We compare various notions of algorithmic randomness. First we consider relativized randomness. A set is n-random if it is Martin-Löf random relative to ∅. We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C ≥ |x|-c. The ‘only if' direction was obtained independently by Joseph Miller. This characterization can be extended to the case of time-bounded C-complexity. Next we prove some results (...) on lowness. Among other things, we characterize the 2-random sets as those 1-random sets that are low for Chaitin's Ω. Also, 2-random sets form minimal pairs with 2-generic sets. The r.e. low for Ω sets coincide with the r.e. K-trivial ones. Finally we show that the notions of Martin-Löf randomness, recursive randomness, and Schnorr randomness can be separated in every high degree while the same notions coincide in every non-high degree. We make some remarks about hyperimmune-free and PA-complete degrees. (shrink)

We study and compare two combinatorial lowness notions: strong jump-traceability and well-approximability of the jump, by strengthening the notion of jump-traceability and super-lowness for sets of natural numbers. A computable non-decreasing unbounded function h is called an order function. Informally, a set A is strongly jump-traceable if for each order function h, for each input e one may effectively enumerate a set Te of possible values for the jump JA, and the number of values enumerated is at most h. A′ (...) is well-approximable if can be effectively approximated with less than h changes at input x, for each order function h. We prove that there is a strongly jump-traceable set which is not computable, and that if A′ is well-approximable then A is strongly jump-traceable. For r.e. sets, the converse holds as well. We characterize jump-traceability and strong jump-traceability in terms of Kolmogorov complexity. We also investigate other properties of these lowness properties. (shrink)

We investigate the strength of a randomness notion ${\cal R}$ as a set-existence principle in second-order arithmetic: for each Z there is an X that is ${\cal R}$-random relative to Z. We show that the equivalence between 2-randomness and being infinitely often C-incompressible is provable in $RC{A_0}$. We verify that $RC{A_0}$ proves the basic implications among randomness notions: 2-random $\Rightarrow$ weakly 2-random $\Rightarrow$ Martin-Löf random $\Rightarrow$ computably random $\Rightarrow$ Schnorr random. Also, over $RC{A_0}$ the existence of computable randoms is equivalent (...) to the existence of Schnorr randoms. We show that the existence of balanced randoms is equivalent to the existence of Martin-Löf randoms, and we describe a sense in which this result is nearly optimal. (shrink)

A mass problem is a set of functions $\omega \to \omega $. For mass problems ${\mathcal {C}}, {\mathcal {D}}$, one says that ${\mathcal {C}}$ is Muchnik reducible to ${\mathcal {D}}$ if each function in ${\mathcal {C}}$ is computed by a function in ${\mathcal {D}}$. In this paper we study some highness properties of Turing oracles, which we view as mass problems. We compare them with respect to Muchnik reducibility and its uniform strengthening, Medvedev reducibility.For $p \in [0,1]$ let ${\mathcal {D}}$ (...) be the mass problem of infinite bit sequences y such that for each computable bit sequence x, the bit sequence $ x {\,\leftrightarrow\,} y$ has asymptotic lower density at most p = y$ ). We show that all members of this family of mass problems parameterized by a real p with $0 p$ for each computable set x. We prove that the Medvedev complexity of the mass problems ${\mathcal {B}}$ is the same for all $p \in $, by showing that they are Medvedev equivalent to the mass problem of functions bounded by ${2^{2}}^{n}$ that are almost everywhere different from each computable function.Next, together with Joseph Miller, we obtain a proper hierarchy of the mass problems of type $\text {IOE}$ : we show that for any order function g there exists a faster growing order function $h $ such that $\text {IOE}$ is strictly above $\text {IOE}$ in the sense of Muchnik reducibility.We study cardinal characteristics in the sense of set theory that are analogous to the highness properties above. For instance, ${\mathfrak {d}} $ is the least size of a set G of bit sequences such that for each bit sequence x there is a bit sequence y in G so that $\underline \rho >p$. We prove within ZFC all the coincidences of cardinal characteristics that are the analogs of the results above. (shrink)

A real x is -Kurtz random if it is in no closed null set . We show that there is a cone of -Kurtz random hyperdegrees. We characterize lowness for -Kurtz randomness as being -dominated and -semi-traceable.

An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first (...) main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n−g. Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic.Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree.Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α<1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. (shrink)

We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relationsR,S, a componentwise reducibility is defined byR≤S⇔ ∃f∀x, y[x R y↔fS f].Here,fis taken from a suitable class of effective functions. For us the relations will be on natural numbers, andfmust be computable. We show that there is a${\rm{\Pi }}_1^0$-complete equivalence relation, but no${\rm{\Pi }}_k^0$-complete fork≥ 2. We show that${\rm{\Sigma }}_k^0$preorders arising naturally in the above-mentioned areas are${\rm{\Sigma }}_k^0$-complete. This includes polynomial timem-reducibility on (...) exponential time sets, which is${\rm{\Sigma }}_2^0$, almost inclusion on r.e. sets, which is${\rm{\Sigma }}_3^0$, and Turing reducibility on r.e. sets, which is${\rm{\Sigma }}_4^0$. (shrink)

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy of (...) subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

How many factors, i.e. departures from normality, are necessary to explain a delusion? Maher’s classic one-factor theory argues that the only factor is the patient’s anomalous experience, and a delusion arises as a normal explanation of this experience. The more recent two-factor theory, on the other hand, contends that a second factor is also needed, with reasoning abnormality being a potential candidate, and a delusion arises as an abnormal explanation of the anomalous experience. In the past few years, although there (...) has been an increasing number of scholars offering a variety of arguments in defence of Maher’s one-factor theory, these arguments have not been adequately addressed by two-factor theorists. This paper aims to address this gap by critically examining the arguments on three crucial issues: the intelligibility of delusions, the dissociation between anomalous experiences and delusions, and the empirical evidence of a second factor. I will argue that the Maherian notion of anomalous experience is not sufficient for explaining delusions and the two-factor theory is on the right track in its search for the missing factor in the aetiology of delusions. (shrink)

Two ways of describing a group are considered. 1. A group is finite-automaton presentable if its elements can be represented by strings over a finite alphabet, in such a way that the set of representing strings and the group operation can be recognized by finite automata. 2. An infinite f.g. group is quasi-finitely axiomatizable if there is a description consisting of a single first-order sentence, together with the information that the group is finitely generated. In the first part of the (...) paper we survey examples of FA-presentable groups, but also discuss theorems restricting this class. In the second part, we give examples of quasi-finitely axiomatizable groups, consider the algebraic content of the notion, and compare it to the notion of a group which is a prime model. We also show that if a structure is bi-interpretable in parameters with the ring of integers, then it is prime and quasi-finitely axiomatizable. (shrink)

We describe a strongly minimal theory S in an effective language such that, in the chain of countable models of S, only the second model has a computable presentation. Thus there is a spectrum of an -categorical theory which is neither upward nor downward closed. We also give an upper bound on the complexity of spectra.

本书分为七篇,即:传统的中道和两极矛盾观、辩证法的“中介”观、辩证法的“两极”观、二类范畴与三大规律的说明和发挥、时空观和意识观的再发挥、认识论和思想方法的“两极与中介”、若干具体关系的“两极与中介” 。.

The ideas of continental philosopher Martin Heidegger have been influential in cognitive science and artificial intelligence, despite the fact that there has been no effort to analyze these ideas empirically. The experiments reported here are designed to lend empirical support to Heidegger’s phenomenology and more specifically his description of the transition between ready-to-hand and unready-to-hand modes in interactions with tools. In experiment 1, we found that a smoothly coping cognitive system exhibits 1/fβ type positively correlated noise and that its correlated (...) character is reduced when the system is perturbed. This indicates that the participant and tool constitute a self-assembled, extended device during smooth coping and this device is disrupted by the perturbation. In experiment 2, we examine the re-organization of awareness that occurs when a smoothly coping, self-assembled, extended cognitive system is perturbed. We found that the disruption is accompanied by a change in attention which interferes with participants’ performance on a simultaneous cognitive task. Together these experiments show that a smoothly coping participant-tool system can be temporarily disrupted and that this disruption causes a change in the participant’s awareness. Since these two events follow as predictions from Heidegger’s work, our study offers evidence for the hypothesized transition from readiness-to-hand to unreadiness-to-hand. (shrink)

v. [1]. Ru -- v. [2]. Shi -- v. [3]. Dao.

According to a bodily view of pain, pains are objects which are located in body parts. This bodily view is supported by the locative locutions for pain in English, such as that “I have a pain in my back.” Recently, Liu and Klein (Analysis, 80(2), 262–272, 2020) carry out a cross-linguistic analysis, and they claim that (1) Mandarin has no locative locutions for pain and (2) the absence of locative locutions for pain puts the bodily view at risk. This paper (...) rejects both claims. Regarding the philosophical claim, I argue that a language without locative locutions for pain only poses a limited challenge to the bodily view. Regarding the empirical claim, I identify the possible factors which might have misled Liu and Klein about the locative locutions for pain in Mandarin, and argue that Mandarin has a wide range of locative locutions for pain by conducting a corpus analysis. I conclude that compared to English, Mandarin lends no less, if not more, support to the bodily view of pain. (shrink)

Covering the basics as well as recent research results, this book provides a very readable introduction to the exciting interface of computability and ...

Military metaphors are pervasive in biomedicine, including HIV research. Rooted in the mind set that regards pathogens as enemies to be defeated, terms such as “shock and kill” have become widely accepted idioms within HIV cure research. Such language and symbolism must be critically examined as they may be especially problematic when used to express scientific ideas within emerging health-related fields. In this article, philosophical analysis and an interdisciplinary literature review utilizing key texts from sociology, anthropology, history, and Chinese and (...) African studies were conducted to investigate the current proliferation of military metaphors. We found the use of these metaphors to be ironic, unfortunate, and unnecessary. To overcome military metaphors we propose to give them less aggressive meanings, and/or replace them with more peaceful metaphors. Building on previous authors' work, we argue for the increased use of “journey” metaphors as meaningful, cross-culturally app... (shrink)

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts (...) and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

We give a simple structural property which characterizes the r.e. sets whose (Turing) degrees are cappable. Since cappable degrees are incomplete, this may be viewed as a solution of Post's program, which asks for a simple structural property of nonrecursive r.e. sets which ensures incompleteness.

Since the early 1970s, despite popular opposition, to control the rapid growth of population the Chinese government has been carrying out the strictest and most comprehensive family planning policy in the world. In addition to contraceptive methods and sterilization, artificial abortionhas been used as an important measure of birth control under the policy. Many women have been required, persuaded, and even forced by the authorities to abort fetuses no matter how much they want to give birth.

In this paper we investigate computable models of -categorical theories and Ehrenfeucht theories. For instance, we give an example of an -categorical but not -categorical theory such that all the countable models of except its prime model have computable presentations. We also show that there exists an -categorical but not -categorical theory such that all the countable models of except the saturated model, have computable presentations.

This study focuses on the effects of socially responsible human resource management practices on female employees’ turnover intentions and the moderating effect of supervisor gender on this relationship. With a sample of 212 female employees from eight different industries in Finland, the results indicate that SR-HRM practices promoting equal career opportunities and work–family integration play a significant role in reducing women's turnover intentions. The study adds to the academic discourse of corporate social responsibility by highlighting the impact of the organizational-level (...) HRM determinants on the individual-level outcome. In addition, supervisor gender makes a difference in the studied relationship: female supervisors have a stronger and more significant impact on the relationship than male supervisors. Our findings suggest that organizational measures which support work–family integration should be taken seriously to decrease female employees’ turnover intentions. Male supervisors could adopt some gender-incongruent leadership behaviors, such as individualized emotional concern and caring when dealing with female employees. In the future, other gender combinations in the supervisor–employee relationship would merit research. (shrink)

We show that the partial order of Σ0 3-sets under inclusion is elementarily definable with parameters in the semilattice of r.e. wtt-degrees. Using a result of E. Herrmann, we can deduce that this semilattice has an undecidable theory, thereby solving an open problem of P. Odifreddi.

Drawing from a wide range of primary historical and sociological sources, this book presents medical ethics in China from a Chinese-Western comparative perspective, and in doing so it provides a fascinating exploration of cultural differences and commonalities exhibited by China and the West in medicine and medical ethics. The book focuses on a number of key issues in medical ethics including: attitudes towards foetuses; disclosure of information by medical professionals; informed consent; professional medical ethics; and human rights. This careful examination (...) not only provides insights into Chinese viewpoints, but also sheds light on the appropriate methods for comparative culture and ethical research. Through its analysis, Jing-Bao Nie seeks to put forward a theory of "transcultural bioethics", an ethical paradigm which upholds the primacy of morality whilst resisting cultural stereotypes, and appreciating the internal plurality, richness, dynamism and openness of medical ethics in any culture. Medical Ethics in China will be of particular interest to students and academics in the fields of Medical Law, Bioethics and Medical Ethics as well as Chinese/Asian Studies and Comparative (Chinese-Western) Cultural Studies. (shrink)

Corlett (2019) raises two groups of challenges against the two-factor theory of delusions: One focuses on weighing “the evidence for … the two-factor theory”; the other aims to question “the logic of the two-factor theory” (p. 166). McKay (2019) has robustly defended the two-factor theory against the first group. But the second group, which Corlett believes is in many aspects independent of the first group and Darby (2019, p. 180) takes as “[t]he most important challenge to the two-factor theory raised (...) by Dr. Corlett”, has by large remained. Here I offer my two cents in response to the second group. More specifically, I argue that Corlett’s challenges to the logic of the two-factor theory, concerning modularity, double dissociation and cognitive penetration, seem to be based on some misunderstandings of the two-factor theory. (shrink)

The leader–member relationship has been identified as a key determinant of successful working relationships and business outcomes in China. A high-quality leader–member relationship helps managers and employees to meet the demands they face and gives them the opportunity to develop socially, emotionally and morally. Such relationships form the basis of the overall well-being and success of the organisation. This article contributes to relationally oriented leadership theories and more specifically to the leader–member exchange theory by examining the theory in the context (...) of Western expatriate managers and Chinese employees in China. The first aim of the study is to analyse the similarities and differences between the LMX theory, which owes its origins to Western corporate experience, and the social and moral norms of guanxi, a crucial element in the Chinese value system. Since Westerners and Chinese people can give different interpretations to guanxi, the second aim of the article is to discuss the ethical challenges to the Western manager arising from guanxi. The findings of this study have implications not only for China, but also for other Chinese communities where guanxi is endorsed and practised. (shrink)

Trust is indispensable not only for interpersonal relationships and social life, but for good quality healthcare. As manifested in the increasing violence and tension in patient-physician relationships, China has been experiencing a widespread and profound crisis of patient–physician trust. And globally, the crisis of trust is an issue that every society, either developing or developed, has to face in one way or another. Yet, in spite of some pioneering works, the subject of patient-physician trust and mistrust – a crucial matter (...) in healthcare especially because there are numerous ethical implications – has largely been marginalized in bioethics as a global discourse. Drawing lessons as well as inspirations from China, this paper demonstrates the necessity of a trust-oriented bioethics and presents some key theoretical, methodological and philosophical elements of such a bioethics. A trust-oriented bioethics moves beyond the current dominant bioethical paradigms through putting the subject of trust and mistrust in the central agenda of the field, learning from the social sciences, and reviving indigenous moral resources. In order for global bioethics to claim its relevance to the things that truly matter in social life and healthcare, trust should be as vital as such central norms like autonomy and justice and can serve as a potent theoretical framework. (shrink)

To monopolize the scientific data gained by Japanese physicians and researchers from vivisections and other barbarous experiments performed on living humans in biological warfare programs such as Unit 731, immediately after the war the United States government secretly granted those involved immunity from war crimes prosecution, withdrew vital information from the International Military Tribunal for the Far East, and publicly denounced otherwise irrefutable evidence from other sources such as the Russian Khabarovsk trial. Acting in “the national interest” and for the (...) security of the US, authorities in the US tramped justice and morality, and engaged in what the English common law tradition clearly defines as “complicity after the fact.” To repair this historical injustice, the US government should issue an official apology and offer appropriate compensation for having covered up Japanese medical war crimes for six decades. To help prevent similar acts of aiding principal offender in the future, international declarations or codes of human rights and medical ethics should include a clause banning any kind of complicity in any unethical medicine—whether before or after the fact—by any state or group for whatever reasons. (shrink)

本书是一部美学理论专著。以20世纪中国美学的历史为论题,包括“百年美学概观”、“现代化过程中的艺术及其哲学”、“走向跨文化美学”、“构建中国马克思主义美学”、“美育与人的全面发展”五篇内容。.

We study ideals in the computably enumerable Turing degrees, and their upper bounds. Every proper ideal in the c.e. Turing degrees has an incomplete upper bound. It follows that there is no prime ideal in the c.e. Turing degrees. This answers a question of Calhoun [2]. Every proper ideal in the c.e. Turing degrees has a low2 upper bound. Furthermore, the partial order of ideals under inclusion is dense.

The Metaphysical Club, a gathering of intellectuals in the 1870s associated with Harvard, is widely recognized as the crucible where pragmatism, America's distinctively original philosophy, was refined and proclaimed. Louis Menand's bestseller about the group was a dramatic publishing success. However, only three actual members - Oliver Wendell Holmes Jr., Charles S. Peirce, and William James - appear in this book, alongside other thinkers such as John Dewey who were never in the Club. The Real Metaphysical Club tells the full (...) story of how this influential group shifted the course of philosophy in America. In addition to pioneering pragmatism, the group explored radical empiricism and idealism, and formulated personalism and process philosophy, equally important developments. This volume contains thirty-seven important writings dating from 1870 to 1885 by the real members of the Metaphysical Club. The first section centers on pragmatism and science; the second part collects writings of the lawyers; and the third part covers idealist and personalist philosophers. Many of these writings have never been reprinted before, and nothing like this impressive collection has ever been attempted. A general introduction provides a narrative history, and the editors' three introductions to the volume's sections vividly bring to life the intense meetings, sustained debates, and pioneering thought from the Metaphysical Club. (shrink)

In order to explain delusional beliefs, one must first consider what factors should be included in a theory of delusion. Unlike a one-factor theory, a two-factor theory of delusion argues that not only anomalous experience (the first factor) but also an impairment of the belief-evaluation system (the second factor) is required. Recently, two-factor theorists have adopted various Bayesian approaches in order to give a more accurate description of delusion formation. By reviewing the progression from a one-factor theory to a two-factor (...) theory, I argue that in light of the second factor’s requirements, different proposed impairments can be unified within a consistent belief-evaluation system. Under this interpretation of the second factor, I further argue that the role of a mechanism responsible for detecting bizarreness is wrongly neglected. I conclude that the second factor is a compound system which consists of differing functional parts, one of which functions to detect bizarreness in different stages of delusion; moreover, I hold that the impairment can be one or several of these functional parts. (shrink)

How does it come about that a person akratically believes that P, while at the same time believing that the available evidence speaks against that P? Among the current accounts, Scanlon offers an intuitive suggestion that one’s seeming experience that P may play an important role in the aetiology of their akratic belief that P. However, it turns out to be quite challenging to articulate what the role of seeming experience is. This paper will offer a novel development of Scanlon’s (...) intuitive suggestion, with a focus on clear-eyed epistemic akrasia. I will argue that the primary role of seeming experience is unlikely to act as the subject’s reason or to provide the subject with prima facie justification; instead, based on the recent work in dogmatism and Cartesian clarity, I will propose a causal account, according to which, when it seems clear to the subject that P, the seeming experience may exert a brute causal force to persistently compel the subject to believe that P. This causal account also has the advantage of helping some existing accounts to explain clear-eyed epistemic akrasia. (shrink)