-/- Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result? -/- The primary purpose (...) of this article is to show that a certain, interesting set of axioms does indeed yield a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely) satisfiable if (and only if) it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊧φ (if and) only if Σ⊢φ ∸2−n for all n < ω. This approximated form of strong completeness asserts that if Σ⊧φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ. -/- Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory (in a countable, recursive language) recursive? Say that a complete theory T is decidable if for every sentence φ, the value φ T is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φ T o is uniformly recursive from φ, where φ T o is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive (or even recursively enumerable) axiomatization then it is decidable. (shrink)

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archimedean condition on an agent’s comparative judgments, it does not require the (...) binary relation reflecting an agent’s comparative judgments to be reflexive, complete or even transitive, and it applies to an absolutely arbitrary collection of gambles, free of structural conditions (e.g., closure, measurability, etc.). Moreover, unlike de Finetti’s criterion of coherence, the qualitative criterion respects the principle of weak dominance, a standard of rational decision making that obliges an agent to reject a gamble that is possibly worse and certainly no better than another gamble available for choice. Despite these weak assumptions, I establish a qualitative analogue of de Finetti’s Fundamental Theorem of Prevision, from which it follows that any coherent system of comparative expectations can be extended to a weakly ordered coherent system of comparative expectations over any collection of gambles containing the initial set of gambles of interest. The extended weakly ordered coherent system of comparative expectations satisfies familiar additivity and scale invariance postulates (i.e., independence) when the extended collection forms a linear space. In the course of these developments, I recast de Finetti’s quantitative account of coherent prevision in the qualitative framework adopted in this article. I show that comparative previsions satisfy qualitative analogues of de Finetti’s famous bookmaking theorem and his Fundamental Theorem of Prevision.The results of this article complement those of another article (Pedersen, Strictly coherent preferences, no holds barred, Manuscript, 2013). I explain how those results entail that any coherent weakly ordered system of comparative expectations over a unital linear space can be represented by an expectation function taking values in a (possibly non-Archimedean) totally ordered field extension of the system of real numbers. The ordered field extension consists of formal power series in a single infinitesimal, a natural and economical representation that provides a relief map tracing numerical non-Archimedean features to qualitative non-Archimedean features. (shrink)

Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call \textit{Good's Principle}: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free information. Although (...) dilation and non-conglomerability share some similarities, some authors maintain that there are important differences between the two that warrant endorsing different normative positions regarding dilation and non-conglomerability. This article reassesses the grounds for treating dilation and non-conglomerability differently. Our analysis exploits a new and general characterization result for dilation to draw a closer connection between dilation and non-conglomerability. (shrink)

A characterization result of dilation in terms of positive and negative association admits an extremal counterexample, which we present together with a minor repair of the result. Dilation may be asymmetric whereas covariation itself is symmetric. Dilation is still characterized in terms of positive and negative covariation, however, once the event to be dilated has been specified.

Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures to various natural classes of complete metric structures. With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result?The primary purpose of this article is to show that a certain, interesting set of axioms does indeed yield a completeness (...) result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is satisfiable if it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊨φ only if Σ⊢φ∸ 2-n for all n < ω. This approximated form of strong completeness asserts that if Σ⊨φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ.Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory recursive? Say that a complete theory T is decidable if for every sentence φ, the value φT is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φT∘ is uniformly recursive from φ, where φT∘is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive axiomatization then it is decidable. (shrink)

In an essay recently published in this journal, Branden Fitelson argues that a variant of Miller’s argument for the language dependence of the accuracy of predictions can be applied to Joyce’s notion of accuracy of credences formulated in terms of scoring rules, resulting in a general potential problem for Joyce’s argument for probabilism. We argue that no relevant problem of the sort Fitelson supposes arises since his main theorem and his supporting arguments presuppose the validity of nonlinear transformations of credence (...) functions that Joyce’s theory, charitably construed, would identify as invalid on the basis of the principle of simple dominance. (shrink)

We present a game mechanic called pseudo-visibility for games inhabited by non-player characters (NPCs) driven by reinforcement learning (RL). NPCs are incentivized to pretend they cannot see pseudo-visible players: the training environment simulates an NPC to determine how the NPC would act if the pseudo-visible player were invisible, and penalizes the NPC for acting differently. NPCs are thereby trained to selectively ignore pseudo-visible players, except when they judge that the reaction penalty is an acceptable tradeoff (e.g., a guard might accept (...) the penalty in order to protect a treasure because losing the treasure would hurt even more). We describe an RL agent transformation which allows RL agents that would not otherwise do so to perform some limited self-reflection to learn the training environments in question. (shrink)

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...) to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

This article elaborates on foundational issues in the social sciences and their impact on the contemporary theory of belief revision. Recent work in the foundations of economics has focused on the role external social norms play in choice. Amartya Sen has argued in [Sen93] that the traditional rationalizability approach used in the theory of rational choice has serious problems accommodating the role of social norms. Sen's more recent work [Sen96, Sen97] proposes how one might represent social norms in the theory (...) of choice, and in a very recent article [BS07] Walter Bossert and Kotaro Suzumura develop Sen's proposal, offering an extension of the classical theory of choice that is capable of dealing with social norms. The first part of this article offers an alternative functional characterization of the extended notion of rationality employed by Bossert and Suzumura in [BS07]. This characterization, unlike the one offered in [BS07], represents a norm-sensitive notion of rationality in terms of a pure functional constraint unmediated by a notion of revealed preference (something that is crucial for the application developed in the second part of this article). This functional characterization is formulated for general domains (as is Bossert and Suzumura's characterization) and is therefore empirically more applicable than usual characterizations of rationality. Interestingly, the functional constraint we propose is a variant of a condition first entertained in [AGM85] by Carlos Alchourrón, Peter Gärdenfors and David Makinson in the area of belief change. The second part of this article applies the theory developed in the first part to the realm of belief change. We first point out that social norms can be invoked to concoct counterexamples against some postulates of belief change (like postulate (*7)) that are necessary for belief change to be relational. These examples constitute the epistemological counterpart of Sen's counterexamples against condition α in rational choice (as a matter of fact, Rott has showed in [Rot01] that condition and postulate (*7) are mutually mappable). These examples are variants of examples Rott has recently presented in [Rot04]. One of our main goals in this article consists in applying the theory developed in the first part to develop a theory of norm-inclusive belief change that circumvents the counterexamples. We offer a new axiomatization for belief change and we furnish correspondence results relating constraints of rational choice to postulates of belief change. (shrink)

Gerd Gigerenzer and Thomas Sturm have recently proposed a modest form of what they describe as a normative, ecological and limited naturalism. The basic move in their argument is to infer that certain heuristics we tend to use should be used in the right ecological setting. To address this argument, we first consider the case of a concrete heuristic called Take the Best (TTB). There are at least two variants of the heuristic which we study by making explicit the choice (...) functions they induce, extending these variants of TTB beyond binary choice. We argue that the naturalistic argument can be applied to only one of the two variants of the heuristic; we also argue that the argument for the extension requires paying attention to other “rational” virtues of heuristics aside from efficacy, speed, and frugality. This notwithstanding, we show that there is a way of extending the right variant of TTB to obtain a very well behaved heuristic that could be used to offer a stronger case for the naturalistic argument (in the sense that if this heuristic is used, it is also a heuristic that we should use). The second part of the article considers attempts to extending the naturalistic argument from algorithms dealing with inference to heuristics dealing with choice. Our focus is the so-called Priority Heuristic, which we extend from risk to uncertainty. In this setting, the naturalist argument seems more difficult to formulate, if it remains feasible at all. Normativity seems in this case extrinsic to the heuristic, whose main virtue seems to be its ability to describe actual patterns of choice. But it seems that a new version of the naturalistic argument used with partial success in the case of inference is unavailable to solve the normative problem of whether we should exhibit the patterns of choice that we actually display. (shrink)

Twentieth-century developments in quantum physics, together with an emerging science of consciousness, have created the need for a new cosmology, or model of the universe. The theory of process contained in THE REFLEXIVE UNIVERSE places consciousness within the context of contemporary science. One of the central themes of this extraordinary work is that each successive organization of matter, from fundamental particles in physics to living organisms, expresses a particular stage in the evolution of mind. Starting with the photon, the basic (...) unit of light, and moving through atomic physics, molecular chemistry, the morphology of plants and animals and finally to levels of human evolution, Young develops his theory in vivid step-by-step detail. Consciousness, in his point of view, is not isolated from the material universe. It exists in a continuum, one in which physical and nonphysical realms can be linked and the teachings of mythology and religion can be integrated. To order: FAX: 415-883-9280; e-mail: [email protected]; or write: Anodos Foundation, c/o Publishers Services, P.O. Box 2510, Novato, CA 94948. Visa and MasterCard only. Trade STOP orders 40% plus postage. (shrink)

Sustainability challenges typically occur across sectoral boundaries, calling the state, market, and civil society to action. Although consensus exists on the merits of cross-sector collaboration, our understanding of whether and how it can create value for various, collaborating stakeholders is still limited. This special issue focuses on how new combined knowledge on cross-sector collaboration and business models for sustainability can inform the academic and practitioner debates about sustainability challenges and solutions. We discuss how cross-sector collaboration can play an important role (...) for the transition to new and potentially sustainability-driven business models given that value creation, delivery, and capture of organizations are intimately related to the collaborative ties with their stakeholders. Sustainable alternatives to conventional business models tend to adopt a more holistic perspective of business by broadening the spectrum of solutions and stakeholders and, when aligned with cross-sector collaboration, can contribute new ways of addressing the wicked sustainability problems humanity faces. (shrink)

Background: A fair distribution of healthcare services for older patients is an important challenge, but qualitative research exploring clinicians’ consideration in daily clinical prioritisation in healthcare services for the aged is scarce.Objectives: To explore what kind of criteria, values, and other relevant considerations are important in clinical prioritisations in healthcare services for older patients.Design: A semi-structured interview-guide was used to interview 45 clinicians working with older patients. The interviews were analysed qualitatively using hermeneutical content analysis and template organising style.Participants: 20 (...) physicians and 25 nurses working in public hospitals and nursing homes in different parts of Norway.Results and interpretations: Important dilemmas relate to under-provision of community care and comprehensive approaches, and over-utilisation of certain specialised services. Overt ageism is generally not reported, but the healthcare services for the aged seem to be inadequate due to more subtle processes, for example, dominating considerations and ideals and operating conditions that do not pay sufficient attention to older patients’ needs and considerations of justice. Clinical prioritisations are described as being dominated by adapting traditional biomedical approaches to the operating conditions. Many of the clinicians indicate that there is a potential for improving end of life decisions and for reducing exaggerated use of life-prolonging treatment and hospitalisations.Conclusion: The interviews in this study indicate that considerations of justice and patients’ perspectives should be given more attention to strike a balance between specialised medical approaches and more general and comprehensive approaches in healthcare services for older patients. (shrink)

The relative merits and demerits of historically prominent views such as the correspondence theory, coherentism, pragmatism, verificationism, and instrumentalism have been subject to much attention in the truth literature and have fueled the long-lived debate over which of these views is the most plausible one. While diverging in their specific philosophical commitments, adherents of these historically prominent views agree in at least one fundamental respect. They are all alethic monists. They all endorse the thesis that there is only one property (...) in virtue of which propositions can be true, and so, in this sense, take truth to be one. The truth pluralist, on the other hand, rejects this idea. There are several properties in virtue of which propositions can be true. The literature on truth pluralism has been growing steadily for the past twenty years. This volume, however, is the first of its kind—the first collection of papers focused specifically on pluralism about truth. Part I is dedicated to the development, investigation, and critical discussion of different forms of pluralism. An additional reason to look at truth pluralism with interest is the significant connections it bears to other debates in the truth literature—the debates concerning traditional theories of truth and the deflationism/inflationism divide being cases in hand. Parts II and III of the volume connect truth pluralism to these two debates. (shrink)

Here is a well-known thought about truth: Truth consists in correspondence with reality. A sentence is true just in case what it says corresponds with how the world is. Theories of truth that incorporate this thought are naturally regarded as robust or “heavyweight”. Truth is to be understood in a realist fashion. The world decides what is true and what is not. A recent incarnation of the correspondence view is found in truth-maker theories, whose adherents maintain that truths are true (...) in virtue of there being something – a truth-maker – in the world that makes them so.2. (shrink)

In this article, I critically assess Hélène Landemore's new model of Open Democracy, asking whether it requires of citizens to blindly defer to the decisions of the mini-public. To address this question, I, first, discuss three institutional mechanisms in Open Democracy, all of which can be read to grant citizens democratic control. I argue that neither the capacity to authorize the selection mechanism (random sortition), nor the lottocratic conception of political equality, nor the self-selection mechanisms of Landemore's model deliver the (...) form of control that would insulate Open Democracy from the charge of blind deference. I then discuss the direct democracy mechanisms that Landemore incorporates into her model. Although these devices grant citizens control and, by extension, offer the resources for repudiating the charge of blind deference, they also, I argue, subvert the logic of Landemore's lottocratic model, rendering Open Democracy predictably unstable. Given the deliberative asymmetries between the mini-public and the citizenry, a high frequency of bottom-up challenges is to be expected that would throw the whole system into jeopardy. Thus, the challenge for lottocrats is to show how democratic control can be achieved in a lottocratic system without undermining the benefits of the legislature by lot. (shrink)

Including empirical examples and theoretical clarifications on many of the analytical issues raised in his recently published Down to Earth, this conversation with Bruno Latour and his collaborator, Danish sociologist Nikolaj Schultz, offers key insights into Latour’s recent and ongoing work. Revolving around questions on political ecology and social theory in our ‘New Climatic Regime’, Latour argues that in order to have politics you need a land and you need a people. This interview present reflections on such politics, such land (...) and such people, and it ends with a call for a sociology that takes up the task of connecting the three by investigating what he and Schultz call ‘geo-social classes’. The interview was conducted by Jakob Stein in Paris in November 2018. (shrink)

It is well-known that a sense of belonging is crucial in relation to gaining and maintaining sound mental health. Work is also known to be an essential aspect of recovery from mental health problems. However, there is scant knowledge of what a sense of belonging in the workplace represents. This study explores the nature and meaning of a sense of belonging in the workplace as experienced by persons struggling with mental health issues.Using a descriptive phenomenological methodology, sixteen descriptions of the (...) lived experience of belonging in the workplace were analyzed. The analysis reveals that the experience of belonging in the workplace is restricted and fragile until the moment one becomes accepted, but grows stronger and more resilient as one chooses how one wants to participate. Nonetheless, the sense of belonging is haunted by mixed emotions and ambivalence between the wish to be taken care of and the longing for professional appreciation. (shrink)

Vann McGee claims that open-ended schemas are more innocuous than ordinary second-order quantification, particularly in terms of ontological commitment. We argue that this is not the case.

This article examines Swedish, Danish and Norwegian governments’ participation in the European Return Platform for Unaccompanied Minors project and its failed attempts to deport unaccompanied minors to Afghanistan. It argues that ERPUM is an interesting and urgent case of a “deportation corridor”, and suggests that this framework can benefit from analysis through normative and applied ethics and in particular discussions of feasibility constraints. It therefore identifies and critically assesses two nationalistic arguments for deportation common in Nordic politics, based on appeals (...) credibility and humanitarianism. Considering the growth of nationalistic immigration policies in Nordic states, the article turns the usual discussions of feasibility on its head by showing that not only cosmopolitan, but also nationalistic ethics must face up to charges of lacking realism. More specifically, it argues that the case of ERPUM illustrates how nationalistic deportation ethics can rely on inconsistent normative and erroneous empirical assumptions, which can be criticized for their arbitrariness, ideological grounding and lacking feasibility. (shrink)

Secretion is a fundamental cellular process involving the regulated release of intracellular products from cells. Physiological functions such as neurotransmission, or the release of hormones and digestive enzymes, are all governed by cell secretion. Anomalies in the processes involved in secretion contribute to the development and progression of diseases such as diabetes and other hormonal disorders. To unravel the mechanisms that govern such diseases, it is essential to understand how hormones, growth factors and neurotransmitters are synthesized and processed, and how (...) their signals are recognized, amplified and transmitted by intracellular signaling pathways in the target cells. Here, we discuss diverse aspects of the detailed mechanisms involved in secretion based on mathematical models. The models range from stochastic ones describing the trafficking of secretory vesicles to deterministic ones investigating the regulation of cellular processes that underlie hormonal secretion. In all cases, the models are closely related to experimental results and suggest theoretical predictions for the secretion mechanisms. (shrink)

In this critical comment, we argue that nondemocratic, but decent regimes fail to constitute legitimate governance under Applbaum’s free group agency account. To make this case, we first introduce the three principles of liberty, equality and agency that Applbaum takes to flow directly from his free agency conception of legitimacy. Against this backdrop, we discuss Applbaum’s claim that a nondemocratic regime along the lines of a Rawlsian decent consultation hierarchy could meet the threshold of legitimacy. Contrary to this suggestion, we (...) argue that nondemocratic, but decent regimes cannot claim legitimacy under Applbaum’s account because they are constitutively inegalitarian, thus failing to adequately grant citizens the equal normative power without which legitimacy is unattainable under the free group agency account. (shrink)

This second volume in the series "Studies in Hellenistic Civilization", published for the Danish Research Council for the Humanities, offers a comprehensive analysis of the Stoic theory of Oikeiosis.

This edited volume brings together 18 state-of-the art essays on pluralism about truth and logic. Parts I and II are dedicated to respectively truth pluralism and logical pluralism, and Part III to their interconnections. Some contributors challenge pluralism, arguing that the nature of truth or logic is uniform. The majority of contributors, however, defend pluralism, articulate novel versions of the view, or contribute to fundamental debates internal to the pluralist camp. The volume will be of interest to truth theorists and (...) philosophers of logic, as well as philosophers interested in relativism, contextualism, metaphysics, philosophy of language, semantics, paradox, epistemology, or normativity. (shrink)

From Stoicism to Platonism describes the change in philosophy from around 100 BCE, when monistic Stoicism was the strongest dogmatic school in philosophy, to around 100 CE, when dualistic Platonism began to gain the upper hand - with huge consequences for all later Western philosophy and for Christianity. It is distinguished by querying traditional categories like 'eclecticism' and 'harmonization' as means of describing the period. Instead, it highlights different strategies of 'appropriation' of one school's doctrines by philosophers from the other (...) school, with all philosophers being highly conscious of their own identity. The book also sets out to break down the traditional boundaries between, on the one hand, the study of Greco-Roman philosophy in the period and, on the other hand, that of contemporary Hellenistic Jewish and early Christian writings with a philosophical profile. In these ways, the book opens up an immensely fruitful period in the history of philosophy. (shrink)

If you want to understand McDowell's spatial metaphors when he talks about perceptual knowledge, place him side-by-side with Dretske on perceptual knowledge. Though McDowell shows no evidence of reading Dretske's writings on knowledge from the late 1960s onwards (McDowell mentions "Epistemic Operators" once in passing), McDowell gives the same four arguments as Dretske for the conclusion that knowledge requires "conclusive" reasons that rule of the possibility of mistake. Despite various differences, we think it is best to read McDowell as re-discovering (...) Dretske on perceptual knowledge. Since Dretske is easy to understand, all of McDowell's metaphors become easy to understand. But what about McDowell's disjunctivism? Turns out McDowell is not an ontological disjunctivist, and his epistemological disjunctivism is really just the banal point that some perceptual experiences provide conclusive reasons for perceptual belief and some do not. Perceptual experiences are either conclusive or inconclusive. Dretske would agree. (shrink)

. . . The book is enhanced by the polished and lucid style of Mr. Waley's translations.

At the top of his ethical system Aristotle placed, as the supreme value, eudai- monia (happiness). But what does this really mean? ...