Is the societal-level of analysis sufficient today to understand the values of those in the global workforce? Or are individual-level analyses more appropriate for assessing the influence of values on ethical behaviors across country workforces? Using multi-level analyses for a 48-society sample, we test the utility of both the societal-level and individual-level dimensions of collectivism and individualism values for predicting ethical behaviors of business professionals. Our values-based behavioral analysis indicates that values at the individual-level make a more significant contribution to (...) explaining variance in ethical behaviors than do values at the societal-level. Implicitly, our findings question the soundness of using societal-level values measures. Implications for international business research are discussed. (shrink)

This is a transcript of a conversation between P F Strawson and Gareth Evans in 1973, filmed for The Open University. Under the title 'Truth', Strawson and Evans discuss the question as to whether the distinction between genuinely fact-stating uses of language and other uses can be grounded on a theory of truth, especially a 'thin' notion of truth in the tradition of F P Ramsey.

Here you can download Torrijos' contribution to this book: the general Presentation and the Introduction to the second part.

Aquinas says that omnipotence means power for everything possible, which is everything not self-contradictory. This view faces various objections; to many of them, it seems that one could respond more easily by saying that omnipotence is God's power for everything that is not self-contradictory for Him to do. But this is a weak answer, and Thomas's support for it is only apparent. A more satisfactory solution is found in a fundamental restriction on the term "power" that Thomas thinks necessary when (...) power is attributed to god. It is exclusively productive power. So omnipotence is the power to produce everything producible. Still, Thomas himself, in earlier works, seems to have adopted an excessive distinction between power and will in God. But in the two Summae, it becomes clear that power is properly power to produce some being; and so omnipotence is power to produce every possible being. (shrink)

What makes a person the same over time is a question dealt with by many philosophers. I too offered a purely metaphysical answer in a different work, however, as with many other theorists, I offered an answer outside of considering the political consequences of the theory I offered. Upon reflection, I now see that this was a mistake in need of correction. This is because I believe that conceptually a theory about how a person remains one and the same over (...) time presupposes an understanding of the nature of personhood as an ontological kind. That is, to remain the same person over time logically requires remaining a person. While being a counting as a person is a purely metaphysical matter, the fact is having the status of being a person is highly significant both morally and politically, as any social movement fighting for being granted this status to groups of individuals who have been denied it. To ignore the moral and political consequences of a metaphysical theory of persons is therefore ethically irresponsible. I argue that many of the assumptions concerning personhood are ethically and politically biased in favor of a conception of persons that disadvantages certain individuals, and that examining and correcting these biases is essential to be ethically responsible theorists of personhood. (shrink)

Tradução para o português do livro "Ceticismo e naturalismo: algumas variedades", Strawson, P. F. . São Leopoldo, RS: Editora da Unisinos, 2008, 114 p. Coleção: Ideias. ISBN: 9788574313214. Capítulo 1 - Ceticismo, naturalismo e argumentos transcendentais 1. Notas introdutórias; 2. Ceticismo tradicional; 3. Hume: Razão e Natureza; 4. Hume e Wittgenstein; 5. “Apenas relacionar”: O papel dos argumentos transcendentais; 6. Três citações; 7. Historicismo: e o passado.

I've previously suggested that the historical evidence used to challenge scientific realism should lead us to embrace what I call Uniformitarianism, but many recently influential forms of scientific realism seem happy to share this commitment. I trace a number of further points of common ground that collectively constitute an appealing Middle Path between classical forms of realism and instrumentalism, and I suggest that many contemporary realists and instrumentalists have already become fellow travelers on this Middle Path without recognizing how far (...) they have thereby diverged from those who share their labels and slogans. I conclude by describing their central remaining disagreement and the sorts of evidence needed to resolve it. (shrink)

Although some authors hold that natural kinds are necessarily relative to disciplinary domains, many authors presume that natural kinds must be absolute, categorical features of the reality —often assuming that without even mentioning the alternative. Recognizing both possibilities, one may ask whether the difference especially matters. I argue that it does. Looking at recent arguments about natural kind realism, I argue that we can best make sense of the realism question by thinking of natural kindness as a relation that holds (...) between a category and a domain. (shrink)

Cover songs are a familiar feature of contemporary popular music. Musicians describe their own performances as covers, and audiences use the category to organize their listening and appreciation. However, until now philosophers have not had much to say about them. This book explores how to think about covers, appreciating covers, and the metaphysics of covers and songs. Along the way, it explores a range of issues raised by covers, from the question of what precisely constitutes a cover, to the history (...) and taxonomy of the category, the various relationships that hold between songs, performances, and tracks, and the appreciation and evaluation of covers. (shrink)

A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic (...) 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR. (shrink)

The underdetermination of theory by evidence is supposed to be a reason to rethink science. It is not. Many authors claim that underdetermination has momentous consequences for the status of scientific claims, but such claims are hidden in an umbra of obscurity and a penumbra of equivocation. So many various phenomena pass for `underdetermination' that it's tempting to think that it is no unified phenomenon at all, so I begin by providing a framework within which all these worries can be (...) seen as species of one genus: A claim of underdetermination involves (at least implicitly) a set of rival theories, a standard of responsible judgment, and a scope of circumstances in which responsible choice between the rivals is impossible. Within this framework, I show that one variety of underdetermination motivated modern scepticism and thus is a familiar problem at the heart of epistemology. I survey arguments that infer from underdetermination to some reëvaluation of science: top-down arguments infer a priori from the ubiquity of underdetermination to some conclusion about science; bottom-up arguments infer from specific instances of underdetermination, to the claim that underdetermination is widespread, and then to some conclusion about science. The top-down arguments either fail to deliver underdetermination of any great significance or (as with modern scepticism) deliver some well-worn epistemic concern. The bottom-up arguments must rely on cases. I consider several promising cases and find them to either be so specialized that they cannot underwrite conclusions about science in general or not be underdetermined at all. Neither top-down nor bottom-up arguments can motivate any deep reconsideration of science. (shrink)

In 1956, a few writings of Wittgenstein that he didn't publish in his lifetime were revealed to the public. These writings were gathered in the book Remarks on the Foundations of Mathematics (1956). There, we can see that Wittgenstein had some discontentment with the way philosophers, logicians, and mathematicians were thinking about paradoxes, and he even registered a few polemic reasons to not accept Gödel’s incompleteness theorems.

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

Nuestro interés en el contenido mental no-conceptual es, principalmente, la articulación de una versión sustantiva (no-trivial) de esta clase de contenido en la experiencia perceptual. El debate acerca del contenido no-conceptual ha girado, en su mayor parte, alrededor de su existencia; y los argumentos que se han ofrecido en su favor abogan por una versión no sustantiva según la cual el contenido no-conceptual es aquel que no satisface ciertos requisitos conceptuales. Así, para desarrollar una versión sustantiva del contenido mental no-conceptual (...) hemos apelado a la versión de la experiencia perceptual de propiedades espaciales ofrecida por Evans (1982 cap. 6). A partir de esto desarrollamos un nuevo argumento a favor del contenido no-conceptual de la experiencia perceptual que lo vincula a la actividad característica de la experiencia perceptual. Por último, exponemos uno de los ataques de McDowell (1996) a la noción de contenido no-conceptual y presentamos nuestras réplicas a este ataque, mostrando su insuficiencia. Al mostrar que la crítica de McDowell no es exitosa, consideramos que podríamos tener una versión del contenido no-conceptual de la experiencia que es inmune a esta línea de argumentación. (shrink)

Sol LeWitt is probably most famous for wall drawings. They are an extension of work he had done in sculpture and on paper, in which a simple rule specifies permutations and variations of elements. With wall drawings, the rule is given for marks to be made on a wall. We should distinguish these algorithmic works from impossible-to-implement instruction works and works realized by following preparatory sketches. Taking the core feature of a wall drawing to be that it is algorithmic, some (...) of LeWitt's later works are wall drawings in name only. (shrink)

Most philosophers who study moral responsibility have done so in isolation of the concept of truth. Here, I show that thinking about the nature of truth has profound consequences for discussions of moral responsibility. In particular, by focusing on the very trivial nature of truth—that truth depends on the world and not the other way around—we can see that widely accepted counterexamples to one of the most influential incompatibilist arguments can be shown not only to be false, but also impossible.

The problem considered in this chapter emerges from the tension we find when looking at the design and architecture of chatbots on the one hand and their conversational aptitude on the other. In the way that LLM chatbots are designed and built, we have good reason to suppose they don't possess second-order capacities such as intention, belief or knowledge. Yet theories of conversation make great use of second-order capacities of speakers and their audiences to explain how aspects of interaction succeed. (...) As we can all bear witness to now though, at the point of use chatbots appear capable of performing language tasks at a level close to that of humans. This creates a tension when we consider something like, for example, the classic Gricean theory of implicature. On a broad summary of this type of account, to utter p and implicate q requires the reflexive occurrence of an audience supposing a speaker believes that q, and the speaker believing that their audience can determine they believe it when they utter p. So taken at face value, if a chatbot doesn’t have the capacity for belief, then either in their role as speaker or audience, they would not seem capable of either generating or comprehending implicatures. Yet on the surface it does seem that chatbots are capable of dealing with (some) implicatures, and as such it raises questions about how we should then correlate this with what we think occurs in cases of implicature with chatbots. (shrink)

Imperatives cannot be true, but they can be obeyed or binding: `Surrender!' is obeyed if you surrender and is binding if you have a reason to surrender. A pure declarative argument — whose premisses and conclusion are declaratives — is valid exactly if, necessarily, its conclusion is true if the conjunction of its premisses is true; similarly, I suggest, a pure imperative argument — whose premisses and conclusion are imperatives — is obedience-valid (alternatively: bindingness-valid) exactly if, necessarily, its conclusion is (...) obeyed (alternatively: binding) if the conjunction of its premisses is. I argue that there are two kinds of bindingness, and that a vacillation between two corresponding variants of bindingness-validity largely explains conflicting intuitions concerning the validity of some pure imperative arguments. I prove that for each of those two variants of bindingness-validity there is an equivalent variant of obedience-validity. Finally, I address alternative accounts of pure imperative inference. (shrink)

This paper continues and extensive exploration of the QG and TOE resulting from the PF interpretation of QM. Some highlights are an exploration of symmetries of the Standard Model, outlines of testable predictions of implications for QG, that this theory can simultaneously give an account of dark matter and dark energy, probabilities and statevector collapse vs. gravity, applications of the causal interaction tensor Cαβγδ(Fi, Fj). Note the first section mentions qualia but this is not a psychological theory this is an (...) ontic theory. (shrink)

One of the predominant debates in AI Ethics is the worry and necessity to create fair, transparent and accountable algorithms that do not perpetuate current social inequities. I offer a critical analysis of Reuben Binns’s argument in which he suggests using public reason to address the potential bias of the outcomes of machine learning algorithms. In contrast to him, I argue that ultimately what is needed is not public reason per se, but an audit of the implicit moral assumptions of (...) societies within which algorithms are built and applied. Public justification is appealing since it offers us the possibility to align the decision-making outcomes of the algorithm with the core moral values of stakeholders within a constitutional democratic society. My concern is that the common moral principles that form the foundation of public reason are not necessarily neutral, as they still express specific moral ideals and normative standards even if there is moral agreement by society as a whole, or among different stakeholders within society. Appealing to such normative standards may thus still lead to algorithmic outcomes being biased as common moral values may very well still be discriminatory even though they are formed from a consensus, and even if public reason is applied as a kind of filter for potential algorithmic outcomes. Hence, I argue that these implicit moral norms within society that we take as a given in public reasoning, need to be audited from generation to generation in order to effectively mitigate potential algorithmic bias. (shrink)

"Over three years of study and fellowship, sixteen Muslim, Jewish, and Christian scholars sought to answer one question: “Do our three scriptures unite or divide us?” They offer their answers in this book: sixteen essays on how certain ways of reading scripture may draw us apart and other ways may draw us, together, into the source that each tradition calls peace. Reading scriptural sources in the classical and medieval traditions, the authors examine how each tradition addresses the “other” within its (...) tradition and without, how all three traditions attend to poverty as a societal and spiritual condition, and what it means to read scripture while facing the challenges of modernity. Ochs and Johnson have assembled a unique approach to inter-religious scholarship and a rare look at scriptural study as a pathway to peace. “Scriptural reasoning, the growing practice of Jews, Christians, and Muslims reading their scriptures together, makes good academic and common sense in a time of crisis. This ground-breaking book, the outcome of an imaginative 3-year experiment by the Princeton Center of Theological Inquiry, shows scholars and thinkers of the Abrahamic traditions going deeper into the traditions and into their contemporary situation. The result is something new, wise, and relevant… full of promise for the future. Where else can one find testimonies to Jews, Christians, and Muslims coming together not only in study, thinking, and wisdom-seeking but also in play, joy, and friendship?”--David F. Ford, Regius Professor of Divinity, University of Cambridge and Director, Cambridge Inter-Faith Programme". (shrink)

Presentist Fragmentalism is a novel interpretation of quantum mechanics. This paper develops the resulting theory of Quantum Gravity.

Typical discussions of virtual reality (VR) fixate on technology for providing sensory stimulation of a certain kind. They thus fail to understand reality as the place wherein we live and work, misunderstanding it instead as merely a sort of presentation. The first half of the paper examines popular conceptions of VR. The most common conception is a shallow one according to which VR is a matter of simulating appearances. Yet there is, even in popular depictions, a second, more subtle conception (...) according to which VR is a matter of facilitating new kinds of interaction. The latter half of the paper turns to questions about the contemporary technology of Internet chatrooms. The fact that chatrooms can be used in certain ways suggests something about the prospects for VR. The penultimate section asks whether chatrooms may legitimately be thought of as places. (In a sense, they may.) The final section asks whether cybersex may legitimately be thought of as sex. (Again, yes.) Chatroom technology thus provides an argument for the second conception of VR over its much ballyhooed rival. (shrink)

General Introduction: In [1] a Calculus of Qualia (CQ) was proposed. The key idea is that, for example, blackness is radically different than █. The former term, “blackness” refers to or is about a quale, whereas the latter term, “█” instantiates a quale in the reader’s mind and is non-referential; it does not even refer to itself. The meaning and behavior of these terms is radically different. All of philosophy, from Plato through Descartes through Chalmers, including hieroglyphics and emojis, used (...) referential terms up until CQ. This paper in this series of papers addresses the question of why is there something rather than nothing, at length, and gives a radical new answer. It has to do with the fact in CQ that, while blackness is contingently possible, █ is necessarily actual, as it was in this sentence. (shrink)

This is the first in a series of papers developing a theory of quantum gravity that is consistent with the PF interpretation of quantum mechanics. "Key Features: Reconciles quantum theory, general relativity, and the PF interpretation in a common framework...".

This paper appears to give a Theory of Everything.

Do the ethical features of an artwork bear on its aesthetic value? This movie endorses misogyny, that song is a civil rights anthem, the clay constituting this statue was extracted with underpaid labor—are facts like these the proper bases for aesthetic evaluation? I argue that this debate has suffered from a false presupposition: that if the answer is yes (for at least some such ethical features), such considerations feature as pro tanto contributions to an artwork's overall aesthetic value, i.e., as (...) merits or flaws which make something have more or less overall aesthetic value. As the case of ethically laden, aesthetic evaluation makes clear, however, good aesthetic judgement is irreducibly multi-dimensional, e.g., "the movie has an engaging soundtrack, tasteful camera work, and takes a misogynistically prurient perspective on its female lead.'' Such a "non-summative" judgement refuses to reduce those various dimensions of aesthetic value to a single aggregate aesthetic evaluation, like "it's a 6/10" or "it's a pretty good movie!" I defend both the modest claim that such non-summative evaluations are not mistaken and the extremist claim that summative (i.e., unidimensional) aesthetic evaluation is defective by considering other domains of normative assessment in which summing seems inappropriate, notably including evaluations of people's character. (shrink)

This paper argues against the common, often implicit view that theories are some specific kind of thing. Instead, I argue for theory concept pluralism: There are multiple distinct theory concepts which we legitimately use in different domains and for different purposes, and we should not expect this to change. The argument goes by analogy with species concept pluralism, a familiar position in philosophy of biology. I conclude by considering some consequences for philosophy of science if theory concept pluralism is correct.

That every expression of language that is {true on the basis of its meaning expressed using language} must have a connection by truth preserving operations to its {meaning expressed using language} is a tautology. The accurate model of the actual world is expressed using formal language and formalized natural language.

General Introduction: In [1] a Calculus of Qualia (CQ) was proposed. The key idea is that, for example, blackness is radically different than █. The former term, “blackness” refers to or is about a quale, whereas the latter term, “█” instantiates a quale in the reader’s mind and is non-referential; it does not even refer to itself. The meaning and behavior of these terms is radically different. All of philosophy, from Plato through Descartes through Chalmers, including hieroglyphics and emojis, used (...) referential terms up until CQ. This paper in this series of papers includes a relatively short but comprehensive discussion with the AI Claude 3.5 Sonnet on how the CQ impacts various theories of consciousness, including Materialism, Dualism, Idealism, and 14 others. (shrink)

A discussion and qualified defense of Philip Kitcher on scientific significance and ‘well-ordered science.’ (Qualified because I argue that Kitcher’s position is made unstable by his reliance on the largely unanalyzed notion of natural curiosity.).

One popular conception of natural theology holds that certain purely rational arguments are insulated from empirical inquiry and independently establish conclusions that provide evidence, justification, or proof of God’s existence. Yet, some raise suspicions that philosophers and theologians’ personal religious beliefs inappropriately affect these kinds of arguments. I present an experimental test of whether philosophers and theologians’ argument analysis is influenced by religious commitments. The empirical findings suggest religious belief affects philosophical analysis and offer a challenge to theists and atheists, (...) alike: reevaluate the scope of natural theology’s conclusions or acknowledge and begin to address the influence of religious belief. (shrink)

Đến khúc này, 3 ông bói cá cũng bí nên chuyển chủ đề. Hướng sang vấn đề ăn cá vậy. Đây là vấn đề truyền thống lâu đời. Có chuyện gì lớn?

Many differences exist between the logical relations “equality” and “equivalence”. In this monograph I point out differences that concern definition, linguistics, computational gates and tables, denotation, application, negation of terms, negation of the relation, relations to other relations, the laws of symmetry, transitivity and reflexivity, the laws of commutation and permutation, the law of tautology, the law of distribution, the law of association, propositional meaning, and “genesis”. I also point out a form of “symmetry breaking”: the negation of some equality (...) may yield some non-equality, while the negation of that non-equality might not yield the same equality. (For full access: use the website link of the title page. -- Copyright License: CC BY-NC-ND. -- DOI: 10.17026/dans-zh3-h2b2 --). (shrink)

The main thrust of this study is to examine the impact of social cost on the corporate performance of petroleum marketing firms in Nigeria. Ex post facto research design was adopted, secondary sources of data were collected for analysis of results and interpretation of data. The results indicated that social cost positively influences the corporate performance of petroleum marketing firms in Nigeria. Hence, it was recommended that the federal government should mandate all petroleum marketing companies to capture and disclose all (...) quantitative data relating to corporate social responsibility which would serve as a boost to the company performances vis-a-vis increased employee productivity. (shrink)

We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...) only because they are self-contradictory we could define them as unsound instead of defining the formal system as incomplete. (shrink)

For any natural (human) or formal (mathematical) language L we know that an expression X of language L is true if and only if there are expressions Γ of language L that connect X to known facts. -/- By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to neither True nor False.

We are political creatures, and we all need others who care about the development of our character and who offer guidance and advice; “if this were not so, we there would be no need for an instructor” (N. Ethics, 1003b12-3). We imitate those who have already successfully developed courage or moderation, acting as if we were brave or moderate, struggling at first, but slowly training ourselves...but, if “acting-as-if” and imitation are the keys to developing virtue, then surely the Poetics will (...) provide a clue to Bk. II of the Ethics, and in a way that may add to our understanding of how ethics and aesthetics are connected. (shrink)

Tradução para o português do ensaio "Freedom and Resentment”, de P. F. Strawson. Publicado originalmente em Proceedings of the British Academy, v. 48, 1960. Republicado em Freedom and Resentment and Other Essays. Londres: Methuen, 1974. [Routledge, 2008, p. 2-28]. Publicado na coletânea: Ensaios sobre a filosofia de Strawson: com a tradução de Liberdade e ressentimento & Moralidade social e ideal individual. Organizadores: Jaimir Conte & Itamar Luís Gelain. Editora da UFSC, 2015. ISBN: 9788532807250.

Tradução para o português do ensaio "Social Morality and Individual Ideal”. Publicado originalmente em Philosophy: The Journal of the Royal Institute of Philosophy, vol. XXXVI, n. 136, p. 1-17, Jan. 1961. Republicado em: STRAWSON, P. F. Freedom and Resentment and Other Essays. Londres: Methuen, 1974. [Routledge, 2008, p. 26-44]. ]. Publicado na coletânea: Ensaios sobre a filosofia de Strawson: com a tradução de Liberdade e ressentimento & Moralidade social e ideal individual. Organizadores: Jaimir Conte & Itamar Luís Gelain. Editora da (...) UFSC, 2015. ISBN: 9788532807250. (shrink)

Both Tarski and Gödel “prove” that provability can diverge from Truth. When we boil their claim down to its simplest possible essence it is really claiming that valid inference from true premises might not always derive a true consequence. This is obviously impossible.

To stimulate research and innovation (R&I), to contribute to the solution of societal challenges and to align R&I with societal values, the European Commission has launched the governance framework of Responsible Research and Innovation (RRI). RRI figures in many high-level EU policies as a means to promote smart growth, and a growing community of R&I practitioners from both the public and private sectors appears committed to it. Although debates on what RRI precisely entails have not reached closure yet, RRI provides (...) an interesting avenue to explore ways of making R&I more societally germane. While recognizing the usefulness of keeping critical reflection on RRI’s meaning alive, we suggest that to make the step from theorizing to implementation, RRI could benefit from a clearer conceptualization. This chapter presents the iterative trajectory in conceptualizing RRI followed as part of RRI Tools, one of a number of EC-funded research projects and support acts aimed at fleshing out what RRI can and should be, and the conceptualization of RRI that this led to. It suggests that RRI is best captured if in R&I governance attention is paid to the five p’s of Purpose, Products, Processes, Preconditions and People, and that further elaborations on the meaning of RRI should happen in dialogue with attempts at practicing RRI. (shrink)

This is the formal YACC BNF specification for Minimal Type Theory (MTT). MTT was created by augmenting the syntax of First Order Logic (FOL) to specify Higher Order Logic (HOL) expressions using FOL syntax. Syntax is provided to enable quantifiers to specify type. FOL is a subset of MTT. The ASSIGN_ALIAS operator := enables FOL expressions to be chained together to form HOL expressions.

The fail-safe makes sure the fee is high enough to meet carbon emission reduction targets. The safeguard keeps the fee from getting any higher than needed. -/- One of the ways that we could account for the unpredictability of the price elasticity of demand for carbon would be to provide a fail-safe mechanism to ensure that we definitely stay on the carbon reduction schedule. If we keep Energy Innovation Act (HR 763) essentially as it is and scale up the annual (...) carbon fee increase by Number-of-Years-Behind-Schedule * 0.15. (shrink)

By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be semantically (...) incorrect. (shrink)