The link between logic and mathematics has long been recognized by theorists from various fields. For instance, the mathematician, Bertrand Russell (1919), described logic and math as intrinsically...

Throughout history, the generation, exercise, and dissemination of knowledge are fraught with dangers, the root causes of which are traceable to the definition of authority relations. The authors compare Greek myths and Chinese legends, setting the stage for a metarelational analysis of authority relations between teacher and students and between scholar-teachers and political rulers in Confucian-heritage cultures. These two relations are rooted in ideological conservatism. They are related in a higher-order relation or metarelation: Political control and the definition of the (...) teacher-student relationship reinforce each other in consolidating authoritarian values. Thus, ideological conservatism shapes educational philosophy and socialization. It conflicts with present demands for creativity in the service of knowledge-based economies. Hence, a major issue in cultural change to be addressed concerns the dilemma between maintaining authoritarian control and enhancing creativity. (shrink)

This paper starts by investigating Ackermann's interpretation of finite set theory in the natural numbers. We give a formal version of this interpretation from Peano arithmetic (PA) to Zermelo-Fraenkel set theory with the infinity axiom negated (ZF−inf) and provide an inverse interpretation going the other way. In particular, we emphasize the precise axiomatization of our set theory that is required and point out the necessity of the axiom of transitive containment or (equivalently) the axiom scheme of ∈-induction. This clarifies the (...) nature of the equivalence of PA and ZF−inf and corrects some errors in the literature. We also survey the restrictions of the Ackermann interpretation and its inverse to subsystems of PA and ZF−inf, where full induction, replacement, or separation is not assumed. The paper concludes with a discussion on the problems one faces when the totality of exponentiation fails, or when the existence of unordered pairs or power sets is not guaranteed. (shrink)

In an earlier paper the first author initiated the study of generic cuts of a model of Peano arithmetic relative to a notion of an indicator in the model. This paper extends that work. We generalise the idea of an indicator to a related neighbourhood system; this allows the theory to be extended to one that includes the case of elementary cuts. Most results transfer to this more general context, and in particular we obtain the idea of a generic cut (...) relative to a neighbourhood system, which is studied in more detail. The main new result on generic cuts presented here is a description of truth in the structure , where I is a generic cut of a model M of Peano arithmetic. The special case of elementary generic cuts provides a partial answer to a question of Kossak [R. Kossak, Four problems concerning recursively saturated models of arithmetic, Notre Dame Journal of Formal Logic 36 519–530]. (shrink)

We prove that any proof of a [Formula: see text] sentence in the theory [Formula: see text] can be translated into a proof in [Formula: see text] at the cost of a polynomial increase in size. In fact, the proof in [Formula: see text] can be obtained by a polynomial-time algorithm. On the other hand, [Formula: see text] has nonelementary speedup over the weaker base theory [Formula: see text] for proofs of [Formula: see text] sentences. We also show that for (...) [Formula: see text], proofs of [Formula: see text] sentences in [Formula: see text] can be translated into proofs in [Formula: see text] at a polynomial cost in size. Moreover, the [Formula: see text]-conservativity of [Formula: see text] over [Formula: see text] can be proved in [Formula: see text], a fragment of bounded arithmetic corresponding to polynomial-time computation. For [Formula: see text], this answers a question of Clote, Hájek and Paris. (shrink)

This paper introduces a new theory of constant regions, which generalizes that of interstices, in nonstandard models of arithmetic. In particular, we show that two homogeneity notions introduced by Richard Kaye and the author, namely, constantness and pregenericity, are equivalent. This led to some new characterizations of generic cuts in terms of existential closedness.

The foundation scheme in set theory asserts that every nonempty class has an ∈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\in $$\end{document}-minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-recursion theory. We take KP set theory without foundation as the base theory. We show that KP-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^-$$\end{document} + Π1\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi _1$$\end{document}-Foundation + V=L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V=L$$\end{document} is enough to carry out finite injury arguments in α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-recursion theory, proving both the Friedberg-Muchnik theorem and the Sacks splitting theorem in this theory. In addition, we compare the strengths of some fragments of KP. (shrink)

The progress of electronic health technologies and biobanks holds enormous promise for efficient research. Evidence shows that studies based on sharing and secondary use of data/samples have the potential to significantly advance medical knowledge. However, sharing of such resources for international collaboration is hampered by the lack of clarity about ethical and legal requirements for transfer of data and samples across international borders. Here, the International Clinical Trial Center Network reports the legal and ethical requirements governing data and sample exchange (...) across four continents. The most recurring requirement is ethical approval, whereas only in specific conditions approval of national health authorities is required. Informed consent is not required in all sharing situations. However, waiver of informed consent is only allowed in certain countries/regions and under certain circumstances. The current legal and ethical landscape appears to be very complex and under constant evolution. Regulations differ between countries/regions and are often incomplete, leading to uncertainty. With this work, ICN illuminates the unmet need for a single international collaborative framework to facilitate DSE. Harmonising requirements for global DSE will reduce inefficiency and waste in research. There are many challenges to realising this ambitious vision, including inconsistent terminology and definitions, and heterogeneous and dynamic legal constraints. Here, we identify areas of agreement and significant difference as a necessary first step towards facilitating international collaboration. We propose the establishment of a working group to continue the comparison across jurisdictions, create a standardised glossary and define a set of basic principles and fundamental requirements for DSE. (shrink)

ABSTRACT This study examined how lifestyle factors and gender affect kidney allocation to transplant patients by 99 British and Singaporean participants. Thirty hypothetical patients were generated from a combination of six factors and randomly paired four times. Participants saw 60 patient pairings and, in each pair, chose which patient would receive treatment priority. A Bradley-Terry model was used to derive coefficients for each factor per participant. A mean factor score was then calculated across all participants for each factor. Participants (...) gave lower priority to patients who drank more, were overweight, smoked more and exercised less. A patient’s diet and gender had no significant effect on allocation. There were no significant cross-cultural differences. There were moderate correlations between participants’ self-reported pre- and post-experiment ordering of decision criteria, and these measures and factor coefficients, suggesting a modest level of decision-making consistency. Between participants, moderate levels of concordance with respect to factor importance were observed for self-reported orderings of factors, and weaker agreement for model-derived coefficients. Very similar results were obtained for both British and Singaporean participants, and the implications of the findings are discussed. (shrink)

Situation theory has been developed over the last decade and various versions of the theory have been applied to a number of linguistic issues. However, not much work has been done in regard to its computational aspects. In this paper, we review the existing approaches towards 'computational situation theory' with considerable emphasis on our own research.

In "Milk, Honey, and the Good Life on Moral Twin Earth", David Copp explores some ways in which a defender of synthetic moral naturalism might attempt to get around our Moral Twin Earth argument. Copp nicely brings out the force of our argument, not only through his exposition of it, but through his attempt to defeat it, since his efforts, we think, only help to make manifest the deep difficulties the Moral Twin Earth argument poses for the synthetic moral naturalist.

Existence monism is defended against priority monism. Schaffer's arguments for priority monism and against pluralism are reviewed, such as the argument from gunk. The whole does not require parts. Ontological vagueness is impossible. If ordinary objects are in the right ontology then they are vague. So ordinary objects are not included in the right ontology; and hence thought and talk about them cannot be accommodated via fully ontological vindication. Partially ontological vindication is not viable. Semantical theorizing outside the ontology room (...) and semantical theorizing in the doorway. Existence monism is theoretically preferable to priority monism. (shrink)

Interpretability logic is a modal formalization of relative interpretability between first‐order arithmetical theories. Verbrugge semantics is a generalization of Veltman semantics, the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. We study various notions of bisimulation between Verbrugge models and develop a new one, which we call w‐bisimulation. We show that the new notion, while keeping the basic property that bisimilarity implies modal equivalence, is weak enough to allow the converse to hold in (...) the finitary case. To do this, we develop and use an appropriate notion of bisimulation games between Verbrugge models. (shrink)

This article discusses the moral principles underlying the idea of humanitarian intervention. The analysis is in two parts, one historical and the other philosophical. First, the article examines arguments made in late medieval and early modern Europe for using armed force to punish the violation of natural law and to defend communities from tyranny and oppression, regardless of where they occur. It seeks to understand how moralists writing before the emergence of modern international law conceived what we now call humanitarian (...) intervention.In the context of international law, humanitarian intervention is usually understood to be an exception to the nonintervention principle. However, the natural law tradition regards international law as less important than the moral imperative to punish wrongs and protect the innocent.Second, the article considers how humanitarian intervention is justified within the reformulation of the natural law tradition displayed in recent efforts to theorize morality along Kantian lines. In this reformulation, humanitarian intervention is a product of the duty of beneficence and, more specifically, of the right to use force to protect the innocent. The article draws upon the biblical injunction “Thou shalt not stand idly by the blood of thy neighbor,” which has become a centerpiece of the modern reformulation, and briefly explores its application to humanitarian intervention in the context of international relations today. This reformulation of natural law explains why, despite modern efforts to make it illegal, humanitarian intervention remains, in principle, morally defensible. (shrink)

Within cognitive science, mental processing is often construed as computation over mental representations—i.e., as the manipulation and transformation of mental representations in accordance with rules of the kind expressible in the form of a computer program. This foundational approach has encountered a long-standing, persistently recalcitrant, problem often called the frame problem; it is sometimes called the relevance problem. In this paper we describe the frame problem and certain of its apparent morals concerning human cognition, and we argue that these morals (...) have significant import regarding both the nature of moral normativity and the human capacity for mastering moral normativity. The morals of the frame problem bode well, we argue, for the claim that moral normativity is not fully systematizable by exceptionless general principles, and for the correlative claim that such systematizability is not required in order for humans to master moral normativity. (shrink)

How is it possible for human subjects who are socially constructed to engage in effective and authoritative acts of resistance to the social norms and institutions within which they were formed? Judith Butler, in her engagement with the work of Pierre Bourdieu, locates this possibility in the nature of `speech acts', and in resistance to social norms emanating from the abjected margins of social life. She criticizes Bourdieu for undermining the promise of agency contained in habitus by reducing it to (...) the social field in which it was constituted, thus re-closing `the iron cage' of structural/institutional determination. For Butler, social norms and institutions, dependent as they are on reiterative performance, are intrinsically open to disruption. It is possible, she claims, using as her example Rosa Parks's historical act of resistance in Montgomery, Alabama in 1955, to resist with authority, yet without prior institutional authorization. This article argues that Butler's theory of iterability works to endow the capacity to authorize against the grain of institutional authority with individuals and their acts and hence neglects the social contexts that inform and de-limit this capacity. `Resisting with authority' is possible precisely because it is not endowed by individuals or their acts, but is collective and interactional. (shrink)

According to legal tradition, the ideal judge is entirely dispassionate. Affective science calls into question the legitimacy of this ideal; further, it suggests that no judge could ever meet this standard, even if it were the correct one. What judges can and should do is to learn to effectively manage—rather than eliminate—emotion. Specifically, an emotion regulation perspective suggests that judicial emotion is best managed by cognitive reappraisal and, often, disclosure; behavioral suppression should be used sparingly; and suppression of emotional experience (...) is rarely helpful. We argue that the dispassionate-judge ideal presents a barrier to achieving the flexibility necessary for adaptive judicial emotion regulation. We suggest a new ideal, that of the emotionally well-regulated judge, and propose several directions for future research to strengthen ties between law and psychology, with particular attention to the study of emotion. (shrink)

By reflecting on a variety of cartoon representations of teachers and their work, this paper outlines a semiotic approach to undertaking research on teachers' professional cultures.

This article argues that a positive engagement between Bourdieu’s sociology of practice and contemporary feminist theory would be mutually profitable. It compares Bourdieu’s account of the social construction of the human subject through practice with Butler’s account of subjectivity as performance. While the one, through the concept of habitus, tends towards an ‘overdetermined’ view of subjectivity in which subjective dispositions are too tightly tied to the social practices in which they were forged, the other pays insufficient attention to the social (...) conditions of performative subversion. The second half of the paper looks at feminist studies of the relationship between class and gender which have drawn fruitfully on Bourdieu’s work, particularly on his concept of ‘cultural capital’, such as those of Moi and Skeggs. (shrink)

The philosophical account of vagueness I call "transvaluationism" makes three fundamental claims. First, vagueness is logically incoherent in a certain way: it essentially involves mutually unsatisfiable requirements that govern vague language, vague thought-content, and putative vague objects and properties. Second, vagueness in language and thought (i.e., semantic vagueness) is a genuine phenomenon despite possessing this form of incoherence—and is viable, legitimate, and indeed indispensable. Third, vagueness as a feature of objects, properties, or relations (i.e., ontological vagueness) is impossible, because of (...) the mutually unsatisfiable conditions that such putative items would have to meet. In this paper I set forth the core claims of transvaluationism in a way that acknowledges and explicitly addresses a challenging critique by Timothy Williamson of my prior attempts to articulate and defend this approach to vagueness. I sketch my favored approach to truth and ontological commitment, and I explain how it accommodates the impossibility of ontological vagueness. I argue that any approach to the logic and semantics of vagueness that both (i) eschews epistemicism and (ii) thoroughly avoids positing any arbitrary sharp boundaries (either first-order or higher-order) will have to be not an alternative to transvaluationism but an implementation of it. I sketch my reasons for repudiating epistemicism. I briefly describe my current thinking about how to accommodate intentional mental properties with vague content within an ontology that eschews ontological vagueness. And I revisit the idea, which played a key role in my earlier articulations of transvaluationism, that moral conflicts provide an illuminating model for understanding vagueness. (shrink)

Elaborating the analogy between the sun and the good, Plato's Socrates tells Glaucon to divide a line αβ into two unequal segments at γ. The result is that αγ represents what is intelligible and γβ what is visible.1 Then Glaucon is to divide each of the two segments by the same ratio as he used in the original division.2 Whatever proportion he used to make the cuts γ, δ, and ε in the divided line, generating its four segments, the geometrical (...) implication is that the two middle segments must be equal in length. As both Nicholas D. Smith and Richard Foley have emphasized, when Socrates reiterates the characteristics of the line at 534a3–5, transposing δγ and γε, there should be no doubt that Plato... (shrink)

In Kant's "fact of reason," there is an apparent paradox of our being subject to laws of which we must regard ourselves as the author, while at the same time being normatively bound by the same laws that we cannot see ourselves as authoring. Working out the implications of this apparent paradox generated much of the response to Kant in post-Kantian idealism. Wilfrid Sellars notes the same paradox when he speaks of the "paradox of man's encounter with himself" in "Philosophy (...) and the Scientific Image of Man." Like some of the idealists, Sellars thus opted for "two track" system of philosophy that combines the two tracks in a metaphor of "stereoscopic vision." This paper argues that understanding Sellars 's own thought in terms of the issues that formed the dynamic of post-Kantian philosophy in Germany puts us in a better position to understand why Sellars 's own conception of experience and of the unreality of the manifest image is not completely consistent with the argumentative direction of his thought. Understanding Sellars in this way helps us understand the limits of post-Kantian idealism just as understanding the dynamic of post-Kantian idealism gives us a more nuanced version of Sellars 's conception of experience. (shrink)

The challenge for those responsible for funding, brokering and assessing the merit of proposed Indigenous research is to identify and then work co-operatively with appropriate representatives of Indigenous interests in order to increase the flow of benefits from research to Indigenous peoples. Experience in Australia has shown that this is not a straightforward process. In this paper we indicate some reasons why it is important for the research community to broker research with representative Indigenous organisations and to involve Indigenous peoples (...) in the ethical assessment and conduct of research. We then identify some barriers to the achievement of these objectives and outline recently developed interventions from the field of health research that aim to promote a more effective working relationship between Indigenous peoples and members of the research community. (shrink)

User intent classification is a vital component of a question-answering system or a task-based dialogue system. In order to understand the goals of users’ questions or discourses, the system categorizes user text into a set of pre-defined user intent categories. User questions or discourses are usually short in length and lack sufficient context; thus, it is difficult to extract deep semantic information from these types of text and the accuracy of user intent classification may be affected. To better identify user (...) intents, this paper proposes a BERT-Cap hybrid neural network model with focal loss for user intent classification to capture user intents in dialogue. The model uses multiple transformer encoder blocks to encode user utterances and initializes encoder parameters with a pre-trained BERT. Then, it extracts essential features using a capsule network with dynamic routing after utterances encoding. Experiment results on four publicly available datasets show that our model BERT-Cap achieves a F1 score of 0.967 and an accuracy of 0.967, outperforming a number of baseline methods, indicating its effectiveness in user intent classification. (shrink)