This paper examines three accounts of the sleeping beauty case: an account proposed by Adam Elga, an account proposed by David Lewis, and a third account defended in this paper. It provides two reasons for preferring the third account. First, this account does a good job of capturing the temporal continuity of our beliefs, while the accounts favored by Elga and Lewis do not. Second, Elga’s and Lewis’ treatments of the sleeping beauty case lead to highly counterintuitive consequences. (...) The proposed account also leads to counterintuitive consequences, but they’re not as bad as those of Elga’s account, and no worse than those of Lewis’ account. (shrink)
Literary beauty was once understood as intertwining sensations and ideas, and thus as providing subjective and objective reasons for literary appreciation. However, as theory and philosophy developed, the inevitable claims and counterclaims led to the view that subjective experience was not a reliable guide to literary merit. Literary theory then replaced aesthetics as did philosophy’s focus on literary truth. Along with the demise of the relevance of sensations, literary form also took a back seat. This suggested to some that (...) either literature communicated truth like any other literal form of communication or it was a mere diversion: a springboard to harmless reverie or daydreaming. Neither response satisfactorily captured what was distinctive about literature: the love readers can have for literary texts and the edification or insight claimed of works within each culture’s respective catalogue of classics. However, a concept of literary beauty has again become viable due to developments in theories of pleasure and imagination. If the defining aspect of literature is the imaginative engagement it occasions, and if this imagining is constrained by plausibility and endorsed as effective relative to our goals, ideals, and interests, then literature is not reduced to either mere fact or wish fulfillment. An account of literary beauty is available which defines literature accordingly and explains how subjective and objective reasons for appreciation intertwine to evoke pleasure and insight. (shrink)
In this article, robust evidence is provided showing that an individual’s moral character can contribute to the aesthetic quality of their appearance, as well as being beautiful or ugly itself. It is argued that this evidence supports two main conclusions. First, moral beauty and ugliness reside on the inside, and beauty and ugliness are not perception-dependent as a result; and, second, aesthetic perception is affected by moral information, and thus moral beauty and ugliness are on the outside (...) as well. (shrink)
The role of judgments of beauty in scientific theory evaluation is the subject of significant debate in contemporary philosophy of science. This book advances that debate by broadening its scope. In Judgments of Beauty in Theory Evaluation, the author argues that judgments of beauty are a justified part of theory evaluation of all sorts: not only scientific theory evaluation, but also philosophical theory evaluation. The author argues for this thesis by providing an account of beauty—inherited from (...) Kant and Mothersill—on which the distinctive nature of judgments of beauty is that they are unprincipled, yet possible. The author then analyzes two important methods of theory evaluation—reflective equilibrium and simplicity—and argues that these methods require making judgments of beauty so understood. Finally, the author argues that these methods of theory evaluation are not anomalies, but that they point to a deeper lesson about the nature of theorizing and the necessity of using judgments of beauty to evaluate systems, like theories. This conclusion has implications for the debate in philosophy of science over judgments of beauty, but also prompts a reckoning in philosophy itself over the use of judgments of beauty in philosophical theory evaluation. (shrink)
Functional beauty in the aesthetic tradition -- Functional beauty in contemporary aesthetic theory -- Indeterminacy and the concept of function -- Function and form -- Nature and environment -- Architecture and the built environment -- Artefacts and everyday aesthetics -- The functions of art.
I defend the suggestion that the rational probability in the Sleeping Beauty paradox is one third. The reasoning in its favour is familiar: for every heads-waking, there are two tails-wakings. To complete the defense, I rebut the reasoning which purports to justify the competing suggestion – that the correct probability is half – by undermining its premise, that no new information has been received.
This paper explores the beauty of religious exemplars Ð those special persons whose conduct and comportment marks their life out as one that exemplifies a religious life. Such exemplars are consistently described as beautiful, but it is not clear how or why. I suggest that we can make sense of the aesthetically aspect of religious exemplarity by adopting a Ôvirtue-centricÕ theory of beauty that understands the beautiful in terms of the expression or manifestation of virtues. Religious exemplars are (...) those who have cultivated their virtues to an advanced degree and are beautiful for that reason. Attending to the beauty of religious exemplars can enrich exemplarist virtue theory, the aesthetics of character, and our understanding of the nature of a religious life. (shrink)
I offer a set of sufficient conditions for beauty, drawing on Parsons and Carlson’s account of ‘functional beauty’. First, I argue that their account is flawed, whilst falling short of...
The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1/3 to be in a heads-awakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1/2. The problem is that she is in a heads-awakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is the (...) problem I address in this article. I suggest that ‘p whenever q and vice versa’ may be consistent with p and q having different probabilities if one of them refers to a sample space containing ordinary possible worlds and the other to a sample space containing centred possible worlds, because such spaces may fail to combine into one composite probability space and, as a consequence, ‘whenever’ may not be well defined; such is the main contribution of this article. 1The Sleeping Beauty Game2Groisman’s and Peter Lewis’s Approaches3Discussing Beauty’s Credences4The Principle of Equivalence's Failure5Making Sense of the Principle of Equivalence's Failure6Elga’s and Lewis’s Approaches7ConclusionAppendix. (shrink)
The chapter challenges hyperbolic claims about the centrality of appreciation of beauty to Buddhism. Within the texts, attitudes are more mixed, except for a form of 'inner beauty' - the beauty found in the expression of virtues or wisdom in forms of bodily comportment. Inner beauty is a stable presence throughout Buddhist history, practices, and art.
Adam Elga takes the Sleeping Beauty example to provide a counter-example to Reflection, since on Sunday Beauty assigns probability 1/2 to H, and she is certain that on Monday she will assign probability 1/3. I will show that there is a natural way for Bas van Fraassen to defend Reflection in the case of Sleeping Beauty, building on van Fraassen’s treatment of forgetting. This will allow me to identify a lacuna in Elga’s argument for 1/3. I will (...) then argue, however, that not all is well with Reflection: there is a problem with van Fraassen’s treatment of forgetting. Ultimately I will agree with Elga’s 1/3 answer. David Lewis maintains that the answer is 1/2; I will argue that cases of forgetting can be used to show that the premiss of Lewis’s argument for 1/2 is false. (shrink)
This is an 18,500 word bibliography of philosophical scholarship on Beauty which was published online in the Oxford Bibliographies Online. The entry includes an Introduction of 800 words, 21 x 400-word sub-themes and 168 annotated references. INTRODUCTION Philosophical interest in beauty began with the earliest recorded philosophers. Beauty was deemed to be an essential ingredient in a good life and so what it was, where it was to be found and how it was to be included in (...) a life were prime considerations. The way beauty has been conceived has been influenced by an author’s other philosophical commitments, metaphysical, epistemological and ethical and such commitments reflect the historical and cultural position of the author. For example, beauty is a manifestation of the divine on earth to which we respond with love and adoration; beauty is a harmony of the soul which we achieve through cultivating feeling in a rational and tempered way; beauty is an idea raised in us by certain objective features of the world; beauty is a sentiment which can nonetheless be cultivated to be appropriate to its object; beauty is the object of a judgment by which we exercise the social, comparative and inter-subjective elements of cognition and so on. Such views on beauty not only reveal underlying philosophical commitments but also reflect positive contributions to understanding the nature of value and the relation of mind and world. One way to distinguish between beauty theories is according to the conception of the human being that they assume or imply, for example, where they fall on the continuum from determinism to free will, ungrounded notions of compatibilism notwithstanding. For example, theories at the latter end might carve out a sense of genuine innovation and creativity in human endeavours while at the other end of the spectrum authors may conceive of beauty as an environmental trigger for consumption, procreation or preservation in the interests of the individual. Treating beauty experiences as in some respect intentional, characterises beauty theory prior to the twentieth century and since, mainly in historically inspired writing on beauty. On the other hand, treating beauty as affect or sensation has always had its representatives and is most visible today in evolutionary inspired accounts of beauty (though not all evolutionary accounts fit this classification). Beauty theory falls under some combination of metaphysics, epistemology, meta-ethics, aesthetics and psychology. While in the twentieth century beauty was more likely to be conceived as an evaluative concept for art, recent philosophical interest in beauty can again be seen to exercise arguments pertaining to metaphysics, epistemology, meta-ethics, philosophy of meaning and language in addition to philosophy of art and environmental aesthetics. (shrink)
In the Sleeping Beauty problem, Beauty is uncertain whether the outcome of a certain coin toss was heads or tails. One argument suggests that her degree of belief in heads should be 1/3, while a second suggests that it should be 1/2. Prima facie, the argument for 1/2 appears to be stronger. I offer a diachronic Dutch Book argument in favor of 1/3. Even for those who are not routinely persuaded by diachronic Dutch Book arguments, this one has (...) some important morals. (shrink)
One of the aims of the encyclical "Laudato Si’" is to help us “marvel at the manifold connections existing among creatures”, to show how we are also involved, and to motivate us thereby to care for our common home. Are there new dimensions of beauty available to us today because of recent advances in biology? In this paper I seek to answer this question by first recalling the basic criteria for beauty, as expressed by Aristotle and Aquinas, and (...) then evaluating their applicability as regards three ways in which some prominent twentieth century philosophers of biology have sought to overcome the limitations of reductionism. The overall argument refers especially to the works of Jakob von Uexküll and Georges Canguilhem. The results indicate that harmony, proportion, and integrity in the natural order should be more evident than ever before, especially as regards the way the organism and its environment codetermine each other. This insight allows a deeper appreciation of the message of "Laudato Si’". (shrink)
The Sleeping Beauty problem is test stone for theories about self-locating belief, i.e. theories about how we should reasons when data or theories contain indexical information. Opinion on this problem is split between two camps, those who defend the "1/2 view" and those who advocate the "1/3 view". I argue that both these positions are mistaken. Instead, I propose a new "hybrid" model, which avoids the faults of the standard views while retaining their attractive properties. This model _appears_ to (...) violate Bayesian conditionalization, but I argue that this is not the case. By paying close attention to the details of conditionalization in contexts where indexical information is relevant, we discover that the hybrid model is in fact consistent with Bayesian kinematics. If the proposed model is correct, there are important lessons for the study of self-location, observation selection theory, and anthropic reasoning. (shrink)
Cian Dorr (2002) gives an argument for the 1/3 position in Sleeping Beauty. I argue this is based on a mistake about Sleeping Beauty's epistemic position.
Argues for the "thirder" solution to the Sleeping Beauty puzzle. The argument turns on an analogy with a variant case, in which a coin-toss on Monday night determines whether one's memories of Monday are permanently erased, or merely suspended in such a way that they will return some time after one wakes up on Tuesday.
The traditional solutions to the Sleeping Beauty problem say that Beauty should have either a sharp 1/3 or sharp 1/2 credence that the coin flip was heads when she wakes. But Beauty’s evidence is incomplete so that it doesn’t warrant a precise credence, I claim. Instead, Beauty ought to have a properly imprecise credence when she wakes. In particular, her representor ought to assign \(R(H\!eads)=[0,1/2]\) . I show, perhaps surprisingly, that this solution can account for the (...) many of the intuitions that motivate the traditional solutions. I also offer a new objection to Elga’s restricted version of the principle of indifference, which an opponent may try to use to collapse the imprecision. (shrink)
In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which (...) hypothesis to consider and which to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic factors in mathematical research. (shrink)
Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there (...) are situations in which the latter principle and the principle of Countable Additivity cannot be jointly satisfied. The most plausible response to this tension, I argue, is to accept both of these principles, and to maintain that when an agent cannot satisfy them both, she is faced with a rational dilemma. (shrink)
What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
This paper engages with the aesthetics of knowl-edge, both in its sense as the connection between knowledge and ‘aesthetic’ judgements of beauty, or ugliness, and of the many ‘aesthetic’ – that is to say sensually perceivable – dimensions of knowledge, which are always to be seen to be constituting an epistemic factor in its production and consumption. On the one hand I analyse how in recent decades the connection between beauty and truth has been systematically employed to both (...) inspire and guide research in high-energy physics; at the same time I also show how this use of aesthetic judgement only reveals its constitutive role in physics research when paying attention to the broad range of aesthetic strategies employed for expressing scientific knowledge. (shrink)
In chapters ranging from "The Beautiful, the Dainty, and the Dumpy" to "Skin-deep or In the Eye of the Beholder?" Nick Zangwill investigates the nature of beauty as we conceive it, and as it is in itself. The notion of beauty is currently attracting increased interest, particularly in philosophical aesthetics and in discussions of our experiences and judgments about art. In The Metaphysics of Beauty, Zangwill argues that it is essential to beauty that it depends on (...) the ordinary features of things. He uses this principle to defend the notion of the aesthetic, to call for a version of aesthetic formalism, and to reconsider the reality of beauty. The Metaphysics of Beauty brings beauty to the center of intellectual consciousness in a manner informed by contemporary metaphysics and engages with beauty as an enduring object of human thought and experience. (shrink)
Which traits are beautiful? And is their beauty perceptual? It is argued that moral virtues are partly beautiful to the extent that they tend to give rise to a certain emotion— ecstasy—and that compassion tends to be more beautiful than fair-mindedness because it tends to give rise to this emotion to a greater extent. It is then argued, on the basis that emotions are best thought of as a special, evaluative, kind of perception, that this argument suggests that moral (...) virtues are partly beautiful to the extent that they tend to give rise to a certain kind of evaluative perceptual experience. (shrink)
The first book to focus on the intersection of Western philosophy and the Asian martial arts, _Striking Beauty_ comparatively studies the historical and philosophical traditions of martial arts practice and their ethical value in the modern world. Expanding Western philosophy's global outlook, the book forces a theoretical reckoning with the concerns of Chinese philosophy and the aesthetic and technical dimensions of martial arts practice. _Striking Beauty_ explains the relationship between Asian martial arts and the Chinese philosophical traditions of Confucianism, Buddhism, (...) and Daoism, in addition to Sunzi's _Art of War_. It connects martial arts practice to the Western concepts of mind-body dualism and materialism, sports aesthetics, and the ethics of violence. The work ameliorates Western philosophy's hostility toward the body, emphasizing the pleasure of watching and engaging in martial arts, along with their beauty and the ethical problem of their violence. (shrink)
It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest that Kant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the common (...) view that Kant's aesthetics leaves no room for beauty in mathematics. More specifically, I show that on the Kantian account beauty in mathematics is a non-conceptual response felt in light of our own creative activities involved in the process of mathematical reasoning. The Kantian proposal I thus develop provides a promising alternative to Platonist accounts of beauty widespread among mathematicians. While on the Platonist conception the experience of mathematical beauty consists in an intellectual insight into the fundamental structures of the universe, according to the Kantian proposal the experience of beauty in mathematics is grounded in our felt awareness of the imaginative processes that lead to mathematical knowledge. The Kantian account I develop thus offers to elucidate the connection between aesthetic reflection, creative imagination and mathematical cognition. (shrink)
Terence Horgan defends the thirder position on the Sleeping Beauty problem, claiming that Beauty can, upon awakening during the experiment, engage in “synchronic Bayesian updating” on her knowledge that she is awake now in order to justify a 1/3 credence in heads. In a previous paper, I objected that epistemic probabilities are equivalent to rational degrees of belief given a possible epistemic situation and so the probability of Beauty’s indexical knowledge that she is awake now is necessarily (...) 1, precluding such updating. In response, Horgan maintains that the probability claims in his argument are to be taken, not as claims about possible rational degrees of belief, but rather as claims about “quantitative degrees of evidential support.” This paper argues that the most plausible account of quantitative degree of support, when conjoined with any of the three major accounts of indexical thought in such a way as to plausibly constrain rational credence, contradicts essential elements of Horgan’s argument. (shrink)
The concept of functional beauty is analysed in terms of the role played by beliefs, in particular expectations, in our perceptions. After finding various theories of functional beauty unsatisfying, I introduce a novel approach which explains how aesthetic judgements on a variety of different kinds of functional objects (chairs, buildings, cars, etc.) can be grounded in perceptions influenced by beliefs.
I defend the suggestion that the rational probability in the Sleeping Beauty paradox is one third. The reasoning in its favour is familiar: for every heads-waking, there are two tails-wakings. To complete the defense, I rebut the reasoning which purports to justify the competing suggestion – that the correct probability is half – by undermining its premise, that no new information has been received.
At the end of section §6 in the Analytic of the Beautiful, Kant defines taste as the “faculty for judging an object or a kind of representation through a satisfaction or dissatisfaction without any interest”. On the face of it, Kant’s definition of taste includes both; positive and negative judgments of taste. Moreover, Kant’s term ‘dissatisfaction’ implies not only that negative judgments of taste are those of the non-beautiful, but also that of the ugly, depending on the presence of an (...) actual displeasure. (shrink)
In Beauty and Revolution in Science, James McAllister advances a rationalistic picture of science in which scientific progress is explained in terms of aesthetic evaluations of scientific theories. Here I present a new model of aesthetic evaluations by revising McAllister’s core idea of the aesthetic induction. I point out that the aesthetic induction suffers from anomalies and theoretical inconsistencies and propose a model free from such problems. The new model is based, on the one hand, on McAllister’s original model (...) and on further developments by Theo Kuipers in his “Beauty, a Road to the Truth?”. On the other hand, it is based on empirical findings about affection and emotion, and a naturalistic aesthetic theory. The new model is thus a naturalistic model with a wider explanatory range and much more internal consistency that McAllister’s. (shrink)
The Sleeping Beauty problem is presented in a formalized framework which summarizes the underlying probability structure. The two rival solutions proposed by Elga and Lewis differ by a single parameter concerning her prior probability. They can be supported by considering, respectively, that Sleeping Beauty is “fuzzy-minded” and “blank-minded”, the first interpretation being more natural than the second. The traditional absent -minded driver problem is reinterpreted in this framework and sustains Elga’s solution.
Contemporary philosophical attitudes toward beauty are hard to reconcile with its importance in the history of philosophy. Philosophers used to allow it a starring role in their theories of autonomy, morality, or the good life. But today, if beauty is discussed at all, it is often explicitly denied any such importance. This is due, in part, to the thought that beauty is the object of “disinterested pleasure”. In this paper I clarify the notion of disinterest and develop (...) two general strategies for resisting the emphasis on it, in the hopes of getting a clearer view of beauty’s significance. I present and discuss several literary depictions of the encounter with beauty that motivate both strategies. These depictions illustrate the ways in which aesthetic experience can be personally transformative. I argue that they present difficulties for disinterest theories and suggest we abandon the concept of disinterest to focus instead on the special kind of interest beauty fuels. I propose a closer look at the Platonic thought that beauty is the object of love. (shrink)
The world’s spiritual traditions incorporate a variety of types of exemplar, persons who exemplify a life of aspiration to, or attainment of, spiritual goods. Within Buddhism, the range of exemplars includes monastics, boddhisattvas, the Zen masters, and the Buddha himself. Spiritual exemplars are typically described as having a distinctive form of bodily beauty, closely related to their ethical and spiritual qualities, that manifests as a form of radiance, luminosity, or charisma. Drawing on recent work on beauty, virtue, and (...) the body in the Buddhist tradition, I propose an aesthetics of spiritual exemplarity, arguing that certain spiritual traditions – including Buddhism – are kaligenic, able to generate new forms or experiences of embodied moral beauty. (shrink)
In this article I give a naturalistic-cum-formal analysis of therelation between beauty, empirical success, and truth. The analysis is based on the onehand on a hypothetical variant of the so-called `mere-exposure effect'' which has been more orless established in experimental psychology regarding exposure-affect relationshipsin general and aesthetic appreciation in particular (Zajonc 1968; Temme 1983; Bornstein 1989;Ye 2000). On the other hand it is based on the formal theory of truthlikeness andtruth approximation as presented in my From Instrumentalism to Constructive (...) Realism (2000).The analysis supports the findings of James McAllister in his beautifulBeauty and Revolution in Science (1996), by explaining and justifying them.First, scientists are essentially right in regarding aesthetic criteria useful for empiricalprogress and even for truth approximation, provided they conceive of them as less hard thanempirical criteria. Second, the aesthetic criteria of the time, the `aesthetic canon'', maywell be based on `aesthetic induction'' regarding nonempirical features of paradigms of successfultheories which scientists have come to appreciate as beautiful. Third, aestheticcriteria can play a crucial, schismatic role in scientific revolutions. Since they may well be wrong, they may, in the hands of aesthetic conservatives, retard empirical progress and hence truth approximation, but this does not happen in the hands of aesthetically flexible, `revolutionary'' scientists. We may find totallyopposite things beautiful: a simplemathematical principle as well as a series of unrepeatable complex contingencies. It is a matter of psychology.(Stephen Jay Gould, translated passage from (Kayzer 2000, 30)). (shrink)
The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs (...) or centered propositions. We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the experiment. (shrink)
Animal beauty provides a significant aesthetic reason for protecting nature. Worries about aesthetic discrimination and the ugliness of predation might make one think otherwise. Although it has been argued that aesthetic merit is a trivial and morally objectionable basis for action, beauty is an important value and a legitimate basis for differential treatment, especially in the case of animals. While the suffering and death of animals due to predation are important disvalues that must be recognized, predation’s tragic (...) class='Hi'>beauty has positive aesthetic value that can be appropriately aesthetically appreciated. (shrink)
"--J.M.Coetzee "Here is a writer almost magically summoning up the world through words and ideas, in a new way, and so guiding the reader, lovingly, to receive the treasures and accept the pleasures of this book as naturally as breathing.
Arthur Danto argued from the premise that artworks are essentially cognitive to the conclusion that they are incidentally aesthetic. I wonder why Danto, and the very many of us he persuaded, came to believe that the cognitive and the aesthetic oppose one another. I argue, contrary to Danto’s historical claims, that the cognitive and the aesthetic did not come into opposition until the late nineteenth or early twentieth century, and that they were brought into opposition for reasons of art-critical expediency (...) rather than philosophical necessity. I conclude that a robustly cognitive notion of the aesthetic remains an option for us. (shrink)
In this paper, I argue for a view largely favorable to the Thirder view: when Sleeping Beauty wakes up on Monday, her credence in the coin’s landing heads is less than 1/2. Let’s call this “the Lesser view.” For my argument, I (i) criticize Strict Conditionalization as the rule for changing de se credences; (ii) develop a new rule; and (iii) defend it by Gaifman’s Expert Principle. Finally, I defend the Lesser view by making use of this new rule.
One argument for the thirder position on the Sleeping Beauty problem rests on direct inference from objective probabilities. In this paper, I consider a particularly clear version of this argument by John Pollock and his colleagues (The Oscar Seminar 2008). I argue that such a direct inference is defeated by the fact that Beauty has an equally good reason to conclude on the basis of direct inference that the probability of heads is 1/2. Hence, neither thirders nor halfers (...) can find direct support in an appeal to objective probabilities. (shrink)
