Virtue epistemology is among the dominant influences in mainstream epistemology today. An important commitment of one strand of virtue epistemology – responsibilist virtue epistemology (e.g., Montmarquet 1993; Zagzebski 1996; Battaly 2006; Baehr 2011) – is that it must provide regulative normative guidance for good thinking. Recently, a number of virtue epistemologists (most notably Baehr, 2013) have held that virtue epistemology not only can provide regulative normative guidance, but moreover that we should reconceive the primary epistemic aim of all education as (...) the inculcation of the intellectual virtues. Baehr’s picture contrasts with another well-known position – that the primary aim of education is the promotion of critical thinking (Scheffler 1989; Siegel 1988; 1997; 2017). In this paper – that we hold makes a contribution to both philosophy of education and epistemology and, a fortiori, epistemology of education – we challenge this picture. We outline three criteria that any putative aim of education must meet and hold that it is the aim of critical thinking, rather than the aim of instilling intellectual virtue, that best meets these criteria. On this basis, we propose a new challenge for intellectual virtue epistemology, next to the well-known empirically-driven ‘situationist challenge’. What we call the ‘pedagogical challenge’ maintains that the intellectual virtues approach does not have available a suitably effective pedagogy to qualify the acquisition of intellectual virtue as the primary aim of education. This is because the pedagogic model of the intellectual virtues approach (borrowed largely from exemplarist thinking) is not properly action-guiding. Instead, we hold that, without much further development in virtue-based theory, logic and critical thinking must still play the primary role in the epistemology of education. (shrink)

Philosophers have claimed that education aims at fostering disparate epistemic goals. In this paper we focus on an important segment of this debate involving conversation between Alvin Goldman and Harvey Siegel. Goldman claims that education is essentially aimed at producing true beliefs. Siegel contends that education is essentially aimed at fostering both true beliefs and, independently, critical thinking and rational belief. Although we find Siegel’s position intuitively more plausible than Goldman’s, we also find Siegel’s defence (...) of it wanting. We suggest novel argumentative strategies that draw on Siegel’s own arguments but look to us more promising. (shrink)

My replies to Errol Lord, Adam Pautz, and Peter Railton's commentaries on The Rationality of Perception (2017).

Positive review of Laats and Siegel (2016) *Teaching Evolution in a Creation Nation* (University of Chicago Press).

I distinguish between two kinds of selection effects on experience: selection of objects or features for experience, and anti-selection of experiences for cognitive uptake. I discuss the idea that both kinds of selection effects can lead to a form of confirmation bias at the level of perception, and argue that when this happens, selection effects can influence the rational role of experience.

Siegel and Byrne debate whether perceptual experiences present rich properties or exclusively thin properties.

chapter on perception and bias including implicit bias.

An overview of the epistemology of perception, covering the nature of justification, immediate justification, the relationship between the metaphysics of perceptual experience and its rational role, the rational role of attention, and cognitive penetrability. The published version will contain a smaller bibliography, due to space constraints in the volume.

In this paper I offer a theory of what makes certain influences on visual experiences by prior mental states (including desires, beliefs, moods, and fears) reduce the justificatory force of those experiences. The main idea is that experiences, like beliefs, can have rationally assessable etiologies, and when those etiologies are irrational, the experiences are epistemically downgraded.

I discuss the roles of journalism in aspirational democracies, and argue that they generate set of pressures on attention that apply to people by virtue of the type of society they live in. These pressures, I argue, generate a problem of democratic attention: for journalism to play its roles in democracy, the attentional demands must be met, but there are numerous obstacles to meeting them. I propose a principle of salience to guide the selection and framing of news stories that (...) I argue may help address the puzzle: the public-as-protagonist principle. -/- . (shrink)

This article discusses Harvey Siegel’s general justification of the epistemological theory of argumentation in his seminal essay “Arguing with Arguments." On the one hand, the achievements of this essay are honoured—in particular, a thorough differentiation of the different meanings of ‘argument’ and ‘argumentation,’ the semantic justification of the fundamentality of arguments as sequences of propositions, and the detailed critiques of alternative theories of argumentation. On the other hand, suggestions for strengthening the theory are added to Siegel's expositions, (...) which make different perspectives within the epistemological theory of argumentation recognisable. (shrink)

This article discusses Harvey Siegel’s general justification of the epistemological theory of argumentation in his seminal essay “Arguing with Arguments." On the one hand, the achievements of this essay are honoured—in particular, a thorough differentiation of the different meanings of ‘argument’ and ‘argumentation,’ the semantic justification of the fundamentality of arguments as sequences of propositions, and the detailed critiques of alternative theories of argumentation. On the other hand, suggestions for strengthening the theory are added to Siegel's expositions, (...) which make different perspectives within the epistemological theory of argumentation recognisable. (shrink)

A summary of The Rationality of Perception, and my replies to symposium papers on it by Andy Clark and Christopher Peacocke.

Some people commonly know a proposition just in case they all know it, they all know that they all know it, they all know that they all know that they all know it, and so on. They commonly believe a proposition just in case they all believe it, they all believe that they all believe it, they all believe that they all believe that they all believe it, and so on. A long tradition in economic theory, theoretical computer science, linguistics (...) and philosophy has held that people have some approximation of common knowledge or common belief in a range of circumstances, for example, when they are looking at an object together, or when they have just discussed something explicitly in conversation. In this paper, I argue that people do not have any approximation of common knowledge or common belief in these circumstances. The argument suggests that people never have any approximation of common knowledge or common belief. (shrink)

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to do (...) by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

This is a much shorter version of our entry on the Epistemology of Perception, which will be published in the Oxford Handbook for the Philosophy of Perception in 2013. The longer version has far more references in it, whereas this version is pared down to the essentials.

Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior μ, that it is the common prior; (2) that agents commonly know that each of them updates (...) on the prior by conditionalization; (3) that agents commonly know that if an agent knows a proposition, she knows that she knows that proposition (the “K K” principle); (4) that agents commonly know that they each update only on true propositions. It is shown that natural weakenings of any one of these strong assumptions can lead to countermodels to Aumann’s key conditional. Examples are given in which agents who have a common prior and commonly know what probability they each assign to a proposition nevertheless assign that proposition unequal probabilities. To alter Aumann’s famous slogan: people can “agree to disagree”, even if they share a common prior. The epistemological significance of these examples is presented in terms of their role in a defense of the Uniqueness Thesis: If an agent whose total evidence is E is fully rational in taking doxastic attitude D to P, then necessarily, any subject with total evidence E who takes a different attitude to P is less than fully rational. (shrink)

This article presents a new interpretation of the great Ming dynasty philosopher Wang Yangming’s celebrated doctrine of the “unity of knowledge and action”. Wang held that action was not unified with all knowledge, but only with an elevated form of knowledge, which he sometimes called “genuine knowledge”. I argue for a new interpretation of this notion, according to which genuine knowledge requires freedom from a form of doxastic conflict. I propose that, in Wang’s view, a person is free from this (...) form of doxastic conflict if and only if they are acting virtuously. (shrink)

Are LLMs cultural technologies like photocopiers or printing presses, which transmit information but cannot create new content? A challenge for this idea, which we call "bibliotechnism", is that LLMs often do generate entirely novel text. We begin by defending bibliotechnism against this challenge, showing how novel text may be meaningful only in a derivative sense, so that the content of this generated text depends in an important sense on the content of original human text. We go on to present a (...) different, novel challenge for bibliotechnism, stemming from examples in which LLMs generate “novel reference”, using novel names to refer to novel entities. Such examples could be smoothly explained if LLMs were not cultural technologies but possessed a limited form of agency (beliefs, desires, and intentions). According to interpretationism in the philosophy of mind, a system has beliefs, desires and intentions if and only if its behavior is well-explained by the hypothesis that it has such states. In line with this view, we argue that cases of novel reference provide evidence that LLMs do in fact have beliefs, desires, and intentions, and thus have a limited form of agency. (shrink)

This paper studies one aspect of the great Ming dynasty philosopher Wang Yangming’s (王陽明 1472-1529) celebrated doctrine of the unity of knowledge and action (zhi xing he yi 知行合一). Wang states that his doctrine does not apply to all knowledge, but only to an elevated form of knowledge, which he sometimes calls “genuine knowledge” (zhen zhi 真知). But what is “genuine knowledge”? I develop and compare four different interpretations of this notion: the perceptual, practical, normative and introspective models. The main (...) aim of the paper is to develop these models in more detail than has been done before. But at the end of the paper I argue that the introspective model is to be preferred over the alternatives. (shrink)

I observe that the “concept-generator” theory of Percus and Sauerland (2003), Anand (2006), and Charlow and Sharvit (2014) does not predict an intuitive true interpretation of the sentence “Plato did not believe that Hesperus was Phosphorus”. In response, I present a simple theory of attitude reports which employs a fine-grained semantics for names, according to which names which intuitively name the same thing may have distinct compositional semantic values. This simple theory solves the problem with the concept-generator theory, but, as (...) I go on to show, it has problems of its own. I present three examples which the concept-generator theory can accommodate, but the simple fine-grained theory cannot. These examples motivate the full theory of the paper, which combines the basic ideas behind the concept-generator theory with a fine-grained semantics for names. The examples themselves are of interest independently of my theory: two of them constrain the original concept-generator theory more tightly than previously discussed examples had. (shrink)

An opinionated introduction to philosophical issues connected to common knowledge.

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative (...) Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

This work presents a novel formulation of quantum mechanics as the solution to an entropy maximization problem constrained by empirical measurement outcomes. By treating the complete set of possible measurement outcomes as an optimization constraint, our entropy maximization problem derives the axioms of quantum mechanics as theorems, demonstrating that the theory's mathematical structure is the least biased probability measure consistent with the observed data. This approach reduces the foundation of quantum mechanics to a single axiom, the measurement constraint, from which (...) the full theory emerges through entropy maximization. In contrast to the conventional axiomatic approach, the framework grounds the axioms directly in empirical data, substantially restricting the interpretational landscape ruling out interpretations inconsistent with this empirical foundation. (shrink)

Remarks on method in the history of Chinese philosophy for analytic philosophy.

AbstractThis essay argues for a new interpretation of the notion of “unity” in Yangming’s 王陽明 famous doctrine of the “unity of knowledge and action” (zhi xing he yi 知行合一). I distinguish two parts of Wang’s doctrine: one concerning training (gong fu 工夫), and one concerning the “original natural condition” of knowledge and action (ben ti 本體). I focus on the latter aspect of the doctrine, and argue that Wang holds, roughly, that a person exhibits knowledge in its original natural condition (...) if and only if the person exhibits action in its original natural condition. Moreover, I argue that Wang denies that knowledge in its original natural condition is identical to action in its original natural condition. (shrink)

Among philosophers, Fregeanism and sententialism are widely considered two of the leading theories of the semantics of attitude reports. Among linguists, these approaches have received little recent sustained discussion. This paper aims to bridge this divide. I present a new formal implementation of Fregeanism and sententialism, with the goal of showing that these theories can be developed in sufficient detail and concreteness to be serious competitors to the theories which are more popular among semanticists. I develop a modern treatment of (...) quantifying in for Fregeanism and sententialism, in the style of Heim and Kratzer, and then show how these theories can—somewhat surprisingly—account for “third readings” on the model of the “Standard Solution” from possible-worlds semantics. The resulting Fregean/sententialist proposal has a distinctive attraction: it treats data related to counterfactual attitudes —which have proven challenging to accommodate in the setting of possible worlds semantics—straightforwardly as third readings. (shrink)

I present a problem for an influential argument of Chen Lai's, and argue that Wang Yangming may have believed that all "motivating concerns" are actions. (The archived version is a Chinese preprint; the published Chinese version is available by the external link in the entry. An English version is available on my website.).

The difficult phrase ὅ ποτε ὄν ἐστι (hereafter ‘OPO’), which occurs in key passages in Aristotle’s discussions of blood and of time, has long vexed interpreters of Aristotle. This paper proposes a new interpretation of OPO, which resolves some textual and interpretative problems about Aristotle’s theories of blood and of time. My interpretation will also shed light on more general issues in Aristotle’s metaphysics. In the passages I will discuss, Aristotle takes both blood and time to be examples of his (...) peculiar ‘coupled entities’. He then uses OPO to provide explanations which differ from what we might call his ‘standard’ metaphysical explanations. On the ‘standard’ approach, Aristotle explains derivative entities—non-substances—by describing their relationship to substances. By contrast to this standard form of explanation, when Aristotle uses OPO he explains blood and time by describing their relationship to non-substances. This paper thus identifies a new species of metaphysical dependence in Aristotle. In addition, it provides detailed examination of evidence concerning whether Aristotle himself used coupled entities in his own physical and metaphysical theories. (shrink)

Introduction to Special Issue of Review of Philosophy and Psychology. Overview of the central issues in cognitive architecture, epistemology, and ethics surrounding cognitive penetrability. Special issue includes papers by philosophers and psychologists: Gary Lupyan, Fiona Macpherson, Reginald Adams, Anya Farennikova, Jona Vance, Francisco Marchi, Robert Cowan.

I respond to P. J. Ivanhoe's criticisms of my translation of a key passage in Wang Yangming.

A translation of two untranslated epistolary exchanges of Wang Yangming, which provide a record of how he understood the doctrine of the unity of knowledge and action after 1521.

According to relationism, for Alice to believe that some rabbits can speak is for Alice to stand in a relation to a further entity, some rabbits can speak. But what could this further entity possibly be? Higher-order metaphysics seems to offer a simple, natural answer. On this view (roughly put), expressions in different syntactic categories (for instance: names, predicates, sentences) in general denote entities in correspondingly different ontological categories. Alice's belief can thus be understood to relate her to a sui (...) generis entity denoted by "some rabbits can speak", belonging to a different ontological category than Alice herself. This straightforward account of the attitudes has historically been deemed so attractive that it was seen as providing an important motivation for higher-order metaphysics itself (Prior [1971]). But I argue that it is not as straightforward as it might seem, and in fact that propositional attitudes present a foundational challenge for higher-order metaphysics. (shrink)

We present a novel approach to quantum gravity derived from maximizing the entropy of all possible geometric measurements. Multivector amplitudes emerge as the mathematical structure that solves this maximization problem in its full generality, superseding the complex amplitudes of standard quantum mechanics. The resulting multivector probability measure is invariant under a wide range of geometric transformations, and includes the Born rule as a special case. In this formalism, the gamma matrices become self-adjoint operators, enabling the construction of the metric tensor (...) as a quantum observable. The Schrödinger equation emerges as the active generator of arbitrary metric transformations, and the gauge symmetries SU(3)xSU(2)xU(1) of the Standard Model make their appearances without additional assumptions. Remarkably, the multivector amplitude formalism is found to be consistent only with 3+1-dimensional spacetime, encountering various obstructions in other dimensional configurations. The incorporation of the metric tensor as a quantum observable provides a natural pathway to integrate gravity with quantum mechanics. This entropy maximization approach to quantum gravity offers a parsimonious and unifying framework, bridging the gap between quantum theory and general relativity. (shrink)

In the RNA World hypothesis, it is generally assumed that self-replicating RNA emerged from a primordial soup of amino acids approximately 500 million years before the advent of life on Earth. Recently, prebiotic molecules such as glycolaldehyde and amino acetonitrile have been discovered in abundance in nebulae like Sagittarius B2. This paper proposes that icy grains within these nebulae could act as primordial soups and explores the implications of this hypothesis. It is argued that the sheer abundance of these grains (...) in a typical nebula makes their collective volume astronomically greater than Earth’s primitive oceans, thus favouring the likelihood of an RNA self-replicator emerging within this environment based on volume arguments. The likelihood of naturally producing the first self-replicator may be significantly lower than previously envisioned, necessitating the contribution of a larger primordial soup spread across a nebula and functioning for billions of years before the emergence of life on Earth. According to this model, Earth could have been seeded by panspermia following the emergence of a self-replicator on nearby icy interstellar dust. Finally, we discuss the Fermi paradox in the context of this model. (shrink)

In this paper I argue that it's possible that the contents of some visual experiences are influenced by the subject's prior beliefs, hopes, suspicions, desires, fears or other mental states, and that this possibility places constraints on the theory of perceptual justification that 'dogmatism' or 'phenomenal conservativism' cannot respect.

Commentary on Andy Clark's target article on predictive coding.

The purpose of our lives is to grow step by step toward a fundamental transformation. Instead of always seeking some form of gratification, we can learn to give to others with no self-interest at all. The is the essential teaching of the Kabbalah portrayed in these essays by Baal Hasulam – the greatest modern explicator of Kabbalah. Rabbi Gottlieb provides an illuminating commentary as a living Chassidic rebbe devoted to the practice and teaching of Baal Hasulam’s spiritual path.

Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property of balancedness, a significant (...) relaxation of introspective omniscience. I provide an example which shows that Geanakoplos’s statement is incorrect. I then introduce a new property, local balancedness, which allows us both to correct Geanakoplos’s result, and to extend it to cases where the truth axiom may fail. I exploit this general Agreement Theorem to provide novel epistemic conditions for correlated and Nash equilibrium, both of which relax the assumption of introspective omniscience. In all three cases, the results are also extended to infinite state spaces. (This is Chapter 5 of my 2014 Oxford DPhil (PhD) thesis.). (shrink)

A theory of common ground is proposed and defended. This is Chapter 2 of my 2014 DPhil (PhD) thesis.

Consider the sentence “Lois knows that Superman flies, but she doesn’t know that Clark flies”. In this paper we defend a Millian contextualist semantics for propositional attitude ascriptions, according to which ordinary uses of this sentence are true but involve a mid-sentence shift in context. Absent any constraints on the relevant parameters of context sensitivity, such a semantics would be untenable: it would undermine the good standing of systematic theorizing about the propositional attitudes, trivializing many of the central questions of (...) epistemology, the philosophy of mind, and the philosophy of action. In response to this problem, we prove a series of tenability results. We show that, given certain constraints on the parameters of context sensitivity, there is a broad class of principles of propositional attitude psychology whose good standing follows from corresponding claims about people’s mental representations. But these constraints also have some surprising consequences: they are jointly incompatible with coarse-grained theories of propositions, and they are in tension with a natural picture of how speakers and hearers coordinate on the interpretation of attitude ascriptions. In light of these consequences we explore different ways in which the contextualist picture might be developed, and argue that our preferred way compares favorably with Fregeanism and neo-Russellianism. (shrink)

We provide a general argument against value incomparability, based on a new style of impossibility result. In particular, we show that, against plausible background assumptions, value incomparability creates an incompatibility between two very plausible principles for ranking lotteries: a weak "negative dominance" principle (to the effect that Lottery 1 can be better than Lottery 2 only if some possible outcome of Lottery 1 is better than some possible outcome of Lottery 2) and a weak form of ex ante Pareto (to (...) the effect that, if Lottery 1 gives an unambiguously better prospect to some individuals than Lottery 2, and equally good prospects to everyone else, then Lottery 1 is better than Lottery 2). After spelling out our results, and the arguments based on them, we consider which principle the proponent of incomparability ought to reject. (shrink)

Inquiry is guided, in the minimal sense that it is not haphazard. It is also often thought to have as a natural stopping point ceasing to inquire, once inquiry into a question yields knowledge of an answer. On this picture, inquiry is both telic and guided. By contrast, mind-wandering is unguided and atelic, according to the most extensively developed philosophical theory of it. This paper articulates a puzzle that arises from this combination of claims: there seem to be plenty of (...) examples of inquiry progressing within mind-wandering, yet theories of inquiry and mind-wandering can make wandering inquiry seem impossible or incoherent. I offer several solutions to this puzzle and make the case that taken together, they illuminate a prevalent form of inquiry that the burgeoning literature on that topic overlooks: inquiry that progresses spontaneously. (shrink)

This paper defends the Content View: the thesis that all visual experiences have contents.

Several theorists have observed that attitude reports have what we call “revisionist” uses. For example, even if Pete has never met Ann and has no idea that she exists, Jane can still say to Jim ‘Pete believes Ann can learn to play tennis in ten lessons’ if Pete believes all 6-year-olds can learn to play tennis in ten lessons and it is part of Jane and Jim’s background knowledge that Ann is a 6-year-old. Jane’s assertion seems acceptable because the claim (...) she reports Pete as believing is entailed by Pete’s beliefs if they are revised in light of Jane and Jim’s background knowledge. We provide a semantic theory of revisionist reports based on this idea. We observe that the admissible “revisions” are limited in a striking way. Jane cannot say ‘Pete thinks Ann is a 6-year-old and can play tennis in ten lessons’ in the same context that she can say ‘Pete believes Ann can learn to play tennis ten lessons’, even though this too follows from Jane and Jim’s background knowledge together with what Pete believes. Our theory predicts the infelicity of these latter reports. It also has the resources to predict the truth of “exported” attitude reports and casts the relationship between these reports and “singular thought” in a new light. We conclude by discussing how revisionist reports make trouble for a simplistic view of the connection between the relations expressed by attitude verbs in natural language and the relations of most interest to philosophers of mind and cognitive science. (shrink)

An action is agentially perfect if and only if, if a person tries to perform it, they succeed, and, if a person performs it, they try to. We argue that trying itself is agentially perfect: if a person tries to try to do something, they try to do it; and, if a person tries to do something, they try to try to do it. We show how this claim sheds new light on the logical structure of intentional action, on the (...) question of whether basic actions are tryings, and on the notion of “options” in decision theory. On the way to these central ideas, we argue that a person can try to do something even if they believe it is impossible that they will succeed, that a person can try to do something even if they do not want to succeed, and that a person can try to do something even if they do not intend to succeed. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In (...) this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

Can perceptual experiences be states of uncertainty? We might expect them to be, if the perceptual processes from which they're generated, as well as the behaviors they help produce, take account of probabilistic information. Yet it has long been presumed that perceptual experiences purport to tell us about our environment, without hedging or qualifying. Against this long-standing view, I argue that perceptual experiences may well occasionally be states of uncertainty, but that they are never probabilistically structured. I criticize a powerful (...) line of reasoning that we should expect perceptual experience to be probabilistic, given their interfaces with unconscious probabilistic information, with behavior responsive to it, and with credences. (shrink)