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...

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)

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)

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)

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)

ABSTRACT Lewtas [2017] recently articulated an argument claiming that emergent conscious causal powers are impossible. In developing his argument, Lewtas makes several assumptions about emergence, phenomenal consciousness, categorical properties, and causation. We argue that there are plausible alternatives to these assumptions. Thus, the proponent of emergent conscious causal powers can escape Lewtas’s challenge.

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 →.

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)

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)

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)

There are a number of recent attempts to introduce Confucian values to the ethical analysis of technology. These works, however, have not attended sufficiently to one central aspect of Confucianism, namely Ritual (‘Li’). Li is central to Confucian ethics, and it has been suggested that the emphasis on Li in Confucian ethics is what distinguishes it from other ethical traditions. Any discussion of Confucian ethics for technology, therefore, remains incomplete without accounting for Li. This chapter aims to elaborate on the (...) concept of Confucian Li and discuss its relevance to ethics of technology. Particularly, by referring to Li’s communicative, formative, and aesthetic function, I formulate an approach to ethics of technology with an emphasis on community, performance, and the aesthetic and demonstrate how this approach proceeds with the ethical analysis of technology. In doing so, I attempt to answer the question: why Confucianism matters in ethics of technology. (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)

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)

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)

The essence of the associated-proposition strategy is to distinguish the necessary proposition _expressed by_ a sentence.

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 only recently 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)

When two people need a kidney transplant, but only one kidney is available, we need to decide who gets it. If one of the potential recipients needs the kidney because of their own voluntary behavior, but the other is not at all responsible for needing a kidney, then we need to decide whether this fault should be a consideration in favor of the other patient getting the kidney. While there has been considerable philosophical debate on this issue, there is far (...) less research into the views of the public. To explore opinions on these issues, we first asked survey participants to ascribe or deny responsibility for the risky behavior for kidney disease, and for being deprived of a kidney in cases of drinking alcohol, drug abuse, smoking and unhealthy eating when the patient did or did not stop the risky behavior after being diagnosed with kidney disease. Next, we asked participants who should get the kidney when the patient who engaged in risky behavior did or did not know, or have easy access to, the information that the behavior was risky. We found that participants generally ascribed responsibility on the basis of knowledge but allocated the kidney on the basis of access to information. These findings have important implications for moral theories as well as medical policies. (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)

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)

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.

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)

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.

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.

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.

Confucianism supports partiality because of its heavy emphasis on filial piety, but this may not always be true. Some assertions in the Analects appear to support comprehensive cosmopolitanism . Filial piety can simply be a requirement for moral training, and once this virtue is cultivated, the individual should extend the same love to all human beings. Impartiality as a requirement of morality is clearly exhibited in Mencius. If it is human nature to feel fear and pity for a child on (...) the verge of falling into a well, and if the right thing to do is to save this child, then one must do so even if she were the child of one’s enemy. However, this attempt to show that Confucianism exhibits a degree of impartiality is challenged by other compiled works on Confucian thought which consider filial piety as the most important virtue. Can we really reconcile the pivotal position of filial piety with aspects of impartiality in Confucian ethics? (shrink)