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)

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.

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)

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 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...

In this paper, we describe four broad ‘meta-methods’ employed in scientific and philosophical research of qualia. These are the theory-centred metamethod, the property-centred meta-method, the argument-centred meta-method, and the event-centred meta-method. Broadly speaking, the theory-centred meta-method is interested in the role of qualia as some theoretical entities picked out by our folk psychological theories; the property-centred meta-method is interested in some metaphysical properties of qualia that we immediately observe through introspection ; the argument-centred meta-method is interested in the role of (...) qualia in some arguments for non-physicalism; the event-centred metamethod is interested in the role of qualia as some natural events whose nature is hidden and must be uncovered empirically. We will argue that the event-centred metamethod is the most promising route to a comprehensive scientific conception of qualia because of the flexibility of ontological and methodological assumptions it can provide. We also reveal the hidden influences of the different meta-methods and in doing so show why consideration of meta-methods has value for the study of consciousness. (shrink)

McTaggart’s argument for the unreality of time was first published in the 1908 article “The Unreality of Time,” and a revised version appeared in the 1927 book The Nature of Existence. I argue that these two versions are significantly different. The second construction of the argument is important because it neutralizes a compelling objection. McTaggart’s initial argument tries to show that the conception of an A-series is self-contradictory. A natural objection is that the apparent contradiction can be resolved by making (...) clear that an event has incompatible A-properties only successively. McTaggart anticipates and responds to the objection. My main contention is this: McTaggart’s initial response to the objection fails, but in the second construction of his argument he succeeds in showing that the contradiction cannot be resolved in the way suggested by the objection. I also explain why the second construction has been overlooked for so long. (shrink)

I propose and argue for an account of humility in Zhuangzi, which I call perspectival humility. In the opening of the article, I will present a view of humility found in pre-Qin Confucian texts; then, I will explain the idea of Zhuangist humility, which provides a contrast to Confucian humility. Zhuang Zhou does not think that any ideas of right and wrong can be absolutely correct. People must see that their beliefs may not be absolutely correct, and should always consider (...) alternative perspectives. Those who recognise the limitations of their perspective are led to perspectival humility. Moreover, perspectival humility encourages people to learn extensively and to harmonise the differences between other perspectives. The Zhuangist approach takes various perspectives into account and is an inclusive notion of humility that prompts people to appreciate different ways of life, engages in harmonious social relationships, and preserves cultural diversity. (shrink)

A beautifully clear and accessible explanation of how to live a Taoist life--by reknowned Taoist master Eva Wong. Being Taoist is one of the most readable books on Taoist philosophy available. It shines a light on exactly what it takes to live a Taoist life. Taoist living rests on four pillars--the public, the domestic, the private, and the spirit lives. Not only do Taoists strive to live these four aspects fully and in a balanced way, they also believe there (...) is an outlook and an art to each of them. Eva Wong uses the teachings of Taoist masters (one for each pillar) to explain the essential concepts. She then gives voice to these texts--simplifying them, removing barriers to understanding, and making them completely accessible and relevant to the modern reader. Wong is a clear and enthusiastic guide to this intriguing spiritual Way, and she challenges us to stop, reflect, and ask ourselves: Do we balance the public, domestic, private, and spirit aspects in our lives? Do we emphasize some at the expense of the others? Do we ever think about unifying worldly and spiritual wisdom in our lives? (shrink)

Since the announcement and establishment of the Oversight Board (OB) by the technology company Meta as an independent institution reviewing Facebook and Instagram’s content moderation decisions, the OB has been subjected to scholarly scrutiny ranging from praise to criticism. However, there is currently no overarching framework for understanding the OB’s various strengths and weaknesses. Consequently, this article analyses, organises, and supplements academic literature, news articles, and Meta and OB documents to understand the OB’s strengths and weaknesses and how it can (...) be improved. Significant strengths include its ability to enhance the transparency of content moderation decisions and processes, to effect reform indirectly through policy recommendations, and its assertiveness in interpreting its jurisdiction and overruling Meta. Significant weaknesses include its limited jurisdiction, limited impact, Meta’s control over the OB’s precedent, and its lack of diversity. The analysis of a recent OB case in Ethiopia shows these strengths and weaknesses in practice. The OB’s relationship with Meta and governments will lead to challenges and opportunities shaping its future development. Reforms to the OB should improve the OB’s control over its precedent, apply OB precedent to currently disputed cases, and clarify the standards for invoking OB precedent. Finally, these reforms provide the foundation for an additional improvement to address the OB’s institutional weaknesses, by involving users in determining whether the OB’s precedent should be applied to decide current content moderation disputes. (shrink)

Russellian monism – an influential doctrine proposed by Russell (1927/1992) – is roughly the view that the natural sciences can only ever tell us about the causal, dispositional, and structural properties of physical entities and not about their categorical properties, and, moreover, that our qualia are constituted by categorical properties. Recently, Stoljar (2001a, 2001b), Strawson (2008), Montero (2010, 2015), Alter and Nagasawa (2012), and Chalmers (2015) have attempted to develop this doctrine into a version of physicalism. Russellian monism faces the (...) so-called combination problem, according to which it is difficult to see how categorical properties could collectively constitute qualia. In this paper, I suggest that there is an insufficiently discussed aspect of the combination problem which I call the difference-maker problem. Taking the difference-maker problem into account, I argue that the combination problem – whether or not it can be solved – results in a dilemma for the project of developing Russellian physicalism. That is, Russellian monism is either physicalistically unacceptable or it is implausible; hence, Russellian monism and physicalism are incompatible. (shrink)

The Humility Thesis is a persistent thesis in contemporary metaphysics. It is known by a variety of names, including, but not limited to, Humility, Intrinsic Humility, Kantian Humility, Kantian Physicalism, Intrinsic Ignorance, Categorical Ignorance, Irremediable Ignorance, and Noumenalism. According to the thesis, we human beings, and any knowers that share our general ways of knowing, are irremediably ignorant of a certain class of properties that are intrinsic to material entities … Continue reading Humility Regarding Intrinsic Properties →.

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)

Neuropsychiatrist Michael T. H. Wong argues that the notions of soul, mind, brain, self and consciousness are no longer adequate on their own to explain humanity. He formulates a “third discourse” that brings philosophy neuroscience theology and psychiatry together as an innovative multilayered narrative for the person in the twenty-first century.

The disciplinary characterisation (DC) is the most popular approach to defining metaphysical naturalism and physicalism. It defines metaphysical naturalism with reference to scientific theories and defines physicalism with reference to physical theories, and suggests that every entity that exists is a posited entity of these theories. DC has been criticised for its inability to solve Hempel’s dilemma and a list of problems alike. In this paper, I propose and defend a novel version of DC that can be called a historical (...) paths approach. The idea is (roughly) that metaphysical naturalism can be defined with reference to the historical ideas that current scientific ideas descend from. I argue that it is not rendered implausible by the above problems, and hence that DC is more defensible and attractive than it may first appear. I then argue that the approach also provides a useful framework for the naturalisation of the philosophy of mind and phenomenology. (shrink)

Russellian monism—an influential doctrine proposed by Russell (The analysis of matter, Routledge, London, 1927/1992)—is roughly the view that physics can only ever tell us about the causal, dispositional, and structural properties of physical entities and not their categorical (or intrinsic) properties, whereas our qualia are constituted by those categorical properties. In this paper, I will discuss the relation between Russellian monism and a seminal paradox facing epiphenomenalism, the paradox of phenomenal judgment: if epiphenomenalism is true—qualia are causally inefficacious—then any judgment (...) concerning qualia, including epiphenomenalism itself, cannot be caused by qualia. For many writers, including Hawthorne (Philos Perspect 15:361–378, 2001), Smart (J Conscious Stud 11(2):41–50, 2004), and Braddon-Mitchell and Jackson (The philosophy of mind and cognition, Blackwell, Malden, 2007), Russellian monism faces the same paradox as epiphenomenalism does. I will assess Chalmers’s (The conscious mind: in search of a fundamental theory. Oxford University Press, New York, 1996) and Seager’s (in: Beckermann A, McLaughlin BP (eds) The Oxford handbook of philosophy of mind. Oxford University Press, New York, 2009) defences of Russellian monism against the paradox, and will put forward a novel argument against those defences. (shrink)

The aim of this paper is to situate the early Indian (Nikāya) Buddhist notion of karmic causation within the mental causation discourse in the Western analytic tradition, which concerns causal transactions involving mental events, such as desires, beliefs, and intentions, whether the transactions are between mental events, or between mental events and physical events. Karmic causation involves actional causes, in concert with non-actional causes, and their experiential effects on the actor, in concert with non-experiential effects. The problems generated by karmic (...) causation in Buddhism overlap with those generated by mental causation in the Western analytic tradition. They include how the mental aspects relate to the physical aspects of the self, sense perception, and action, as well as how the mental and physical aspects of an actional cause relate to the experiential and non-experiential aspects of an effect on the actor. -/- To make sense of mental causation, it is crucial to understand a cluster of associated concepts such as causation, the self, sense perception, and action. Similarly, to make sense of karmic causation, it is crucial to understand a cluster of associated concepts such as dependent arising (paṭiccasamuppāda), the fivefold laws of nature (pañca-niyāma), the five aggregates (pañca-khandha), the six sense bases (Saḷayatana), action (karma), and results (vipāka). I shall discuss these concepts under the headings of causation, the self, sense perception, and action before I move on to address karmic causation in the context of the mental causation debate. (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)

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)

Alexander Bird (2001; 2002; 2007) offers a powerful argument showing that, regardless of whether necessitarianism or contingentism about laws is true, salt necessarily dissolves in water. The argument is that the same laws of nature that are necessary for the constitution of salt necessitate the solubility of salt. This paper shows that Bird’s argument faces a serious objection if the possibility of emergentism – in particular, C. D. Broad’s account – is taken into account. The idea is (roughly) that some (...) emergent laws in some possible worlds may disrupt the solubility of salt without disrupting its constitution. (shrink)

Global engineering ethics is the engineering ethics’ response to globalization. It plays a major role in the received narrative about the need for a global engineering ethics, which is often illustrated by stories of some engineers A (of culture X) who interact with people or organizations of culture Y, and as a result encounter conflicts between their (i.e. culture X’s) ethical values and culture Y’s ethical values that generate ethical conundrums to the engineers. Global engineering ethics is thus needed to (...) help engineers to navigate through these ethical conundrums. However, the received narrative is insufficient in attending to the different nature and scope of ethical challenges for engineers and engineering practices in a globalized context, or so I shall argue. To understand these differences, I elaborate three basic presuppositions that create the need for global engineering ethics and explain their various interpretations. These presuppositions will then form the basis of my discussion of current approaches to global engineering ethics. I also argue that global engineering ethics is not merely reactive but also proactive, but the existing approaches have paid insufficient attention to the proactive dimension of global engineering ethics. So, I will end this chapter by arguing for the importance of the proactive dimension and exploring what it demands from engineers and engineering practices. (shrink)

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.

Qualifying post-Westphalian sovereign statehood as a 'power' as argued for in Hendrik Berkhoff's political theology, this book addresses the decades-long theological-spiritual debate between Christian realism and Christian pacifism in U.S. foreign policy and global Christian circles. It approaches the debate by delving into the pacifist Anabaptist political theology and delineates empirically how sovereign statehood in post-colonial Africa and Asia has fallen into the hands of the devil Satan, as a 'fallen power' in the Foucaultian terms of power structures, techniques and (...) episteme. While the book offers intervention schemes and options, it holds that Christian statecraft remains the source of hope to effectively address a number of serious global issues. By extension, the book is thus an invitation to ignite debates on the suitability of Christian statecraft and the nexus between spirituality and world politics, making it especially interesting for scholars and students in the fields of International Politics, Politics of Asian and African States, Post-colonial Studies and Political Theology.. (shrink)

The argument for metaethical relativism, the view that there is no single true or most justified morality, is that it is part of the best explanation of the most difficult moral disagreements. This Element discusses the latest arguments in ethical theory in an accessible manner, with many examples and cases.

In contrast to standard possible worlds semantics, possible worlds in a two-dimensional semantic framework play two kinds of roles, rather than just one. This allows the framework to assign two kinds of intensions to expressions, rather than just one. Its fruitful use in explicating modal operators and the meanings of referential expressions like indexicals has led to two-dimensional accounts that seek to revive the Fregean conception of meaning, or more specifically the descriptivist view of reference, which has fallen into disrepute (...) due to intense criticisms, most famously, by Saul Kripk’s seminal work Naming and Necessity (1972). This entry provides a critical overview of the two most prominent of such accounts, proposed by Frank Jackson and David Chalmers. Unfortunately, there is not space to describe either account in detail, so I rely largely on brief descriptions and plenty of references to primary and secondary sources. More importantly, I rely on focusing on how the accounts explain the phenomenon of necessary a posteriori identity that Kripke’s well-known examples (such as ‘Hesperus is Phosphorus’) have brought to light. Focusing on and structuring our discussions around this phenomenon is by no means just an expository convenience. These cases are of central importance in themselves. They epitomize a large part of the contribution of Naming and Necessity to the theory of reference. This is why section 2 outlines Kripke’s critique of the Fregean theory of referential expressions and section 3 explains rigid designation and identity statements. Section 4 discusses rigidification and the notion of a world considered as actual, leading to the introduction of two-dimensional functions in Section 5. I discuss, finally, Frank Jackson’s and David Chalmers’ two-dimensionalism in Sections 6 and 7. Section 8 makes a few critical remarks on Jackson’s handling of the semantic argument. I conclude (Section 8) by discussing the important distinction between semantics and metasemantics. (shrink)

Monism is our name for a range of views according to which the connection between dispositions and their categorical bases is intimate and necessary, or on which there are no categorical bases at all. In contrast, Dualist views hold that the connection between dispositions and their categorical bases is distant and contingent. This paper is a defence of Monism against an influential conceivability argument in favour of Dualism. The argument suggests that the apparent possibility of causal behaviour coming apart from (...) categorical bases is best explained by Dualism. We argue that Monism can explain the apparent possibility as well, if we take metaphysically alien laws — namely, laws whose metaphysical nature is alien to the actual world — into account. (shrink)

Untruthfulness is surprisingly common in the U.S. military even though members of the profession are loath to admit it. Further, much of the deception and dishonesty that occurs in the profession of arms is actually encouraged and sanctioned by the military institution. The end result is a profession whose members often hold and propagate a false sense of integrity that prevents the profession from addressing -- or even acknowledging -- the duplicity and deceit throughout the formation. It takes remarkable courage (...) and candor for leaders to admit the gritty shortcomings and embarrassing frailties of the military as an organization in order to better the military as a profession. Such a discussion, however, is both essential and necessary for the health of the military profession"--Publisher's web site. (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)

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)

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.