resoluciones y tesis jurisprudenciales. Al hacerlo, se exhibe la necesidad de erradicar concepciones erróneas subyacentes al antropocentrismo jurídico, para ajustar la interpretación y aplicación del derecho a realidades ecológicas científicamente más precisas. (shrink)