Carey leaves unaddressed an important evolutionary puzzle: In the absence of a numeral list, how could a concept of natural number ever have arisen in the first place? Here we suggest that the initial development of natural number must have bootstrapped on a material culture scaffold of some sort, and illustrate how this might have occurred using strings of beads.

Cognitive archaeology is a relatively new interdisciplinary science that uses cognitive and psychological models to explain archaeological artifacts like stone tools, figurines, and art. Edited by cognitive archaeologist Karenleigh A. Overmann and psychologist Frederick L. Coolidge, Squeezing Minds From Stones is a collection of essays, from both early pioneers and 'up and coming' newcomers in the field, that addresses a wide variety of cognitive archaeology topics, including the value of experimental archaeology, primate archaeology, the intent of ancient tool makers, (...) and how they may have lived and thought. (shrink)

"Ethical thought has no chance of being everything it seems." Bernard Williams offered this cryptic remark in Ethics and the Limits of Philosophy, and in this chapter I argue that understanding it is the key to understanding Williams' skepticism about moral theory and about systematization in ethics. The difficulty for moral philosophy, Williams believed, is that ethics looks one way to embodied, active agents, but looks entirely different when considered from the standpoint of theory. This, in turn, means that following (...) a moral theory is a sure route to practical alienation. I argue that once we see it for what it is, we can see that Williams own skepticism undermines his later attempts to vindicate Truthfulness. Moreover, given the pervasiveness of reflective practical alienation in ordinary life, it leaves us with a difficult question: what would a non-alienated ethical existence even look like for us? (shrink)

This reissue of his collection of early essays, Logico-Linguistic Papers, is published with a brand new introduction by Professor Strawson but, apart from minor ...

In this paper, I critically analyze the notion that self-interest distorts moral belief-formation. This belief is widely shared among modern moral epistemologists, and in this paper, I seek to undermine this near consensus. I then offer a principle which can help us to sort cases in which self-interest distorts moral belief from cases in which it does not. As it turns out, we cannot determine whether such distortion has occurred from the armchair; rather, we must inquire into mechanisms of social (...) power and advantage before declaring that some moral position is distorted by self-interest. (shrink)

David Benatar has argued both for anti-natalism and for a certain pessimism about life's meaning. In this paper, I propose that these positions are expressions of a deeply impersonal philosophical temperament. This is not a problem on its own; we all have our philosophical instincts. The problem is that this particular temperament, I argue, leads Benatar astray, since it prevents him from answering a question that any moral philosopher must answer. This is the question of rational authority, which requires the (...) moral philosopher to say why existing human agents have strong practical reasons to comply with the philosopher's dictates. A purely impersonal ethical system can never do this, and this is why Benatar has no answer to this question. (shrink)

Analytic moral philosophers have generally failed to engage in any substantial way with the cultural history of morality. This is a shame, because a genealogy of morals can help us accomplish two important tasks. First, a genealogy can form the basis of an epistemological project, one that seeks to establish the epistemic status of our beliefs or values. Second, a genealogy can provide us with functional understanding, since a history of our beliefs, values or institutions can reveal some inherent dynamic (...) or pattern which may be problematically obscured from our view. In this paper, I try to make good on these claims by offering a sketchy genealogy of emancipatory values, or values which call for the liberation of persons from systems of dominance and oppression. The real history of these values, I argue, is both epistemologically vindicatory and functionally enlightening. (shrink)

That about sums up what is wrong with Clark's view.

Hannah Arendt disavowed the title of “philosopher,” and is known above all as a political theorist. But the relationship between philosophy and politics animates her entire oeuvre. We find her addressing the topic in The Human Condition (1958), in Between Past and Future (a collection of essays written in the early 1960s), and in Men in Dark Times (another collection of essays, this one from the late sixties). It is treated in her Lectures on Kant’s Political Philosophy, composed during the (...) seventies, and also in the posthumous Life of the Mind, two of three projected volumes of which were complete when she died in 1975. Certainly, Arendt’s thought cannot be understood without taking into account her deep suspicion of and equally deep commitment to philosophy in the context of political reflection. For all that, her writings on this abiding preoccupation do not gel into a systematically articulated theory or programmatic statement. Instead, they reflect Arendt’s appreciation of what remained for her a “vital tension” – an enigma. (shrink)

A structural harm results from countless apparently innocuous interactions between a great many individuals in a social system, and not from any agent’s intentionally producing the harm. Iris Young has influentially articulated a model of individual moral responsibility for such harms, and several other philosophers have taken it as their starting point for dealing with the phenomenon of structural injustice. In this paper, I argue that this social connection model is far less realistic and socially effective than it aims to (...) be. This is because the model systematically neglects the key role played by the emotions in human moral life. (shrink)

In this article, we argue that John Henry Newman was right to think that our passional nature can play a legitimate epistemic role. First, we unpack the standard objection to Newman’s understanding of the relationship between our passional nature and the evidential basis of faith. Second, we argue that the standard objection to Newman operates with a narrow definition of evidence. After challenging this notion, we then offer a broader and more humane understanding of evidence. Third, we survey recent scholarship (...) arguing that emotions, a key aspect of our passional nature, are cognitive. In this light, they plausibly have a proper epistemic role. Fourth, we defend Newman’s reliance on the passional nature in epistemic matters by showing how reasonable it is in light of this recent work on evidence and the nature of emotions. Newman’s insistence that the formation of a right state of heart and mind is crucial for epistemic success is far from untenable. (shrink)

Alvin Plantinga has famously responded to the logical problem of evil by appealing to the intrinsic value of significant free will. A problem, however, arises because traditional theists believe that both God and the redeemed who go to heaven cannot do wrong acts. This entails that both God and the redeemed in heaven lack significant freedom. If significant freedom is indeed valuable, then God and the redeemed in heaven would lack something intrinsically valuable. However, if significant freedom is not intrinsically (...) valuable, then Plantinga’s reply to the logical problem of evil fails. In this paper, we assess three contemporary solutions to the dilemma above. The first is the love solution, which proposes that significant freedom is necessary for agents to love, and loving others is intrinsically good. The second is the soul-making solution, which argues that significant freedom is necessary for self-developing one’s moral character, and having a self-developed moral character is intrinsically good. The third is the derivative free will solution, which argues that significant freedom is necessary for derivative free will in heaven, and derivative free will is intrinsically good. We raise problems against all three solutions and instead defend a fourth solution – the ultimate responsibility solution. That is, significant freedom is instrumentally valuable as it gives agents ultimate responsibility with regards to morally significant acts. Finally, we defend the ultimate responsibility solution against two major objections. (shrink)

Can we feel emotions about abstract objects, assuming that abstract objects exist? I argue that at least some emotions can have abstract objects as their intentional objects and discuss why this conclusion is not just trivially true. Through critical engagement with the work of Dacher Keltner and Jonathan Haidt, I devote special attention to awe, an emotion that is particularly well suited to show that some emotions can be about either concrete or abstract objects. In responding to a possible objection, (...) according to which we can only feel emotions about things that we take to matter to our flourishing, and thus cannot feel emotions about causally inefficacious abstract objects, I explore how abstract objects can be relevant to human flourishing and discuss someemotions other than awe that can be about abstract objects. I finish by explaining somereasons why my conclusion matters, including the fact that it presents a challenge to perceptual theories of emotion and causal theories of intentionality. (shrink)

This article examines two arguments that a worship-worthy agent cannot command worship. The first argument is based on the idea that any agent who commands worship is egotistical, and hence not worship-worthy. The second argument is based on Campbell Brown and Yujin Nagasawa's (2005) idea that people cannot comply with the command to worship because if people are offering genuine worship, they cannot be motivated by a command to do so. One might then argue that a worship-worthy agent would have (...) no reason to issue a command to worship. I argue that both these arguments fail. (shrink)

Religious disagreements are widespread. Some philosophers have argued that religious disagreements call for religious skepticism, or a revision of one’s religious beliefs. In order to figure out the epistemic significance of religious disagreements, two questions need to be answered. First, what kind of disagreements are religious disagreements? Second, how should one respond to such disagreements? In this paper, I argue that many religious disagreements are cases of unconfirmed superiority disagreements, where parties have good reason to think they are not epistemic (...) peers, yet they lack good reason to determine who is superior. Such disagreements have been left relatively unexplored. I then argue that in cases of unconfirmed superiority disagreements, disputants can remain relatively steadfast in holding to their beliefs. Hence, we can remain relatively steadfast in our beliefs in such cases of religious disagreements. (shrink)

In recent years, Duncan Pritchard has developed a position in religious epistemology called quasi‐fideism that he claims traces back to John Henry Newman's treatment of the rationality of religious belief. In this paper, we give three reasons to think that Pritchard's reading of Newman as a quasi‐fideist is mistaken. First, Newman's parity argument does not claim that religious and non‐religious beliefs are on a par because both are groundless; instead, for Newman, they are on a par because both often stem (...) from implicit rather than explicit reasoning. Second, pace Pritchard, Newman's distinction between simple and complex assent does not map onto the Wittgensteinian distinction between groundless hinge commitments and beliefs that flow from these hinges. For Newman, simple and complex assent differ in terms of the believer's level of awareness of their grounds. Third, and finally, Newman does not reject Locke's evidentialism in toto. Instead, he argues that certitude is not restricted to beliefs stemming from intuition and demonstration but often rightly includes probabilistically supported (or fallibly evidenced) beliefs. (shrink)

What is the function of morality? On this question, something approaching a consensus has recently emerged. Impressed by developments in evolutionary theory, many philosophers now tell us that the function of morality is to reduce social tensions, and to thereby enable a society to efficiently promote the well-being of its members. In this paper, I subject this consensus to rigorous scrutiny, arguing that the functional hypothesis in question is not well supported. In particular, I attack the supposed evidential relation between (...) an evolutionary genealogy of morals and the functional hypothesis itself. I show that there are a great many functionally relevant discontinuities between our own culture and the culture within which morality allegedly emerged, and I argue that this seriously weakens the inference from morality’s evolutionary history to its present-day function. (shrink)

This paper examines the moral arguments for and against employees' blowing the whistle on illegal or immoral actions of their employers. It asks whether such professional dissidents are justified in disclosing wrongdoing by others while concealing their own identity. Part I examines the concept of anonymity, distinguishing it from two similar concepts — secrecy and privacy. Part II analyzes the concept of whistleblowing using recent definitions by Bok, Bowie and De George. Various arguments against anonymous whistleblowing are identified and evaluated. (...) The author concludes with a defense of the practice in terms of social benefits — primarily the redressing of wrongdoing. (shrink)

1. Do models formulated in programming languages use explicit rules where connectionist models do not? 2. Are rules as found in programming languages hard, precise, and exceptionless, where connectionist rules are not? 3. Do connectionist models use rules operating on distributed representations where models formulated in programming languages do not? 4. Do connectionist models fail to use structure sensitive rules of the sort found in "classical" computer architectures? In this chapter we argue that the answer to each of these questions (...) is negative. (shrink)

Legal decisions and theories are frequently condemned as formalistic, yet little discussion has occurred regarding exactly what the term "'formalism" means. In this Article, Professor Schauer examines divergent uses of the term to elucidate its descriptive content. Conceptions offormalism, he argues, involve the notion that rules constrict the choice of the decisionmaker. Our aversion to formalism stems from denial that the language of rules either can or should constrict choice in this way. Yet Professor Schauer argues that this aversion to (...) formalism should be rethought: At times language both can and should restrict decisionmakers. Consequently, the term "'formalistic" should not be used as a blanket condemnation of a decisionmaking process; instead the debate regarding decision according to rules should be confronted on its own terms. (shrink)

Can it ever be morally justifiable to tell others to do what we ourselves believe is morally wrong to do? The common sense answer is no. It seems that we should never tell others to do something if we think it is morally wrong to do that act. My first goal is to argue that in Analects 17.21, Confucius tells his disciple not to observe a ritual even though Confucius himself believes that it is morally wrong that one does not (...) observe the ritual. My second goal is to argue against the common sense answer and explain how Confucius can be justified in telling his disciple to do what Confucius thought was wrong. The first justification has to do with telling someone to do what is second best when the person cannot do what is morally best. The second justification has to do with the role of a moral advisor. (shrink)

The existence of deep and persistent moral disagreement poses a problem for a defender of moral knowledge. It seems particularly clear that a philosopher who thinks that we know a great many moral truths should explain how human populations have failed to converge on those truths. In this paper, I do two things. First, I show that the problem is more difficult than it is often taken to be, and second, I criticize a popular response, which involves claiming that many (...) false moral beliefs are the product of nonmoral ignorance. (shrink)

If Martin Heidegger was a philosopher who poetized, Wallace Stevens was a poet who philosophized. In "The Sail of Ulysses," one of his later poems, Stevens speaks enigmatically of a "right to be." The phrase is straightforward, if taken to indicate the right to life. But Stevens is rarely, if ever, straightforward. The poem is much more understandable if we take "being" in a Heideggerian sense, as an understanding of what it means to be.

In this paper, I argue that in order to explain our own moral reliability, we must provide a theory of error for those who disagree with us. Any story that seeks to vindicate our own reliability must also explain how so many others have gone wrong, otherwise it is not actually a vindicatory story. Thus, we cannot claim to have vindicated our own moral reliability unless we can explain the unreliability of those who hold contrary beliefs. This, I show, requires (...) us to engage directly with cultural history, a topic which has been unfortunately obscured by the meta-ethicist’s near-exclusive focus on evolutionary challenges to moral belief. (shrink)

This article presents a critical reevaluation of the thesis—closely associated with H. L. A. Hart, and central to the views of most recent legal philosophers—that the idea of state coercion is not logically essential to the definition of law. The author argues that even laws governing contracts must ultimately be understood as “commands of the sovereign, backed by force.” This follows in part from recognition that the “sovereign,” defined rigorously, at the highest level of abstraction, is that person or entity (...) identified by reference to game theory and the philosophical idea of “convention” as the source of signals with which the subject population has become effectively locked, as a group, into conformity. (shrink)

The study analyzed the Agogo Presbyterian College of Education (1930-1971) and when it was taken over by the Government (1972-2013). This became relevant in the wake of the recent plea by the churches that the Government should hand over Mission Schools to the churches. The study therefore examines the state of management and leadership and infrastructural development both under the regime of the Missionaries and the Government. It also sought to assess academic standard of the students, and the discipline of (...) the College, qualification of the teachers, supervision, and students’ patronage of library and entry grade of students to the College with the view of establishing the progression or retrogression over the period. In doing this, a comparative study was undertaken and data were derived from archival materials of the Agogo Presbyterian College of Education, and direct interviews with past Principals and Administrators of the College. The results revealed that despite an increase in student-intake (210 students in 1942 to 750 students in 2014) with a corresponding increase of teachers (from 5 missionary teachers with lower academic degrees in 1931 to 28 teachers with masters qualifications), inadequate infrastructural development; lack of discipline and competitions among students have characterized APCE since it was managed by the Government as compared to the Missionaries. The study recommends that the Government would complete the construction of the students‟ hall complex, and also put up large auditorium and classroom blocks to accommodate the high students’ intake in the College to enhance education delivery. (shrink)

In this paper, I try to pin down the essence of conservative political theory. I then show that no-one really believes this theory, because all of us embrace progressive values and principles under the right circumstances. This doesn't mean that there aren't such things as conservative political reasons, and I offer an account of such reasons here. But in my view no-one really thinks that such reasons are the sole or even the primary political reasons.

The ethics of biological procreation has received a great deal of attention in recent years. Yet, as I show in this paper, much of what has come to be called procreative ethics is conducted in a strangely abstract, impersonal mode, one which stands little chance of speaking to the practical perspectives of any prospective parent. In short, the field appears to be flirting with a strange sort of practical irrelevance, wherein its verdicts are answers to questions that no-one is asking. (...) I go on to articulate a theory of what I call existential grounding, a notion which explains the role that prospective children play in the lives of many would-be parents. Procreative ethicists who want their work to have real practical relevance must, I claim, start to engage with this markedly first-personal kind of practical consideration. (shrink)

The 21st century, otherwise unremarkable after the Great Climate Change Scare of its early decades was revealed to be a hoax, is remembered for its solution to an age-old problem.

In this paper, I clarify and defend a provocative hypothesis offered by Bernard Williams, namely, that modern people are much more likely to speak in terms of master-concepts like “good” or “right,” and correspondingly less likely to think and speak in the pluralistic terms favored by certain Ancient societies. By conducting a close reading of the Platonic dialogues Charmides and Laches, I show that the figure of Socrates plays a key historical role in this conceptual shift. Once we understand that (...) our narrow, reductionist focus on “thin” ethical concepts is a contingent historical development, we are, I claim, in a much better position to evaluate it. (shrink)

This book describes how scientists bring their own interests and passions to their work, illustrates the dynamics between researchers and the research community ...

I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the (...) spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition. (shrink)

Journal of Social Philosophy, Volume 53, Issue 2, Page 255-272, Summer 2022.

Pragmatic Genealogy involves constructing fictional, quasi-historical models in order to discover what might explain and justify our concepts, ideas or practices. It arguably originated with Hume, but its most prominent practitioners are Edward Craig, Bernard Williams and Mathieu Queloz. Its defenders allege that the method allows us to understand “what the concept does for us, what its role in our life might be” (Craig, 1990), and that this in turn can ground practical reasons to preserve or further a conceptual practice. (...) In this paper, I argue that none of this is true, and that only a turn to the actual recent history of such practices can reveal those sorts of practical reasons. (shrink)

Four decades ago, Bernard Williams accused Kantian moral theory of providing agents with ‘one thought too many’. The general consensus among contemporary Kantians is that this objection has been decisively answered. In this paper, I reconstruct the problem, showing that Williams was not principally concerned with how agents are to think in emergency situations, but rather with how moral theories are to be integrated into recognizably human lives. I show that various Kantian responses to Williams provide inadequate materials for solving (...) this ‘integration problem’, and that they are correspondingly ill-positioned to account for the authority of morality, as Williams suspected all along. (shrink)

In this paper we critically evaluate an argument put forward by William Lane Craig for the existence of God based on the assumption that if there were no God, there could be no objective morality. Contrary to Craig, we show that there are some necessary moral truths and objective moral reasoning that holds up whether there is a God or not. We go on to argue that religious faith, when taken alone and without reason or evidence, actually risks undermining morality (...) and is an unreliable source of moral truths. We recommend a viewpoint on morality that is based on reason and public consensus, that is compatible with science, and that cuts across the range of religious and non-religious positions. (shrink)

I argue that we are sometimes morally responsible for having and using (or not using) our concepts, despite the fact that we generally do not choose to have them or have full or direct voluntary control over how we use them. I do so by extending an argument of Angela Smith's; the same features that she says make us morally responsible for some of our attitudes also make us morally responsible for some of our concepts. Specifically, like attitudes, concepts can (...) be (a) conceptually and rationally connected to our evaluative judgments, (b) in principle subject to rational revision (reasons‐responsive), and (c) the basis for actual and potential moral assessments of people that we have good reasons to endorse. Thus, we are open to moral appraisal on the basis of having and using (or not using) our concepts when they reflect our evaluative judgments, though even then it is not always appropriate to praise or blame us on that basis. (shrink)

A Review of Committee on Science, Engineering, and Public Policy, panel report, Responsible Science: Ensuring the Integrity of the Research Process Volume I, Washington, DC: National Academy Press, 1992.

We should give courage a more significant place in our understanding of how familiar virtues can and should be reshaped to capture what it is to be virtuous relative to the environment. Matthew Pianalto’s account of moral courage helps explain what a specifically environmental form of moral courage would look like. There are three benefits to be gained by recognizing courage as an environmental virtue: it helps us to recognize the high stakes nature of much environmental activism and to act (...) accordingly; it can make environmental activism more appealing to a broader audience by helping us dismantle stereotypes associated with environmentalism, including sexist and homophobic ones; and it aides in the de-militarization of the concept of courage. (shrink)

Highlights: -/- • Breastfeeding and breastfeeding support can contribute to mitigating climate change. • Achieving global nutrition targets will save more emissions than fuel-switching. • Breastfeeding support programmes support a just transition. • This work can support the expansion of mitigation options in energy system models. -/- Abstract: -/- Renewable gas has been proposed as a solution to decarbonise industrial processes, specifically heat demand. As part of this effort, the breast-milk substitutes industry is proposing to use renewable gas as a (...) substitute for fossil natural gas. However, decarbonising the industrial processing of breast-milk substitutes can increase social license for these products, potentially undermining breastfeeding. World Health Organisation nutrition targets aim to increase exclusive breastfeeding to at least 50% globally by 2025 to improve maternal, infant, and young child health and nutrition. This target will have implications for the energy transition. A weakness of existing energy models is that demands for end-use products such as breast-milk substitutes are typically not considered explicitly. This paper develops an analytical framework for explicitly representing infant feeding methods in energy systems models. We compare the emissions saved in Ireland from decarbonising the industrial processing of breast-milk substitutes with renewable gas with the emissions saved by an increase in exclusive breastfeeding to 50% in both Ireland and a key export market, China. We demonstrate that the emissions saved from achieving the minimum global breastfeeding target are greater than when renewable gas is used to displace natural gas in the production of breast-milk substitutes in Ireland. We discuss the decarbonisation of breast-milk substitutes in relation to the principle of justice as non-maleficence, a principle based on the commitment to avoid harm, a novel application of a principle of justice. We conclude that breastfeeding support can be considered a demand-side measure for mitigating climate change by reducing the demand for energy services to produce breast-milk substitutes. A key recommendation is to position breastfeeding support as both a public health and a climate justice issue that is relevant for a just transition. The framework developed for this paper could be applied to support the inclusion of a wider range of mitigation options with social justice outcomes in energy system models. [Open access]. (shrink)

I propose a reading of The Book of Ruth that takes seriously the pastoral concern for refugees, migrants, and their families that was embodied in the life and teaching of Pope John Paul II.The Book of Ruth models virtues and practices that can help build up a society in solidarity, kindness, and peace. Ruth’s decision to stand beside Naomi demonstrates the value of solidarity in creating a hopeful future for families and communities. Naomi’s role in bringing Ruth and Boaz together (...) shows prudence and a sense of responsibility for shaping the common good. As for Boaz, he is an exemplary model of generosity and kindness. With respect to peacemaking, The Book of Ruth shows how enmity and distrust between nations might be overcome, with God’s help. (shrink)

In Escape from Leviathan, Jan Lester sets out a conception of liberty as absence of imposed cost which, he says, advances no moral claim and does not premise an assignm..

Many philosophers have recently become interested in conceptual engineering, or the activity of producing better conceptual schemes in human populations. But few, if any, are asking the question: what would it mean for actual human agents to possess the social authority to modify a conceptual scheme in this way? This paper argues for a deontological approach to conceptual engineering, wherein we have to secure social authority qua engineers before attempting to modify social concepts. I show that the dominant, consequentialist conception (...) of engineering violates basic rights that concept-users have, particularly over their own identity-constituting concepts. Using examples from the philosophy of race and sexuality, I show that conceptual engineers cannot authoritatively modify social concepts if they employ consequentialist reasoning about those concepts. (shrink)

We argue that individual and institutional caregivers have a defeasible moral duty to provide dependent children with plant-based diets and related education. Notably, our three arguments for this claim do not presuppose any general duty of veganism. Instead, they are grounded in widely shared intuitions about children’s interests and caregivers’ responsibilities, as well as recent empirical research relevant to children’s moral development, autonomy development, and physical health. Together, these arguments constitute a strong cumulative case against inculcating in children the dietary (...) practice of regularly eating meat (and other animal products)—a practice we call “carnism.”. (shrink)

Here I call attention to a class of desires that I call exclusionary desires. To have an exclusionary desire is to desire something under a description such that, were the desire satisfied, it would be logically impossible for people other than the desiring subject to possess the desired object. Assuming that we are morally responsible for our desires insofar as and because they reflect our evaluative judgments and are in principle subject to rational revision, I argue that we should, morally (...) speaking, alter both social structures and our individual psychologies to minimize, or at least substantially reduce, exclusionary desires. (shrink)

This paper presents 59 new studies (N = 72,310) which focus primarily on the “bat and ball problem.” It documents our attempts to understand the determinants of the erroneous intuition, our exploration of ways to stimulate reflection, and our discovery that the erroneous intuition often survives whatever further reflection can be induced. Our investigation helps inform conceptions of dual process models, as “system 1” processes often appear to override or corrupt “system 2” processes. Many choose to uphold their intuition, even (...) when directly confronted with simple arithmetic that contradicts it – especially if the intuition is approximately correct. (shrink)