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 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...

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)

In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal squaring principle; more precisely, its instance for the (infinite) universe (VCSP), which is a theorem of NFU + Inf + AC. Therefore, we have a justification for proposing a new axiomatic extension of NFU, in order to obtain type-level ordered pairs almost (...) from the beginning. This axiomatic extension is NFU + Inf + AC + VCSP, which is equivalent to NFU + Inf + AC, but easier to reason about. (shrink)

In this book, David B. Wong defends an ambitious and important new version of moral relativism. He does not espouse the type of relativism that says anything goes, but he does start with a relativist stance against alternative theories such that there need not be only one universal truth. Wong proposes that there can be a plurality of true moralities existing across different traditions and cultures, all with one core human question as to how we can all live (...) together. (shrink)

The view defended is one sense externalist on the relation between moral reasons and motivation: A's having a moral reason to do X does not necessarily imply that A has a motivation that would support A's doing X via some appropriate deliberative route. However, it is in another sense externalist in holding that there are the kind of moral reasons there are only if the relevant motivational capacities are "generally present" in human beings, if not in all individuals. The process (...) of socialization is an attempt to embed the recognition of what we have moral reason to do in the intentional content of one's feelings. E.g., learning that about others' suffering embeds their suffering as a reason to help in the intentional content of incipient compassionate feelings. This endows the reason with motivational efficacy while conferring further direction to the feelings in ways that shape us for social cooperation. (shrink)

The main feature of NF/NFU is the notion of stratification, which sets it apart from other set theories. We define stratification and prove constructively that every stratified formula has the (unique) least assignment of types. The basic notion of stratification is concerned only with variables, but we extend it to abstraction terms in order to simplify further development. We reflect on nested abstraction terms, proving that they get the expected types. These extensions enable us to check whether some complex formula (...) is stratified without rewriting it in the basic language. We also introduce natural numbers and a variant of the axiom of infinity, in order to precisely introduce type level ordered pairs, which are crucial in simplifying the definitions in the last part of the article. Using these notions we can easily define the sets of ordinal and cardinal numbers, which we show at the end of the article. The same approach can be readily applied to NF. (shrink)

Since the emergence of Pakistan the history of Pak-Afghan relations can best be analyzed from conflict to cooperation. Some of the early problems are mainly responsible for conflict and cooperation in both countries relations. After the establishment of democratic setup in both states, different CBMs indicate positive sign in Pak-Afghan diplomatic relationship. The drawdown of US forces has created security concern for Pakistan and Afghanistan that the creation of power vacuum can push the country again into civil war like situation. (...) In such state of security Pakistan’s engagement to bring the Taliban to the negotiation table will smooth the way for a broad-based government in Afghanistan. Some of the Afghan domestic political issues also created mistrust i.e., the refugee’s problem, cross border militant’s infiltrations, drug problem and issue of the Taliban. However, the paper will highlight the measures to keep intact the reconciliation more effective and replace the mistrust by trust. How domestic political issues effect their bilateral relations and why various methods taken in the prescribe time not effective in bilateral relations of the two states. (shrink)

The present study investigates the dynamics of emotional processing and awareness using an affective facial priming paradigm in conjunction with a multimodal assessment of awareness. Key facial primes are visually masked, and are presented for brief and extended durations. Using a preference measure, we examine whether the effects of the primes differ qualitatively . We show that: unconscious affective priming with faces emerges strongly in initial presentations and diminishes rapidly with repetition; conscious affective priming also emerges strongly in initial presentations, (...) however it persists in strength with repetition; and in contrast to other reports on the salience of negative stimuli, happy faces appear more salient than sad faces when presented outside awareness. We discuss the limits and extensions of unconscious affective priming with faces, and consider several methodological and conceptual questions concerning emotional processing out of awareness. (shrink)

Response to Floridi et al, 2008/2009. Based on insufficient evidence, and inadequate research, Floridi and his students report inaccuracies and draw false conclusions in their Minds and Machines evaluation, which this paper aims to clarify. Acting as invited judges, Floridi et al. participated in nine, of the ninety-six, Turing tests staged in the finals of the 18th Loebner Prize for Artificial Intelligence in October 2008. From the transcripts it appears that they used power over solidarity as an interrogation technique. As (...) a result, they were fooled on several occasions into believing that a machine was a human and that a human was a machine. Worse still, they did not realise their mistake. This resulted in a combined correct identification rate of less than 56%. In their paper they assumed that they had made correct identifications when they in fact had been incorrect. (shrink)

This paper is to inform the recent situations of work by the foreign domestic workers (FDWs) in Hong Kong through the lens of Covid-19. Through the interviews with seven informants — two employers and five FDWs, stories describing the changes in their working conditions, rights and entitlement, and the contextual environment related to the impacts of Covid-19 were collected. They were analysed through three theoretical tools — visibility/invisibility, mobility/immobility, and work boundary. The findings show that under the Covid-19 crisis, the (...) FDWs experienced more hardships and struggles in both the home country and host country. The paradoxes of visibility/invisibility and mobility/immobility together with blurred work boundary were found in their experience of work, rights and entitlement, and the contextual environment. On one hand, the employers’ power of controlling FDWs has increased, but the agency to resist by the FDWs has decreased making them to turn to more passive means of resistance which could harm the FDWs’ physical and mental health and wellbeing. (shrink)

I thought the paper by Kai-yee Wong and Chris Fraser was fascinating and insightful. Two things I especially appreciated are the clarity with which they summarize my views. I think they are quite fair and accurate. Second, I appreciate their suggestion that the way to deal with the practical problem of weakness of will has much to do with the role of the Background in shaping our actions. I think they are especially on the right track when they say (...) that the improvement of Background skills may actually narrow the range of real options for action, (p. 21) nonetheless, they do not decrease freedom. As they say, “It is a process of strengthening the self, and the agent is likely to experience the concomitant restriction of ‘live’ options not as a limitation but as strength of character.” (p. 21). That seems to me very much on the right track. What they are suggesting, and it is a powerful addition to my own writings, is that we should not just think of the Background as facilitating languages, games and social practices generally, but for morality as well (p. 23). (shrink)

This is a critical discussion of Paul Humphreys's fusion view of emergence, focusing on the basal loss feature of his ontology. The discussion yields some general morals for special science ontology.

I argue that it is a main theme of Davidson's theory of interpretation that interpretive charity implies the impossibility of massive disagreement. There is clear textual support for that. I then argue that from the first-person point of view of a full-blooded interpreter, the theme must be accepted; and that is precisely why Davidson accepts it. If massive disagreement between speaker and interpreter seems to us easy to imagine, it is only because the imagination involved is third-personal and not full-blooded.

Biometric technologies are becoming more pervasive in the workplace, augmenting managerial processes such as hiring, monitoring and terminating employees. Until recently, these devices consisted mainly of GPS tools that track location, software that scrutinizes browser activity and keyboard strokes, and heat/motion sensors that monitor workstation presence. Today, however, a new generation of biometric devices has emerged that can sense, read, monitor and evaluate the affective state of a worker. More popularly known by its commercial moniker, Emotional AI, the technology stems (...) from advancements in affective computing. But whereas previous generations of biometric monitoring targeted the exterior physical body of the worker, concurrent with the writings of Foucault and Hardt, we argue that emotion-recognition tools signal a far more invasive disciplinary gaze that exposes and makes vulnerable the inner regions of the worker-self. Our paper explores attitudes towards empathic surveillance by analyzing a survey of 1015 responses of future job-seekers from 48 countries with Bayesian statistics. Our findings reveal affect tools, left unregulated in the workplace, may lead to heightened stress and anxiety among disadvantaged ethnicities, gender and income class. We also discuss a stark cross-cultural discrepancy whereby East Asians, compared to Western subjects, are more likely to profess a trusting attitude toward EAI-enabled automated management. While this emerging technology is driven by neoliberal incentives to optimize the worksite and increase productivity, ultimately, empathic surveillance may create more problems in terms of algorithmic bias, opaque decisionism, and the erosion of employment relations. Thus, this paper nuances and extends emerging literature on emotion-sensing technologies in the workplace, particularly through its highly original cross-cultural study. (shrink)

The Art of War application to education is about solving problems to improve student and school success. The Art of War describes the significance of a leader and his knowledge and prudent application of the strategies. At the core of theses strategies is the non-negotiable moral purpose of the leader to be reinforced by other fine qualities as wisdom, commitment, discipline, and courage.

In this paper, we look at the possibility of a machine having a sense of humour. In particular, we focus on actual machine utterances in Turing test discourses. In doing so, we do not consider the Turing test in depth and what this might mean for humanity, rather we merely look at cases in conversations when the output from a machine can be considered to be humorous. We link such outpourings with Turing’s “arguments from various disabilities” used against the concept (...) of a machine being able to think, taken from his seminal work of 1950. Finally we consider the role that humour might play in adding to the deception, integral to the Turing test, that a machine in practice appears to be a human. (shrink)

Serious thinking about the computational aspects of situation theory is just starting. There have been some recent proposals in this direction (viz. PROSIT and ASTL), with varying degrees of divergence from the ontology of the theory. We believe that a programming environment incorporating bona fide situation-theoretic constructs is needed and describe our very recent BABY-SIT implementation. A detailed critical account of PROSIT and ASTL is also offered in order to compare our system with these pioneering and influential frameworks.

While situation theory and situation semantics provide an appropriate framework for a realistic model-theoretic treatment of natural language, serious thinking on their 'computational' aspects has just started. Existing proposals mainly offer a Prolog- or Lisp-like programming environment with varying degrees of divergence from the ontology of situation theory. In this paper, we introduce a computational medium (called BABY-SIT) based on situations. The primary motivation underlying BABY-SIT is to facilitate the development and testing of programs in domains ranging from linguistics to (...) artificial intelligence in a unified framework built upon situation-theoretic constructs. (shrink)

We describe a novel approach to the analysis of pronominal anaphora in Turkish. A computational medium which is based on situation theory is used as our implementation tool. The task of resolving pronominal anaphora is demonstrated in this environment which employs situation-theoretic constructs for processing.

This article synthesizes the current theoretical attempts to understand human-machine interactions and introduces seven premises to understand our emerging dynamics with increasingly competent, pervasive, and instantly accessible algorithms. The hope that these seven premises can build toward a social theory of human-AI cocreation. The focus on human-AI cocreation is intended to emphasize two factors. First, is the fact that our machine learning systems are socialized. Second, is the coevolving nature of human mind and AI systems as smart devices form an (...) indispensable part of our cognitive scaffolds, thus, shaping how we perceive the world and ourselves. The seven premises include: primacy of social structures; human’s desire for freedom and autonomy; AI systems will form inseparable parts of our cognitive/affective scaffolds and can change our self-understanding; philosophy and humanistic foundations on human flourishing as a guide to human-AI interaction; mindsponge information-filtering process; acculturative process of how values change and emerge from human-AI interaction; overlapping Venn diagram of the human-human, human-nature, and human-machine interactions. This article concludes with a discussion on human agency in our entanglements with socialized machines and the illusoriness of the Cartesian agent view of the mind. (shrink)

A possibility of defining logical constants within abstract logical frameworks is discussed, in relation to abstract definition of logical consequence. We propose using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality.