Bear bile has long been used in the Asian traditional pharmacopoeia. Bear farming first started in China ~30 years ago in terms of reducing the number of poached bears and ensuring the supply of bear bile. Approximately 13,000 bears are today captivated on Asia’s bear farms: their teeth are broken and the claws are also pulled out for the sake of human safety; the bears are imprisoned in squeeze cages for years; and a catheter is daily inserted into a bear’s (...) gall bladder or a tube is implanted inside its body in order to collect the dripped bile—captive bears moan in severe pain whenever the bile is extracted. When the bears cannot produce sufficient bile, they are often left to die of starvation. It must be impossible to justify the bile extraction from living bears because (1) medicinal/herbal alternatives are similar to bear bile; (2) there is no evidence to suggest that bear farming has any beneficial effects on wild bear populations; and (3) ethical problems lie not only in the painful bile extraction but also the whole lifecycle of captive bears. In conclusion, human welfare (health care) based on traditional medicine is upheld by sacrificing bear welfare. Since a trial calculation suggests that it is economically unfeasible to keep a proper balance between bear welfare and the traditional pharmacopeia, the cultivation of herbal alternatives seems to be a possible solution to phase out bear faming and maintain the practice of traditional medicine in Asia. (shrink)
We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved (...) in a syntactic way by modifying Gentzen's method. Thisdual-context style system exemplifies the effectiveness of dual-contextformulation in formalizing various non-classical logics. (shrink)
Kawada Makoto (2011). Foreword. In Shengzhe Nie (ed.), Business Management the Chinese Way. Foreign Language Teaching and Research Press = Wai Yu Jiao Xue Yu Yan Jiu Chu Ban She.score: 30.0
Makoto (sincerity, truth, or faithfulness) is an important concept in haikai (Japanese comic linked verse) poetics. The discussions on makoto by the seventeenth-century haikai master Uejima Onitsura (1661-1738) clearly refer to the Daoist discourse on ziran (the Natural), and the clarification of this intertextuality is crucial to the understanding of the theoretical connotations of the term.
This note is a reply to "On the Lumping Semantics of Counterfactuals" by Makoto Kanazawa, Stefan Kaufmann, and Stanley Peters. It shows first that the first triviality result obtained by Kanazawa, Kaufmann, and Peters is already ruled out by the constraints on admissible premise sets listed in Kratzer (1989). Second, and more importantly, it points out that the results obtained by Kanazawa, Kaufmann, and Peters are obsolete in view of the revised analysis of counterfactuals in Kratzer..
Among various views on intergenerational justice, the most widely accepted theory invokes the rights of future generations. However, the rights theory seems to suffer from the non-identity problem addressed by Derek Parfit. Some rights theorists attempt to circumvent the problem by examining causal links between actions taken by preceding generations and their effects on succeeding ones. Others try to do so by replacing future individual rights with such collective rights. This paper argues that both individualist and collectivist versions of the (...) rights theory fail to supply grounds for intergenerational concern. The paper then offers an alternative theory that refines the idea of duty of fair play developed by John Rawls and applies it to the context of intergenerational relationships. To begin with, I identify several characteristics of posterity and explicate the adverse implications these characteristics have for other major theories of intertemporal concern than the rights theory. Next, different versions of the rights theory are closely examined from the perspective of the non-identity problem. Then, I offer an alternative argument for caring about future people, which is founded on the idea of intergenerational fair play. This paper concludes by noting that the fairness theory, unlike its rivals, does not face the non-identity problem or any other problems stemming from the features of posterity previously identified. (shrink)
One of the primary views on our supposed obligation towards our descendants in the context of environmental problems invokes the idea of the rights of future generations. A growing number of authors also hold that the descendants of those victimized by historical injustices, including colonialism and slavery, have the right to demand financial reparations for the sufferings of their distant ancestors. However, these claims of intergenerational rights face theoretical difficulties, notably the non-identity problem. To circumvent this problem in a relationship (...) between present and future generations, some rights theorists replace future individual rights with such collective rights. Others advance the threshold conception of harm in discussing intergenerational relationships in general. Despite the significant implications these revisionist views might have, few efforts have been made to scrutinize their solidity. To plug such a gap in the literature, this paper examines to what extent the collective understanding of intergenerational rights is pertinent. I also explore the virtues and drawbacks of the threshold interpretation of harm. The paper concludes by suggesting that the motivation behind these and other versions of the rights theory suffers from the ambiguity of a traditional dichotomy between perfect and imperfect duties. (shrink)
Most cosmopolitans who are concerned about world poverty assume that for citizens of affluent societies, justice beyond national borders is a matter of their positive duty to provide aid to distant people suffering from severe poverty. This assumption is challenged by some authors, notably Tomas Pogge, who maintains that these citizens are actively involved in the incidence of poverty abroad and therefore neglect their negative duty of refraining from harming others. This paper examines the extent to which it is pertinent (...) to contend that citizens in economically advanced countries are morally liable for the impoverishment of a sizable population of the developing world. The contention in question can be interpreted in two nonexclusive ways. First, it might imply that historical injustices, including colonialism and slavery, contributed to both contemporary affluence in some parts of the world and poverty in others. Second, it could imply that the present global economic system, instituted and implemented by the governments of rich and powerful countries acting in the name of their citizens, is benefiting the citizens while harming the world’s disadvantaged. The author argues that the idea of reparation for historical injustices suffers from serious philosophical difficulties, including the non-identity problem presented by Derek Parfit, and thus fails to provide a satisfactory approach to the existing problem of poverty. This paper then examines the alleged liability of citizens in affluent countries, with a special reference to empirical observations on the policy process. The paper concludes by suggesting a twofold theory of global justice, which combines material, managerial, and moral assistances for a society lacking a competent government and proposes institutional reforms in the global order in order to achieve poverty reduction. (shrink)
This article inquires into a paradoxical position held by the concept of ‘nature’ in Derrida's thought. While a pivotal part of his project of deconstruction is devoted to a critique of the metaphysical privileging of nature over its others (technics, culture, and so on), the same project also aims at dismantling the hierarchical binary opposition of man/animal. Insofar as the term ‘animal’ or ‘animality’ to a large extent overlaps with nature, these two strands of his thought appear to stand in (...) a significant tension with each other. I explore this conceptual tension by re-examining Derrida's early critique of the notion of nature – specifically in his reading of Rousseau – in conjunction with his later engagement with the question of animality. As my reading shows, deviating from his early approach, his later work indicates the way in which animal others (and, by extension, all living and non-living others) are indeed constituted by supplementarity and yet, in their irreplaceable singularity, exceed the very structure of supplementarity. This opens up a new way of conceiving nature, no longer as originary presence nor simply as an effect of supplementary play, but in terms of the aporetic relation between supplementarity and what may be termed ‘the unsupplementable’. (shrink)
In this paper, I show that the availability of what some authors have called the weak reading and the strong reading of donkey sentences with relative clauses is systematically related to monotonicity properties of the determiner. The correlation is different from what has been observed in the literature in that it concerns not only right monotonicity, but also left monotonicity (persistence/antipersistence). I claim that the reading selected by a donkey sentence with a double monotone determiner is in fact the one (...) that validates inference based on the left monotonicity of the determiner. This accounts for the lack of strong reading in donkey sentences with MON determiners, which have been neglected in the literature. I consider the relevance of other natural forms of inference as well, but also suggest how monotonicity inference might play a central role in the actual process of interpretation. The formal theory is couched in dynamic predicate logic with generalized quantifiers. (shrink)
In this collection on the Kyoto School of Philosophy, the author offers the reader Tanabe's religious philosophy, but also, and for the first time, his ...
In the past decade, a growing number of authors, notably Thomas Pogge, have maintained that citizens in economically advanced societies are responsible for extreme and extensive poverty in the developing world. Iris Marion Young proposed the social connection model of responsibility, which asserts that these citizens participate in networks that give rise to global structural injustices. While Pogge’s argument for the existence of citizens’ responsibility has been the subject of widespread debate, few efforts have been made to scrutinise the solidity (...) of Young’s perspective. To plug this gap in the literature, this paper assesses the pertinence of Young’s view. A more traditional view than those of Pogge and Young considers poverty as indicating a lack of respect for the human rights of those living in less-developed countries. Rights theorists of global justice, however, have paid scant attention to philosophical observations concerning redistribution within the borders of a society. To remedy this shortcoming, this paper endeavours to develop the theory that citizens in affluent societies bear a duty correlative to the subsistence right of the global needy, by exploring sufficientarianism, which is one of the primary views on domestic redistribution. To begin with, I make a distinction between the responsibility-based theory and the right-based theory of global justice. This is followed by a close examination of Young’s social connection model as a significant version of the former position. I then offer a right-based argument that invokes the sufficientarian idea of the human right to live above the threshold of safe and healthy subsistence. (shrink)
In newly emerging democracies, succeeding governments have numerous policy tasks for the purpose of developing the free market and the democratic process. In such legal systems, policy-oriented views of law, which regard law as a policy tool for diminishing public problems, seem descriptively pertinent and prescriptively helpful. This is also the case in mature democratic legal systems, where the public problems faced by governments become more and more complex. Policy-directional views of law do not necessarily imply that law is a (...) value-neutral means that can serve any possible political ends. It is widely recognized among legal theorists and practitioners, with notable exceptions represented by exclusive legal positivists, that the law involves moral values, including justice and liberty. In the present essay, I focus on one version of policy-oriented views of law that is based on the fundamental ideals of justice and interest. By sketching out this version, I attempt to shed new light on some concepts and issues in jurisprudence. To begin, I articulate the concept of justice and identify the difficulties that interest-based conceptions of justice encounter, by referring to some classical works. I also make a distinction between different conceptions of interest. Next, the two basic concepts in law — rights and liberty — are explained in terms of justice and interest. Efficiency, which has been largely neglected in traditional jurisprudence notwithstanding its practical significance, is also briefly discussed. Then, I turn to exploring the implications that the law-as-policy theory grounded on justice and interest might have for the foundations of two legal domains: criminal law and laws governing political participation. Some allegations and objections against this theory are described, and responses to them are given. The essay concludes by noting the questions that remain open in this theory. (shrink)
In the transition from a repressive to a democratic society, the successor government faces the problem of how to deal with grave human rights violations such as killings and torture committed under its predecessor. This paper analyzes the dilemma a new government may encounter when it attempts to prosecute and punish those found responsible. On one hand, trials of chargeable officers may be able to prevent human rights abuses in the future and to facilitate instituting or restoring democracy. On the (...) other, in the case that there were no legal rules definitively prohibiting the abuses committed by these officers, the trials require ex post facto laws, which breach the principle of nulla poena sine lege, and more generally violate the rule of law. These retroactive laws not only break legal predictability but treat individuals unfairly. After identifying both the need for, and the legal and political losses incurred by such criminal trials, the author examines the claims that international law resolves the dilemma of retroactive justice or that prosecution is justified as a fulfillment of international obligation. Then the author refers to this dilemma as “dirty hands” to characterize a circumstance in which one cannot avoid using the wrong means to obtain the best ends. Such characterization has normative implications for three aspects of trials: the process of enacting retroactive laws and the process of conducting the trials; the choice of other possible legal remedies; and the principles related to reactions in the international community. (shrink)
Building on Ben-Avi and Winter’s (2007) work, this paper provides a general “intensionalization” procedure that turns an extensional semantics for a language into an intensionalized one that is capable of accommodating “truly intensional” lexical items without changing the compositional semantic rules. We prove some formal properties of this procedure and clarify its relation to the procedure implicit in Montague’s (1973) PTQ.
This paper presents a new algorithm to find an appropriate similarityunder which we apply legal rules analogically. Since there may exist a lotof similarities between the premises of rule and a case in inquiry, we haveto select an appropriate similarity that is relevant to both thelegal rule and a top goal of our legal reasoning. For this purpose, a newcriterion to distinguish the appropriate similarities from the others isproposed and tested. The criterion is based on Goal-DependentAbstraction (GDA) to select a (...) similarity such that an abstraction basedon the similarity never loses the necessary information to prove the ground (purpose of legislation) of the legal rule. In order to cope withour huge space of similarities, our GDA algorithm uses some constraintsto prune useless similarities. (shrink)
Identity, difference, and the associated subject of cultural diversity pose challenges for nursing. As the demographics of the world change, demands are rising for nurses to provide sensitive, individualized care to people living in our ever-changing global community. Issues concerning gender, sexuality, disability, age, language, economic and occupational status, multiculturalism, and ethnicity are made more complex because many of these topics strike a personal chord for individual nurses. In order for nursing to provide appropriate care to the world's people and (...) to meet future challenges, nursing must define itself in new ways. Kikuchi and Simmons have stated that the best way for nursing to approach this task is through the development of a 'sound' philosophy of nursing that will 'accommodate diversity in nursing thought'. They contend that before we can establish a philosophy of nursing, nurses will have to agree upon the nature of reality, human beings, truth, and knowledge. This paper will suggest that neopragmatism, as described by Richard Rorty, is a way to assure diversity of thought in nursing. However, I will argue against the requirement for this philosophy to be 'sound' in the sense that Kikuchi and Simmons use this term. In place of their call for 'truth and unity in nursing thought'. I will attempt to demonstrate how neopragmatic ideas relate to the construction of what Rorty called a unifying 'plausible narrative of progress'. This change will allow nursing to abandon the dead end debate over epistemologies and instead focus on more important issues related to improving nursing practice. (shrink)
Hajime Tanabe (1885-1962), the Kyoto- School philosopher of modern Japan, attempts to interpret Aristotle's ontology as being involved in the logic of self-identical being without self-negative conversion in action from his own dialectical perspective. For Tanabe, the eternal essence or Form is to be mediated by the dynamic character of matter, i.e., the temporality pertinent to the changing movement. For Aristotle, however, the essence or pure activity as the principle of being is devoid of such a dynamic mediation, but is (...) rather regarded as the past being, i.e., what it should be originally and eternally. In other words, for Aristotle, evil and matter are the lacks of goodness and the eternal Form that are identical with the essence of the individual substance. Evil is to be self-negatively mediated to goodness in free action through conversion in Tanabe's perspective. Movement pertaining to matter is not simply an incompletion of pure activity, but is rather self-negatively converted into the activity as the transcendent principle of the dialectical unification of time and eternity, matter and Form, evil and Goodness. The individual existence has freedom to unify the self-contradistinctive opposed moments, i.e., subjective action and objective being in a way of mutually negating conversion. The difference between Tanabe and Aristotle lies in that for Tanabe practice is relevant to the future, whereas for Aristotle contemplation is concerned with eternity as invariable and imperishable being since the past. While Aristotle's logic is confined to the self-identity of being in contemplation, Tanabe's logic is structured by the triadic elements of individuality, species as the relative universal, and genus as the absolute universal in terms of the negative conversion in action. (shrink)
Second-order abstract categorial grammars (de Groote in Association for computational linguistics, 39th annual meeting and 10th conference of the European chapter, proceedings of the conference, pp. 148–155, 2001) and hyperedge replacement grammars (Bauderon and Courcelle in Math Syst Theory 20:83–127, 1987; Habel and Kreowski in STACS 87: 4th Annual symposium on theoretical aspects of computer science. Lecture notes in computer science, vol 247, Springer, Berlin, pp 207–219, 1987) are two natural ways of generalizing “context-free” grammar formalisms for string and tree (...) languages. It is known that the string generating power of both formalisms is equivalent to (non-erasing) multiple context-free grammars (Seki et al. in Theor Comput Sci 88:191–229, 1991) or linear context-free rewriting systems (Weir in Characterizing mildly context-sensitive grammar formalisms, University of Pennsylvania, 1988). In this paper, we give a simple, direct proof of the fact that second-order ACGs are simulated by hyperedge replacement grammars, which implies that the string and tree generating power of the former is included in that of the latter. The normal form for tree-generating hyperedge replacement grammars given by Engelfriet and Maneth (Graph transformation. Lecture notes in computer science, vol 1764. Springer, Berlin, pp 15–29, 2000) can then be used to show that the tree generating power of second-order ACGs is exactly the same as that of hyperedge replacement grammars. (shrink)
This paper deals with intercultural aspects of privacy, particularly with regard to important differences between Japanese and the Western views. This paper is based on our discussions with Rafael Capurro – a dialogue now represented by two separate but closely interrelated articles. The companion paper is broadly focused on the cultural and historical backgrounds of the concepts of privacy and individualism in “Western” worlds; our main theme focuses on different concepts of privacy in Japan and their sources in related aspects (...) of Japanese culture. The interrelationship between our two papers is apparent in our taking up identical or similar topics in each paper. Reading our two papers in conjunction with each other will bring about deeper and broader insights into the diverse values and worldviews of Japan and Western cultures that underlie concepts of privacy that at a surface level appear to be similar. (shrink)
It is proved that for any k, the class of classical categorial grammars that assign at most k types to each symbol in the alphabet is learnable, in the Gold (1967) sense of identification in the limit from positive data. The proof crucially relies on the fact that the concept known as finite elasticity in the inductive inference literature is preserved under the inverse image of a finite-valued relation. The learning algorithm presented here incorporates Buszkowski and Penn's (1990) algorithm for (...) determining categorial grammars from input consisting of functor-argument structures. (shrink)
Some formal properties of enriched systems of Lambek calculus with analogues of conjunction and disjunction are investigated. In particular, it is proved that the class of languages recognizable by the Lambek calculus with added intersective conjunction properly includes the class of finite intersections of context-free languages.
This paper points out an error of Parigot's proof of strong normalization of second order classical natural deduction by the CPS-translation, discusses erasing-continuation of the CPS-translation, and corrects that proof by using the notion of augmentations.
One of the primary views on our supposed obligation towards our descendants in the context of environmental problems invokes the idea of the rights of future generations. A growing number of authors also hold that the descendants of those victimized by historical injustices, including colonialism and slavery, have the right to demand financial reparations for the sufferings of their distant ancestors. However, these claims of intergenerational rights face theoretical difficulties, notably the non-identity problem. To circumvent this problem in a relationship (...) between present and future generations, some rights theorists replace future individual rights with such collective rights. Others advance the threshold conception of harm in discussing intergenerational relationships in general. Despite the significant implications these revisionist views might have, few efforts have been made to scrutinize their solidity. To plug such a gap in the literature, this paper examines to what extent the collective understanding of intergenerational rights is pertinent. I also explore the virtues and drawbacks of the threshold interpretation of harm. The paper concludes by suggesting that the motivation behind these and other versions of the rights theory suffers from the ambiguity of a traditional dichotomy between perfect and imperfect duties. (shrink)
This paper points out an error of Parigot's proof of strong normalization of second order classical natural deduction by the CPS-translation, discusses erasing-continuation of the CPS-translation, and corrects that proof by using the notion of augmentations.
This is a review article of Tokuyasu Kakuta, Makoto Haraguchi, and Yoshiaki Okubo, "A Goal-Dependent Abstraction for Legal Reasoning by Analogy," /Artificial Intelligence and Law/ 5(March 1997): 97-118.
This article examines the practice of "co-participant completion" in Japanese conversation, and explores what kinds of resources are mobilized to provide the opportunity to complete another participant's utterance-in-progress. It suggests the following observations as potential characteristics of Japanese co-participant completion: (i) Syntactically-defined two-part formats (e.g. [If X] + [then Y]) may not play as prominent a role as in English; (ii) The majority of cases of co-participant completion take the form of 'terminal item completion;' (iii) Locally emergent structures like 'contrast' (...) and 'list' as well as 'unprojected' features of turn construction often play an important role in enhancing the opportunity for completing another participant's utterance-in-progress. The article then discusses the implications of these findings for the investigation of the mutual bearing of grammar and social interaction. In particular, the discussion focuses on what we can learn from the practice of co-participant completion about how projection of turn-shapes is accomplished in Japanese conversation. (shrink)
The historical origins of the Kyoto School of Philosophy of modern Japan, represented by Kitaro Nishida and Hajime Tanabe, may be derived from both the ancient Chinese idea of Change and the ancient Indian Upanishadic idea of the mutual identity of Brahman and Atman. The ancient Chinese idea of Change signifies change as well as non-change, and even their dialectical unification. Both origins are structured by the self-identity of the opposed in logic, and these historical prototypes have been developed into (...) the various forms of Confucian, Taoist, and Buddhist philosophy. The notion of Nothingness or Emptiness rather than Being has been set up as the fundamental principle. The principle of Nothingness as ultimate reality has been connected with the logic of self-identity of theopposed, and this is evident in Nishida’s concept of the self-identity in absolute contradistinction that is equivalent to the Place of Absolute Nothingness. Even though Nishida’s idea of Place is directly and explicitly influenced by the ancient Greek idea of Topos, it has indirectly and implicitly been affected by the traditional agricultural society as well, in which the land is regarded as the self-identical substratum despite the cyclic time of the four-seasons change. The ancient Chinese idea of Change also reflects the agricultural society in which the cyclic time plays an important role on the basis of the unchanging self-identical land as the underlying substratum. Nishida succeeds in establishing the new logical expression of Eastern traditional thought, deeply hidden in consciousness, in relation toWestern philosophy. The uniqueness of Nishida’s idea of Place may have its main source in the traditional agricultural background, and in this sense his way of thinking may be rural in character. On the other hand, Tanabe, though following Nishida at first, turns to making criticism of the mentor with the establishment of the triadic logic of species as the dialectic, which is characterized by the perpetual self-negating conversion in action. In contrast to Nishida, Tanabe represents the urban type of thinking, which is in pursuit of transforming in life. While Nishida’s idea of Absolute Nothingness has an affinity with the ancient Chinese philosopher Laotzu’s idea of Nothingness from and into which every entity comes and goes, Tanabe’s concept of Absolute Nothingness as the principle ofconversion is more closed to the Buddhist idea of sunyata, i.e., Emptiness, which is devoid of any substance in itself. As regards evil, the difference between them is obvious in that for Nishida evil and time or history disappear into the ultimate horizon or place of Nothingness with the tendency toward a kind of monism of goodness, whereas for Tanabe evil copes with goodness and retains its own status throughout, never being reduced to the opposed. Even if so, both of them, however, fail to construct a philosophy of history from the epochal or durational viewpoint, compared to Heidegger and Jaspers. (shrink)
On sait que Platon fait grand cas des êtres intelligibles en instaurant la théorie des Idées. Mais il n’est pas approprié de le considérer comme penseur qui néglige le rôle de l’apparence sensible. Ce philosophe demeure très sensible à la modalité par laquelle les phénomènes apparaissent dans le champ de notreperception. En distinguant deux types d’apparence : image et simulacre, il donne à l’image le rôle d’intermédiaire actif entre le sensible et l’intelligible. L’examen des modalités des actions humaines qui reçoivent (...) et créent des images, nous aide à voir comment Platon intègre la fonction des images dans la structure de sa philosophie. La réception et la création des images sont étroitement reliées et synthétisées pour former le système original de Platon, système dans lequel le fondement de la théorie des Idées relève d’un certain dynamisme de l’action humaine. Dans la recherche relative à la modalité de réception et de création des images, je porte mon attention sur l’usage platonicien du terme tupos qui exprime le principe de la conformité de l’image et de son modèle.Notamment dans la théorie de la formation des futurs gardiens de la cité idéale, le tupos fonctionne, comme un principe qui réglemente et oriente à plusieurs niveaux les activités de la mimèsis et de la poièsis qui portent sur les images. La réflexion sur cette fonction conductrice. (shrink)
We tend to think every ought statement implies that an actual agent can comply. However, our uses of “ought” suggest that some ought statements fail to have this implication: it is possible that the actual agent ought to do something she has no chance of accomplishing even if she intends to do so. Rather they imply that if the agent and her circumstances were defect-free, she could and would perform the prescribed action. There are two types of evaluation for ought (...) statements. One type of evaluation addresses the question of what to do given the agent’s peculiar capacity and condition. The point of this evaluation is giving personalized action guidance, and so recommends only what the actual agent can do under the actual condition. Another type of evaluation addresses a different question, that of what to do as a type of agents. The point of this evaluation is the coordination of individuals by selecting a shared norm for them: the standard that prescribes all of them to perform the same action and classifies for all of them the same traits as defect. This is why it endorses the ought statements that some actual agents cannot comply with, but that a normal agent could and would do so under normal conditions. (shrink)
A minimal formula is a formula which is minimal in provable formulas with respect to the substitution relation. This paper shows the following: (1) A β-normal proof of a minimal formula of depth 2 is unique in NJ. (2) There exists a minimal formula of depth 3 whose βη-normal proof is not unique in NJ. (3) There exists a minimal formula of depth 3 whose βη-normal proof is not unique in NK.
