We show that versions of the prime number theorem as well as equivalent statements hold in an arbitrary model ofIΔ 0+exp.

We present a comprehensive study of the axiom schemas IΣ - n , BΣ - n (induction and collection schemas for parameter free Σ n formulas) and some closely related schemas.

In this paper, we prove results concerning the existence of proper end extensions of arbitrary models of fragments of Peano arithmetic. In particular, we give alternative proofs that concern a result of Clote :163–170, 1986); :301–302, 1998), on the end extendability of arbitrary models of \-induction, for \, and the fact that every model of \-induction has a proper end extension satisfying \-induction; although this fact was not explicitly stated before, it follows by earlier results of Enayat and Wong and (...) Wong. (shrink)

We study the strength (over bounded induction) of axioms expressing particular cases of the Chinese Remainder Theorem with respect to the axiom ∀ x, y∃ z (z = xy).

. We provide an alternative proof of a theorem of P. Clote concerning end extensions of models of $\Sigma_n$ -induction, for $n \geq 2$.

We study problems of Clote and Paris, concerning the existence of end extensions of models of Σ n -collection. We continue the study of the notion of ‘Γ-fullness’, begun by Wilkie and Paris (Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North- Holland, Amsterdam, 1989) and introduce and study a generalization of it, to be used in connection with the existence of Σ n -elementary end extensions (instead of plain end extensions). (...) We obtain (a) alternative proofs of results (Adamowicz in Fund. Math. 136, 133–145, 1990) and (Wilkie and Paris in Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North-Holland, Amsterdam, 1989) related to the problem of Paris and (b) a partial solution to the problem of Clote. (shrink)

In June 2012, the conference Trends in Logic XI, whose main theme was Advances in Philosophical Logic, took place at the Ruhr University in Bochum. Eight of the invited papers were published in a special issue of the journal Studia Logica. The present volume contains fourteen papers, which the editors selected out of the contributed papers presented at the conference, in order to offer a panorama of the themes developed in philosophical logic in the last two decades or so, as (...) well as to indicate some promising directions for further research. In what follows, we give a brief description of each contribution, following the order in the list of contents.In the first paper, B. Armour-Garb and J.A. Woodbridge discuss a manner in which one can treat semantic pathologies, such as the Liar Paradox. According to their approach, semantically pathological sentences are s-defective, i.e. they can be understood in a sense, but they bear no content, which we can accept or reject. The a .. (shrink)

We give alternative proofs of results due to Paris and Wilkie concerning the existence of end extensions of countable models of $B\Sigma_{1}$, that is, the theory of $\Sigma_{1}$ collection.

Games may seem like a waste of time, where we struggle under artificial rules for arbitrary goals. The author suggests that the rules and goals of games are not arbitrary at all. They are a way of specifying particular modes of agency. This is what make games a distinctive art form. Game designers designate goals and abilities for the player; they shape the agential skeleton which the player will inhabit during the game. Game designers work in the medium of agency. (...) Game-playing, then, illuminates a distinctive human capacity. We can take on ends temporarily for the sake of the experience of pursuing them. Game play shows that our agency is significantly more modular and more fluid than we might have thought. It also demonstrates our capacity to take on an inverted motivational structure. Sometimes we can take on an end for the sake of the activity of pursuing that end. (shrink)

There seems to be a deep tension between two aspects of aesthetic appreciation. On the one hand, we care about getting things right. On the other hand, we demand autonomy. We want appreciators to arrive at their aesthetic judgments through their own cognitive efforts, rather than deferring to experts. These two demands seem to be in tension; after all, if we want to get the right judgments, we should defer to the judgments of experts. The best explanation, I suggest, is (...) that aesthetic appreciation is something like a game. When we play a game, we try to win. But often, winning isn’t the point; playing is. Aesthetic appreciation involves the same flipped motivational structure: we aim at the goal of correctness, but having correct judgments isn’t the point. The point is the engaged process of interpreting, investigating, and exploring the aesthetic object. Deferring to aesthetic testimony, then, makes the same mistake as looking up the answer to a puzzle, rather than solving it for oneself. The shortcut defeats the whole point. This suggests a new account of aesthetic value: the engagement account. The primary value of the activity of aesthetic appreciation lies in the process of trying to generate correct judgments, and not in having correct judgments. -/- *There is an audio version available: look for the Soundcloud link, below.*. (shrink)

I propose to study one problem for epistemic dependence on experts: how to locate experts on what I will call cognitive islands. Cognitive islands are those domains for knowledge in which expertise is required to evaluate other experts. They exist under two conditions: first, that there is no test for expertise available to the inexpert; and second, that the domain is not linked to another domain with such a test. Cognitive islands are the places where we have the fewest resources (...) for evaluating experts, which makes our expert dependences particularly risky. -/- Some have argued that cognitive islands lead to the complete unusability of expert testimony: that anybody who needs expert advice on a cognitive island will be entirely unable to find it. I argue against this radical form of pessimism, but propose a more moderate alternative. I demonstrate that we have some resources for finding experts on cognitive islands, but that cognitive islands leave us vulnerable to an epistemic trap which I will call runaway echo chambers. In a runaway echo chamber, our inexpertise may lead us to pick out bad experts, which will simply reinforce our mistaken beliefs and sensibilities. (shrink)

On the basis of recent work concerning the meaning of the term stoicheion in Aristotle’s Analytics, we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements.

The volume under review contains work dedicated to the memory of Leo Esakia, who died in 2010, after having worked for over 40 years towards developing duality theory for modal and intuitionistic logics. The collection comprises ten technical contributions that follow the first chapter, in which the reader can find information on Esakia’s studies and career, as well as a complete list of his research publications. In the sequel, we will refer briefly to each of these ten chapters, following the (...) order in the list of contents.B. Jónsson and A. Tarski, in two papers they published in the early 1950s in the American Journal of Mathematics, initiated the study of duality for Boolean algebras with additional operations, via the theory of canonical extensions. Esakia was among the first researchers who studied duality for lattices with additional operations [Topological Kripke models. Soviet Math.Dokl. 15 , 147–151], in particular for Heyting algebras and S4 modal algebras. M. Gehrke, a .. (shrink)

An adequate theory of rights ought to forbid the harming of animals to promote trivial interests of humans, as is often done in the animal-user industries. But what should the rights view say about situations in which harming some animals is necessary to prevent intolerable injustices to other animals? I develop an account of respectful treatment on which, under certain conditions, it’s justified to intentionally harm some individuals to prevent serious harm to others. This can be compatible with recognizing the (...) inherent value of the ones who are harmed. My theory has important implications for contemporary moral issues in nonhuman animal ethics, such as the development of cultured meat and animal research. (shrink)

Value capture occurs when an agent’s values are rich and subtle; they enter a social environment that presents simplified — typically quantified — versions of those values; and those simplified articulations come to dominate their practical reasoning. Examples include becoming motivated by FitBit’s step counts, Twitter Likes and Re-tweets, citation rates, ranked lists of best schools, and Grade Point Averages. We are vulnerable to value capture because of the competitive advantage that such crisp and clear expressions of value have in (...) our private reasoning and our public justification. There is, however, a price. In value capture, we take a central component of our autonomy — our ongoing deliberation over the exact articulation of our values — and we outsource it. And the metrics to which we outsource usually engineered for the interests of some external force, like a large-scale institution’s interest in cross-contextual comprehensibility and quick aggregability. That outsourcing cuts off one of the key benefits to personal deliberation. In value capture, we no longer adjust our values and their articulations in light of own rich experience of the world. Our values should often be carefully tailored to our particular selves or our small-scale communities, but in value capture, we buy our values off the rack. In some cases – like decreasing CO2 emissions – the costs of non-tailored values are outweighed by the benefit of precise collective coordination. In other cases, like in our aesthetic lives, they are not. This suggests that we should want different values suited to different scales. We should want value federalism. Some values are perhaps best pursued at the largest-scale level, others at smaller scales. The problem occurs when we exhibit an excess preference for the largest-scale values – when we consistently let the universal metrics swamp our quieter interests. (shrink)

We offer an account of the generic use of the term “porn”, as seen in recent usages such as “food porn” and “real estate porn”. We offer a definition adapted from earlier accounts of sexual pornography. On our account, a representation is used as generic porn when it is engaged with primarily for the sake of a gratifying reaction, freed from the usual costs and consequences of engaging with the represented content. We demonstrate the usefulness of the concept of generic (...) porn by using it to isolate a new type of such porn: moral outrage porn. Moral outrage porn is representations of moral outrage, engaged with primarily for the sake of the resulting gratification, freed from the usual costs and consequences of engaging with morally outrageous content. Moral outrage porn is dangerous because it encourages the instrumentalization of one’s empirical and moral beliefs, manipulating their content for the sake of gratification. Finally, we suggest that when using porn is wrong, it is often wrong because it instrumentalizes what ought not to be instrumentalized. (shrink)

Recent conversation has blurred two very different social epistemic phenomena: echo chambers and epistemic bubbles. Members of epistemic bubbles merely lack exposure to relevant information and arguments. Members of echo chambers, on the other hand, have been brought to systematically distrust all outside sources. In epistemic bubbles, other voices are not heard; in echo chambers, other voices are actively undermined. It is crucial to keep these phenomena distinct. First, echo chambers can explain the post-truth phenomena in a way that epistemic (...) bubbles cannot. Second, each type of structure requires a distinct intervention. Mere exposure to evidence can shatter an epistemic bubble, but may actually reinforce an echo chamber. Finally, echo chambers are much harder to escape. Once in their grip, an agent may act with epistemic virtue, but social context will pervert those actions. Escape from an echo chamber may require a radical rebooting of one's belief system. (shrink)

In The Case for Animal Rights, Tom Regan argues that although all subjects-of-a-life have equal inherent value, there are often differences in the value of lives. According to Regan, lives that have the highest value are lives which have more possible sources of satisfaction. Regan claims that the highest source of satisfaction, which is available to only rational beings, is the satisfaction associated with thinking impartially about moral choices. Since rational beings can bring impartial reasons to bear on decision making, (...) Regan maintains that they have an additional possible source of satisfaction that nonrational beings do not have and, consequently, the lives of rational beings turn out to have greater value.. (shrink)

What is a game? What are we doing when we play a game? What is the value of playing games? Several different philosophical subdisciplines have attempted to answer these questions using very distinctive frameworks. Some have approached games as something like a text, deploying theoretical frameworks from the study of narrative, fiction, and rhetoric to interrogate games for their representational content. Others have approached games as artworks and asked questions about the authorship of games, about the ontology of the work (...) and its performance. Yet others, from the philosophy of sport, have focused on normative issues of fairness, rule application, and competition. The primary purpose of this article is to provide an overview of several different philosophical approaches to games and, hopefully, demonstrate the relevance and value of the different approaches to each other. Early academic attempts to cope with games tried to treat games as a subtype of narrative and to interpret games exactly as one might interpret a static, linear narrative. A faction of game studies, self-described as “ludologists,” argued that games were a substantially novel form and could not be treated with traditional tools for narrative analysis. In traditional narrative, an audience is told and interprets the story, where in a game, the player enacts and creates the story. Since that early debate, theorists have attempted to offer more nuanced accounts of how games might achieve similar ends to more traditional texts. For example, games might be seen as a novel type of fiction, which uses interactive techniques to achieve immersion in a fictional world. Alternately, games might be seen as a new way to represent causal systems, and so a new way to criticize social and political entities. Work from contemporary analytic philosophy of art has, on the other hand, asked questions whether games could be artworks and, if so, what kind. Much of this debate has concerned the precise nature of the artwork, and the relationship between the artist and the audience. Some have claimed that the audience is a cocreator of the artwork, and so games are a uniquely unfinished and cooperative art form. Others have claimed that, instead, the audience does not help create the artwork; rather, interacting with the artwork is how an audience member appreciates the artist's finished production. Other streams of work have focused less on the game as a text or work, and more on game play as a kind of activity. One common view is that game play occurs in a “magic circle.” Inside the magic circle, players take on new roles, follow different rules, and actions have different meanings. Actions inside the magic circle do not have their usual consequences for the rest of life. Enemies of the magic circle view have claimed that the view ignores the deep integration of game life from ordinary life and point to gambling, gold farming, and the status effects of sports. Philosophers of sport, on the other hand, have approached games with an entirely different framework. This has lead into investigations about the normative nature of games—what guides the applications of rules and how those rules might be applied, interpreted, or even changed. Furthermore, they have investigated games as social practices and as forms of life. (shrink)

Анотація. У статті проаналізовані досягнення Соціального Вчительства Католицької Церкви, репрезентовані працями Лева ХІІІ, Пія ХІ, Пія ХІІ, Івана Павла ІІ, що розкривають змістовні характеристики поняття «принцип субсидіарності», його роль і значення в системі християнських цінностей. Принцип субсидіарності робить можливими такі взаємовідносини в соціальному житті, коли спільнота вищого порядку не втручається у внутрішнє життя спільноти нижчого порядку, перебираючи на себе належні тій функції; заради спільного добра, спільного блага вона надає їй у разі потреби підтримку й допомогу, узгоджуючи у такий спосіб її (...) взаємодію з іншими соціальними структурами. Принцип субсидіарності скеровує соціальну практику на утвердження спільного блага в людському співтоваристві. Поширення і застосування принципу субсидіарності протистоїть небезпеці «одержавлення» суспільства та найзагрозливіших проявів колективізму, обмежує абсолютизацію влади, бюрократизацію державних і соціокультурних структур, стає одним із гарантів дотримання прав і свобод громадян своєї країни. (shrink)

In her BBC Reith Lectures on Trust, Onora O’Neill offers a short, but biting, criticism of transparency. People think that trust and transparency go together but in reality, says O'Neill, they are deeply opposed. Transparency forces people to conceal their actual reasons for action and invent different ones for public consumption. Transparency forces deception. I work out the details of her argument and worsen her conclusion. I focus on public transparency – that is, transparency to the public over expert domains. (...) I offer two versions of the criticism. First, the epistemic intrusion argument: The drive to transparency forces experts to explain their reasoning to non-experts. But expert reasons are, by their nature, often inaccessible to non-experts. So the demand for transparency can pressure experts to act only in those ways for which they can offer public justification. Second, the intimate reasons argument: In many cases of practical deliberation, the relevant reasons are intimate to a community and not easily explicable to those who lack a particular shared background. The demand for transparency, then, pressures community members to abandon the special understanding and sensitivity that arises from their particular experiences. Transparency, it turns out, is a form of surveillance. By forcing reasoning into the explicit and public sphere, transparency roots out corruption — but it also inhibits the full application of expert skill, sensitivity, and subtle shared understandings. The difficulty here arises from the basic fact that human knowledge vastly outstrips any individual’s capacities. We all depend on experts, which makes us vulnerable to their biases and corruption. But if we try to wholly secure our trust — if we leash groups of experts to pursuing only the goals and taking only the actions that can be justified to the non-expert public — then we will undermine their expertise. We need both trust and transparency, but they are in essential tension. This is a deep practical dilemma; it admits of no neat resolution, but only painful compromise. (shrink)

According to most accounts of trust, you can only trust other people (or groups of people). To trust is to think that another has goodwill, or something to that effect. I sketch a different form of trust: the unquestioning attitude. What it is to trust, in this sense, is to settle one’s mind about something, to stop questioning it. To trust is to rely on a resource while suspending deliberation over its reliability. Trust lowers the barrier of monitoring, challenging, checking, (...) and questioning. Trust sets up open pipelines between yourself and parts of the external world. Trust permits external resources to have a similar relationship to one as one’s internal cognitive faculties. This creates efficiency, but at the price of exquisite vulnerability. We must trust in this way because we are cognitively limited beings in a cognitively overwhelming world. Crucially, we can hold the unquestioning attitude towards objects and technologies. When I trust my climbing rope, I stop worrying about its reliability. When I trust my online calendaring system, I simply go to the events indicated, without question. But, one might worry, how could one ever hold such a normatively loaded attitude as trust towards mere objects? How could it ever make sense to feel betrayed by an object? Trust is our engine for expanding and outsourcing our agency — for binding external processes into our practical selves. Thus, we can be betrayed by our smartphones in the same way that we can be betrayed by our memory. When we trust, we try to make something a part of our agency, and we are betrayed when our part lets us down. To unquestioningly trust something is to let it in—to attempt to bring it inside one’s practical functioning. This suggests a new form of gullibility: agential gullibility, which occurs when agents too hastily and carelessly integrate external resources into their own agency. (shrink)

Recent discussions in the just war literature suggest that soldiers have a duty to assume certain risks in order to protect the lives of all innocent civilians. I challenge this principle of risk by arguing that it is justified neither as a principle that guides the conduct of combat soldiers, nor as a principle that guides commanders in the US military. I demonstrate that the principle of risk fails on the first account because it requires soldiers both to violate their (...) strict duty of obedience and loyalty and to exceed their special obligations to protect their fellow comrades, the state, the state's constituents and other protected civilians. I then illustrate that the principle of risk fails on the second account since it conflicts with the commander's primary obligation to protect and promote the welfare and lives of his or her soldiers. I conclude by arguing that we cannot reasonably expect soldiers and commanders to adhere to the principle of risk until there is a radical, institutional-level transformation of militaristic goals, values, strategies, policies, warrior codes and expectations of service members in the US Armed Forces. (shrink)

Монографія "Функціональність релігії: український контекст".

Twitter makes conversation into something like a game. It scores our communication, giving us vivid and quantified feedback, via Likes, Retweets, and Follower counts. But this gamification doesn’t just increase our motivation to communicate; it changes the very nature of the activity. Games are more satisfying than ordinary life precisely because game-goals are simpler, cleaner, and easier to apply. Twitter is thrilling precisely because its goals have been artificially clarified and narrowed. When we buy into Twitter’s gamification, then our values (...) shift from the complex and pluralistic values of communication, to the narrower quest for popularity and virality. Twitter’s gamification bears some resemblance with the phenomena of echo chambers and moral outrage porn. In all these phenomena, we are instrumentalizing our ends for hedonistic reasons. We have shifted our aims in an activity, not because the new aims are more valuable, but in exchange for extra pleasure. (shrink)

This classic and controversial book examines the roots of the idea of virtue, diagnoses the reasons for its absence in modern life, and proposes a path for its recovery.

The Statesman is Plato's neglected political work, but it is crucial for an understanding of the development of his political thinking. In some respects it continues themes from the Republic, particularly the importance of knowledge as entitlement to rule. But there are also changes: Plato has dropped the ambitious metaphysical synthesis of the Republic, changed his view of the moral psychology of the citizen, and revised his position on the role of law and institutions. In its presentation of the statesman's (...) expertise, the Statesman modifies, as well as defending in original ways, this central theme of the Republic. (shrink)

The feeling of clarity can be dangerously seductive. It is the feeling associated with understanding things. And we use that feeling, in the rough-and-tumble of daily life, as a signal that we have investigated a matter sufficiently. The sense of clarity functions as a thought-terminating heuristic. In that case, our use of clarity creates significant cognitive vulnerability, which hostile forces can try to exploit. If an epistemic manipulator can imbue a belief system with an exaggerated sense of clarity, then they (...) can induce us to terminate our inquiries too early — before we spot the flaws in the system. How might the sense of clarity be faked? Let’s first consider the object of imitation: genuine understanding. Genuine understanding grants cognitive facility. When we understand something, we categorize its aspects more easily; we see more connections between its disparate elements; we can generate new explanations; and we can communicate our understanding. In order to encourage us to accept a system of thought, then, an epistemic manipulator will want the system to provide its users with an exaggerated sensation of cognitive facility. The system should provide its users with the feeling that they can easily and powerfully create categorizations, generate explanations, and communicate their understanding. And manipulators have a significant advantage in imbuing their systems with a pleasurable sense of clarity, since they are freed from the burdens of accuracy and reliability. I offer two case studies of seductively clear systems: conspiracy theories; and the standardized, quantified value systems of bureaucracies. (shrink)

This edition of Martin Ostwald's revised version of J. B. Skemp's 1952 translation of _Statesman_ includes a new selected bibliography, as well as Ostwald's interpretive introduction, which traces the evolution in Plato's political philosophy from _Republic_ to _Statesman to Laws_--from philosopher-king to royal statesman.