Samuel R. Buss and Aleksandar Ignjatović. Unprovability of Consistency Statements in Fragments of Bounded Arithmetic.

The author gentzenizes the positive fragmentsT + andR + of relevantT andR using formulas with, prefixes (subscripts). There are three main Gentzen formulations ofS +{T+,R +} calledW 1 S +,W 2 S + andG 2 S +. The first two have the rule of modus ponens. All of them have a weak rule DL for disjunction introduction on the left. DL is not admissible inS + but it is needed in the proof of a cut elimination theorem forG 2 S (...) +.W 1 S + has a weak rule of weakeningW 1 and it is not closed under a general transitivity rule. This allows the proof that A inS + iff A inW 1 S +. From the cut elimination theorem forG 2 S + it follows that if A inS +, then A inG 2 S +. In order to prove the converse,W 2 S + is needed. It contains modus ponens, transitivity, and a restricted weakening rule.G 2 S + is contained inW 2 S + and there is a proof that A inW 2 S + iff A inW 1 S +. (shrink)

This paper is a study of four subscripted Gentzen systems G u R +, G u T +, G u RW + and G u TW +. [16] shows that the first three are equivalent to the semilattice relevant logics u R +, u T + and u RW + and conjectures that G u TW + is, equivalent to u TW +. Here we prove Cut Theorems for these systems, and then show that modus ponens is admissible — which (...) is not so trivial as one normally expects. Finally, we give decision procedures for the contractionless systems, G u TW + and G u RW +. (shrink)

The author gentzenizes the positive fragments T₊ and R₊ of relevant T and R using formulas with prefixes (subscripts). There are three main Gentzen formulations of $S_{+}\in \{T_{+},R_{+}\}$ called W₁ S₊, W₂ S₊ and G₂ S₊. The first two have the rule of modus ponens. All of them have a weak rule DL for disjunction introduction on the left. DL is not admissible in S₊ but it is needed in the proof of a cut elimination theorem for G₂ S₊. W₁ (...) S₊ has a weak rule of weakening W₁ and it is not closed under a general transitivity rule. This allows the proof that $\vdash A$ in S₊ iff $\vdash A$ in W₁ S₊. From the cut elimination theorem for G₂ S₊ it follows that if $\vdash A$ in S₊, then $\vdash A$ in G₂ S₊. In order to prove the converse, W₂ S₊ is needed. It contains modus ponens, transitivity, and a restricted weakening rule. G₂ S₊ is contained in W₂ S₊ and there is a proof that $\vdash A$ in W₂ S₊ iff $\vdash A$ in W₁ S₊. (shrink)

In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) intended meaning—the probability of propositional formula α is in the equation image-ball with the center r and the radius ρ. Due to modal nature of the operators Kr, ρ, it was natural to use the probability Kripke like models as equation image-structures, provided that probability functions range over equation image instead of equation image or equation image. (shrink)

In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) intended meaning—the probability of propositional formula α is in the equation image-ball with the center r and the radius ρ. Due to modal nature of the operators Kr, ρ, it was natural to use the probability Kripke like models as equation image-structures, provided that probability functions range over equation image instead of equation image or equation image. (shrink)

How can performance transform places of urban renewal and regeneration? What does performance contribute to the creation of community? These are some of the questions addressed in this study of the relationship of performance to urban space. Marrying theory with a series of international case studies of performance practice and interviews with practitioners, this interdisciplinary study examines how space is performatively produced to create a sense of 'placeness'. Case studies are drawn from Canada, Brazil, the Czech Republic, the UK and (...) Spain. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Christian Ethics and Commonsense Morality: An Intuitionist Account by Kevin JungAleksandar S. SantracChristian Ethics and Commonsense Morality: An Intuitionist Account Kevin Jung NEW YORK AND LONDON: ROUTLEDGE, 2014. 202 PP. $145.00In Christian Ethics and Commonsense Morality: An Intuitionist Account, Kevin Jung boldly constructs and defends a commonsense morality of intuition as a plausible ethical theory against both postmodern constructivist ethical systems and narrow objectivist theories. Following the antifoundationalist (...) ethical methods of postmodern approaches to reality and morality in chapter 1 and a moderate defense of realism in chapter 2, Jung attempts to save both objectivity and de-feasibility of moral realistic accounts, offering some modern reinterpretations of moral realism in chapters 3 and 4. All these forms of Wittgensteinian conceptions of realism unsatisfactorily lead to infinite regress in justifying claims because they are grounded only in the wishes, interests, and sentiments of the individual culture and society (60).After a brief introduction to the unique role of emotions in ethical theories, his investigation leads to reconciliation between objectivist naturalistic ethics [End Page 192] and theological forms of ethical theories. Theological ethicists can remain committed to intuitionism (objectivist and naturalistic forms of common morality) refined by particular religious expressions of morality (112). Intuitionism, broadly defined in chapter 7, is described as "initial appearances" (118); moral truths, according to Jung's intuitionist account, are "mediately self-evident" (128), not "immediately," because it still requires careful reflection and cognitive searching for objectivist grounds of morality. Jung's affirmation of the plausibility of intuitionism seems to be a final blow to all forms of postmodern and skeptical accounts of antifoundationalist forms of ethical theories; he successfully defends an intuitionist account of morality against its naturalist and religious critics.The last chapter offers three types of relationship between commonsense morality and Christian morality. The identity model reduces Christian morality to commonsense morality. The two-tier model considers Christian morality to be a superior form of morality with instrumental value of commonsense morality. And, finally, integration, Jung's favorite model, considers commonsense morality as neither identical nor subordinate but central to Christian morality (163). With this he affirms that Christian morality is unique not because of differences in moral beliefs but because "it is fully committed to recognizing the oneness of humanity and the universally accessible nature of basic moral truths for all human beings" (166). Jung's reflection is exceptionally insightful. Building the case as a good lawyer, he leads us to the defenseless nature of constructivist postmodern moral theories and their revisions as well as to a commitment of Christian morality to the objective commonsense morality. On this view, even heroic moral acts based on obedience to God (such as Christian sacrificial love) might be compatible with commonsense morality. It is surprising, however, that Jung never consulted or quoted Bernard Gert's account of the common morality, especially when discussing differences between moral duty and ideals (167). Additionally, Jung's argument that Christian morality is unexceptional since moral knowledge can be obtained through multiple sources in which God also reveals his will (178) does not sufficiently probe into the distinctiveness of God's sometimes radical demands of Jews/Christians (e.g., Abraham's sacrifice of Isaac), which come not from intuitionist accounts of objective natural reason or common sense but from faith. Christian saints are not heroes of general moral example but heroes of faith, a qualitatively different realm of human experience. Still, audiences interested in all aspects of ethics will greatly benefit from this superb engagement with recent discussions. [End Page 193]Aleksandar S. SantracWashington Adventist UniversityCopyright © 2017 Society of Christian Ethics... (shrink)

The Laozi expounds a thoroughgoing and sustained criticism of government and society. In this paper, I will demonstrate that although this criticism is addressed to the ancient Chinese state, it can also have some validity for the modern state of today. I will first briefly discuss the metaphysical grounds of this criticism and stress that the ruler should use wuwei in governing. Then, I will examine the Laozi’s criticism of the oppressive governments that use unnatural governing through youwei which increases (...) the state disorder, as well as how this criticism is supported by its metaphysical grounds. Third, I will show that the selfish desires may significantly contribute to the state disorder and that the only one to be blamed for the arousing of them is the ruler. At last, I will attempt to show that this criticism may also to a certain extent be directed toward today’s modern state. (shrink)

This research paper focuses on the comprehensive description and analysis of the structure of judgments from the Court of Justice of the European Union (CJEU). Despite the growing interest in examining the rhetorical and linguistic aspects of legal texts, the genre structure of judgments has remained a little-explored area. While headings and paragraph enumeration provide a systematic reference system for citation and cross-referencing they do not reveal the dynamic relations between individual text chunks in judgments. The current analysis combines Swales (...) and Bhatia's genre theory with Hoey's approach to patterning in discourse and corpus linguistics analyses. The findings show that the complexity of CJEU judgments extends beyond surface-level information with linguistic expressions playing a crucial role in highlighting dynamic relations and discourse patterning. The results reveal how the structure of CJEU judgments has changed over time and point to the intratextual relations between different sections. Additionally, the study provides a detailed description of the textual organisation of CJEU judgments in terms of move structures and conventionalised discourse patterns. (shrink)

The story of David and Goliath is one of the most famous biblical stories. It had an impact on many branches of contemporary art. It is also an inevitable part of religious education and general education in all schools. Knowing the fact that the Church Fathers have an essential part in the lives of many Christians today (in the Orthodox Church, they were role models from the very beginning), it is interesting to see how did they, these original theologians, read (...) and interpret the story of David and Goliath. Was it for them, in the time when the Bible was the most sacred book for all, important as it is for us today? Did people during the sports events of that time talk on the markets about the underdog who struck the giant? Additionally, if one looks at the ancient Greek and Hebrew text, one will find out that the Hebrew version, which was used as the source for most modern translations, is 40% longer than the Greek one. Could the works of the Fathers help us to determine which version of the story is the Holy Scripture for Christians today? (shrink)

One facet of Stefan Lorenz Sorgner’s scholarship is immediately visible in his diligent academic production: the 21st Century is a leading spatio-temporal unit of his analyses. Although such assessment could be considered a rough generalization, it should not be taken for granted. To be placed in the contextual core of the current epoch is of particular relevance with respect to multiple academic trajectories Sorgner navigates and is almost always an achievement rather than an expected, ready-made content. Namely, more often than (...) not, especially in authorship with transhumanist labels, the temporal and conceptual curves are not subtly controlled and fine-tuned into a well-balanced thinking product that contributes to facing the current and potential issues of the relatively near and projectively feasible futures. Such gross asymmetry has various dangerous consequences Sorgner unequivocally warns about, opting deliberately to be an active chronicler of the ‘history of the present’ instead. This approach entails the dismissal of ‘guaranteed’ futurity vectors, be it Christian linearity or Kurzweilian exponentiality, but no less of petrified presentism or conventional historical layers of any inherited anthropology and the specific ethical account it is built upon. (shrink)

In this article I will discuss the anarchist and non-anarchist interpretations of the Laozi and argue that the political philosophy of the Laozi does not completely conform to Western anarchism. Thus, firstly I will give a brief introduction to Western anarchism. Then I will present the strongest arguments of the anarchist interpretation and try to find their mistakes and refute them. Finally I will try to give an acceptable non-anarchist interpretation of the political philosophy of the Laozi. In doing steps (...) 2 and 3, I will base my arguments in a way that is consistent with the text of the Laozi itself. Thus, I hope that this article will bring a deeper understanding of the political philosophy of the Laozi and break with the widely spread opinion that the Laozi propounds an anarchist theory. (shrink)

In this article I will discuss the anarchist and non-anarchist interpretations of the Laozi and argue that the political philosophy of the Laozi does not completely conform to Western anarchism. Thus, firstly I will give a brief introduction to Western anarchism. Then I will present the strongest arguments of the anarchist interpretation and try to find their mistakes and refute them. Finally I will try to give an acceptable non-anarchist interpretation of the political philosophy of the Laozi. In doing steps (...) 2 and 3, I will base my arguments in a way that is consistent with the text of the Laozi itself. Thus, I hope that this article will bring a deeper understanding of the political philosophy of the Laozi and break with the widely spread opinion that the Laozi propounds an anarchist theory. (shrink)

In this paper, the authors first emphasise the connection that exists between bioethics and law. However, special attention is given to the link between bioethics and human rights, which share the idea of protecting similar values, especially the protection of life and human dignity. Identifying the interdependence and interrelation of these concepts is a prerequisite for further exploration of how and in what context the European Court of Human Rights decides on bioethical issues it encounters when ruling on classical human (...) rights guaranteed by the European Convention for the Protection of Human Rights and Fundamental Freedoms. Once the important features that determine the relationship between bioethics and human rights are identified, these features will be practically examined through the group of cases in which the Court has addressed the issue of mandatory vaccination, which has been in the public spotlight in recent years. (shrink)

The article examines the patient-doctor relationship, relying on Michel Foucault’s concept of the clinical gaze. We argue that during the last decades, a profound transformation of the social nature of medicine took place, one that Foucault’s understanding of the clinical gaze cannot adequately account for. First, the article offers an elaboration of the three-node network of clinical gaze, the clinic, and nosology to explain the positioning of the doctor and the patient within the specific social ontology generated by the rise (...) of medicine. We then discuss intensive but irresolute developments brought by technological advancements, especially the X-ray tube. Finally, we argue that in the contemporary clinic, equipped with a plethora of sophisticated devices, the position of the doctor endured the most radical transformation in comparison with Foucault’s proponent of the clinical gaze at the dawn of modern medicine. (shrink)

The article examines the patient-doctor relationship, relying on Michel Foucault’s concept of the clinical gaze. We argue that during the last decades, a profound transformation of the social nature of medicine took place, one that Foucault’s understanding of the clinical gaze cannot adequately account for. First, the article offers an elaboration of the three-node network of clinical gaze, the clinic, and nosology to explain the positioning of the doctor and the patient within the specific social ontology generated by the rise (...) of medicine. We then discuss intensive but irresolute developments brought by technological advancements, especially the X-ray tube. Finally, we argue that in the contemporary clinic, equipped with a plethora of sophisticated devices, the position of the doctor endured the most radical transformation in comparison with Foucault’s proponent of the clinical gaze at the dawn of modern medicine. (shrink)

This article aims to give a survey of preparations conducted by Spartan king Agis III before he commenced his war against Macedonians. Based on the remaining narrative sources, mostly Arrian, Diodorus, Curtius Rufus and Justin, the author gives an account of king Agis’ doings up until the very beginning of his war. The author argues also why is that a real, full open war, not a "rebellion" as it is dubbed in some of the literature. Author gives his opinion about (...) the beginning of the preparations for the open war and concludes that they began in November 333 BC, at latest. This article also tackles the question of mercenaries which Agis took after the Battle of Issus. Due to the uncertainty of the sources themselves it can be concluded at best that Agis hired a great number of them after Issus. (shrink)

There is a widespread belief in Hinduism that Vyāsa, the alleged editor of the Vedas and author of the Mahābhārata, is identical with Bādarāyaṇa, the author of the Brahma-sūtra. The identification of these two mythic characters, however, originated between 800–980 CE, after the likes of Śaṅkara, Padmapāda, and Bhāskara, but before Vācaspati Miśra, Prakāśātman, Sarvajñātman, and Yāmuna. The purpose of this paper is to understand how and why such identification took place. The argument developed here is that the Bādarāyaṇa-Vyāsa identity (...) was invented by the author of or community behind the Bhāgavata Purāṇa as part of a complex of self-representation strategies. The Bhāgavata intentionally makes itself a work of Vedānta, indeed the Brahma-sūtra itself, over which it builds a new soteriology that is centered on the idea of bhakti. Two factors in particular stand out in light of the Bhāgavata’s Vedāntic background: Vyāsa’s paradigmatic character as the preserver of old dharma and the innovator, visionary, of new soteriologies; and the image of Vyāsa’s son Śuka as the model ascetic and ideal candidate for the new soteriological vision, through whom the Bhāgavata community chose to represent itself. (shrink)

This paper will use the concept of hyperreality to compare the so-called ideal state described by ancient Chinese philosopher Laozi with the world of The Truman Show. The concept of hyperreality is defined by Jean Baudrillard as the generation by models of a real without origin or reality. A hyperreal world is a simulation, or kind of a copy without its original. It is generally accepted, and confirmed by Baudrillard himself, that the world of The Truman Show is hyperreal. In (...) order to compare Laozi’s ideal state with the world of the film, this paper will give a hyperrealist interpretation of the former, which will be only hypothetical, without intending to substitute any other existing interpretations. Laozi imagines that people live simple lives, with few desires and without traveling to other places. If we accept that the ideal state is a hyperreal world, we can make comparison between the two worlds; find out their similarities, as well as differences. (shrink)

This article explores three dimensions of the current state of gender equality in Serbia: public policy on gender equality, public opinion on gender equality and the context of Serbia’s accession to the EU. Using data from the recent public opinion survey of citizens’ attitudes towards gender equality, the authors address the following issues: harmonization of public policy on gender equality in Serbia with EU policies; differences between public policy on gender equality in Serbia and citizens’ preferences; convergences/divergences between citizens of (...) Serbia and EU citizens regarding gender equality. As Serbia’s policy of promoting gender equality in the last decade has been dominated by the political goal of accession to the EU, it shows where the opinions converge, and where there are certain differences. The authors show the complexity of ideological positions among average Serbian citizens, while highlighting different paradigms in the official public policy on gender equality. While Serbian citizens still do not place gender equality high on their political agenda, they are convinced that it has a certain value, which does provide some important pointers for the future. (shrink)

The paper explores the imagery and constructions of alterity in the contemporary world. The image of the other is at the same time the image of ourselves, mostly through the metaphor of the?stranger.? This?stranger? represents the unknown, so he/she occasionally provokes fear and resentment, if only for appearing physically different in the?mainstream? culture. This paper traces the genesis and development of certain modernist ideals. The apparent lack of comprehension for others is just a symptom of the much deeper disorder - (...) in the quest for rationality, the meaning of simple human communication seems to be forgotten. Just like in a hall of mirrors, the images that people encounter are basically the images of them?selves - only they have been distorted through nationalist or racist rhetoric. Using the examples from theory as well as from specific cultures, and following on the works of scholars like Kristeva, Linke and Balibar, the author demonstrates the logic behind the need to exclude others, as well as the fact that all of these attempts will eventually back?fire. For we cannot exclude others if we do not at the same time exclude ourselves. U tekstu se razmatraju predstave i konstrukcije drugosti u savremenom svetu. Slike drugih su u isto vreme i predstave nas s?mih, pre svega kroz metaforu?stranca?.?Stranac? ovde predstavlja nepoznato i, kao takav, ona/on moze izazvati strah i odbojnost, makar i samo zbog toga sto izgleda drugacije od pripadnika?osnovne? ili?domace? kulture. U tekstu se razmatra razvoj odredjenih modernistickih ideala. Ono sto izgleda kao nedostatak razumevanja za druge samo je simptom mnogo dubljeg poremecaja - u potrazi za racionalnoscu izgleda da je zaboravljeno znacenje jednostavne ljudske komunikacije. Bas kao u dvorani sa ogledalima, predstave na koje ljudi nailaze su slike njih samih - samo sto su izmenjene nacionalistickom ili rasistickom retorikom. Koristeci primere iz teorije, kao i iz razlicitih kultura i pozivajuci se na radove autora poput Kristeve, Linke i Balibara, autor ukazuje na logiku izopstavanja drugih, kao i na cinjenicu da mnogi ovakvi pokusaji izopstavanja prerastaju u sopstvenu suprotnost. Jer nemoguce je izbaciti druge a da u isto vreme ne izbacimo i sebe same. (shrink)

In the first part of this paper we discuss some aspects of Detlefsen's attempt to save Hilbert's Program from the consequences of Godel's Second Incompleteness Theorem. His arguments are based on his interpretation of the long standing and well-known controversy on what, exactly, finitistic means are. In his paper [1] Detlefsen takes the position that there is a form of the ω-rule which is a finitistically valid means of proof, sufficient to prove the consistency of elementary number theory Z. On (...) the other hand, he claims that Z with its first-order logic is not strong enough to allow a formalization of such an ω-rule. This would explain why the unprovability of $\operatorname{Con}(Z)$ in Z does not imply that the consistency of Z cannot be proved by finitistic means. We show that Detlefsen's proposal is unacceptable as originally formulated in [1], but that a reasonable modification of the rule he suggest leads to a partial program already studied for many years. We investigate the scope of such a program in terms of proof-theoretic reducibilities. We also show that this partial program encompasses mathematically important theories studied in the "Reverse Mathematics" program. In order to investigate the provability with such a modified rule, we define new consistency and provability predicates which are weaker than the usual ones. We then investigate their properties, including a few that have no apparent philosophical significance but compare interestingly with the properties of the program based on the iteration of our ω-rule. We determine some of the limitations of such programs, pointing out that these limitations partly explain why partial programs that have been successfully carried out use quite different and substantially more radical extensions of finitistic methods with more general forms of restricted reasoning. (shrink)

In this paper, the author presents Jaspers’ view of the relationship between the state and university. According to Jaspers, universities should be free from any state control. Jaspers’ attitudes are mostly normative. According to Jaspers, the very existence of the institution of universities means that the state strives to provide a space where truth can be investigated, a space that would be independent of any kind of influence. Therefore, according to Jaspers, there is a certain tension, or even hostility, between (...) the state and university. Although Jaspers is aware that freedom to investigate at university may be abused, in the sense that teachers may become indolent, he believes that it is a risk worth taking. As far as political conflict is concerned, it can be a research topic at university, but university must not be an arena for political fighting. Jaspers indicates that, although every university belongs to a certain nation, its mission is supranational. Because of this, universities must not take sides in the struggle between nations. National issues may be investigated alongside other subjects; however, according to Jaspers, national issues must never become the objective and purpose of the existence of universities. (shrink)

Original essays by philosophers of language and philosophers of time exploring the semantics and metaphysics of tense.

Розкрито сутність поняття «рейтинг». Доведено значущість рейтингової оцінки для суб’єктів фінансового ринку, зокрема для страхових компаній, потенційних страхувальників, інвесторів та кредиторів.

This book engages with the conceptual intersections of post-Yugoslav literature, focusing on analyses of postism and temporality.